微積分
極限、導數、最優化與函數性質。
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complete the expression 481 -180 ← 18 × dropdown 301 -180 ← 18 × 121 - …
Top blank: 10, Second blank: 10, Third blank: 5, Bottom blank: 1
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example 1 determine the consecutive integer values of x between which e…
Let's solve these problems one by one. We'll use the Intermediate Value Theorem, which states that if a function \( f(x) \) is continuous on an interval \([a, b]\), and \( f(a) \)…
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which function has a maximum at (2, 0)?
The function represented by the orange graph (third option, with vertex at (2, 0))
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identify a root options: (0,0), (-1,9), (0,-8), (-4,0)
D. (-4,0)
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the picture shows the $4.88 josephine spent on a package of 4 pens. dra…
Each pen costs $\$1.22$
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the function g is defined as follows. $g(x) = -2x^2 + 4$ if the graph o…
\( f(x)=-2x^{2} \)
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calculators are allowed on this portion of the test. 1. the number of p…
$V = 50000(0.97)^t$
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find the product in simplest radical form. \\(\\sqrt3{-13} \\cdot \\sqr…
$\sqrt[3]{26}$
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write the expression in simplest radical form. \\sqrt3{945}
$3\sqrt[3]{35}$
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determine whether the system of equations has no solution, one solution…
one solution, (2, -1)
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which event challenged president thomas jeffersons beliefs about the co…
A. the Louisiana Purchase
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donna is going to rent a truck for one day. there are two companies she…
The inequality is \( 84 < 75 + 0.60m \) and the solution is \( m > 15 \). So when the number of miles driven \( m \) is greater than 15, Company A will charge less than Company B.
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table of values and use the table values to graph. $y = -3x - 5$ | $x$ …
For \(x=-3\): - \(-3x\) value: \(9\) - \(y = -3x - 5\) value: \(4\) The complete table is: | \(x\) | \(-3x\) | \(y=-3x - 5\) | |-------|---------|---------------| | \(-3\) | \(9\)…
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write a cubic function whose graph is shown.
$y = x^3 - 7x^2 + 10x$
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consider the line ( 9x + 6y = -3 ). what is the slope of a line paralle…
Slope of a parallel line: \(-\frac{3}{2}\) Slope of a perpendicular line: \(\frac{2}{3}\)
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consider the line -4x - 5y = 3. what is the slope of a line perpendicul…
Slope of a perpendicular line: \(\frac{5}{4}\) Slope of a parallel line: \(-\frac{4}{5}\)
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the function $f(x)$ is graphed below. how many points on the graph repr…
1
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given the function below, fill in the table of values and use the table…
For \( x = -3 \), \( y = -5 \). The completed table (for all x values) would have: | \( x \) | \( y = x - 2 \) | |--------|----------------| | \( -3 \) | \( -5 \) | | \( -2 \) | \…
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finding asymptotes in exercises 1–4, find all ve asymptotes of the grap…
Let's solve each function for its vertical asymptotes (I'll assume "ve" in the problem is a typo for "vertical"). A vertical asymptote occurs where the function is undefined (deno…
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given the function below, fill in the table of values and use the table…
For \( x = -3 \), \( y = -4 \); for \( x = -2 \), \( y = -4 \); for \( x = -1 \), \( y = -4 \); for \( x = 0 \), \( y = -4 \); for \( x = 1 \), \( y = -4 \); for \( x = 2 \), \( y…
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question given the function below, fill in the table of values and use …
The table is filled with \( y = 5 \) for all given \( x \)-values. The graph is a horizontal line at \( y = 5 \) passing through the plotted points \((-3, 5)\), \((-2, 5)\), \((-1…
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the graph of a function f is shown. how many real zeros does f have? re…
3 real zeros.
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given the function below, fill in the table of values and use the table…
For \( x=-3 \), \( y = 5 \); for \( x=-2 \), \( y = 5 \); for \( x=-1 \), \( y = 5 \); for \( x=0 \), \( y = 5 \); for \( x=1 \), \( y = 5 \); for \( x=2 \), \( y = 5 \); for \( x…
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$\frac{-35}{8}$ or $-4.375$
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the graph of $y = f(x)$ is shown below. which point could be used to fi…
Point A
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$-4$
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-42 ÷ (-1) ÷ 3
14
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the function $f(x)$ is graphed below. how many points on the graph repr…
1
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waterworks is a company that manufactures and sells paddleboards. its p…
Waterworks must produce more than 400 and fewer than 700 paddleboards, or more than 700 paddleboards? No, correction: Wait, no, when $x$ is in thousands, $0<x<4$ means 0 to 400, $…
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(4×3×8 + 9 + 9)
114
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is this point a max or min? max min
max
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describe the transformation from the graph of f to the graph of h. 9. f…
9. The graph of $h(x)$ is a horizontal compression of the graph of $f(x)$ by a factor of $\frac{1}{4}$. 10. The graph of $h(x)$ is a vertical compression of the graph of $f(x)$ by…
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3 for each graph of a polynomial function, state the minimum degree, st…
The zeros of \( f(x)=-\frac{1}{6}P(x) \) are \( x=-2 \) (multiplicity 3) and \( x = 1 \) (multiplicity 2). ### Part 4c(iii): Zeros of \( h(x)=P(x - 10) \)
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*24. write \\(\\frac{1}{2}\\) and \\(\\frac{1}{5}\\) as fractions with …
$\frac{7}{10}$
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evaluate the function for the given value of x.\\(g(x) = x^6 - 64x^4 + …
$-43$
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document 4 le gouvernement libéral de lomer gouin adopte une loi limita…
Since no specific question is provided about these documents, it's not possible to give a targeted answer. If you want to analyze these documents (for example, about historical co…
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3. the median home price in a country over the period january 2011 to j…
The average rate of change is 11.2 thousand dollars per year.
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problem. 19 : calculate the following limit. (if the limit does not exi…
$-\dfrac{1}{3}$
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graph the equation $y = \\frac{1}{3}x + 1$.
The line passes through points $(0, 1)$ and $(3, 2)$, extending infinitely in both directions.
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for the given polynomial p(x) and the given c, use the remainder theore…
$57$
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problem. 13 : evaluate the limit using the appropriate limit law(s). (i…
DNE ### Problem 14
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graph the equation $y = \\frac{1}{2}x + 3$.
To graph \( y=\frac{1}{2}x + 3 \): 1. Plot the y - intercept at \( (0,3) \). 2. Use the slope \( \frac{1}{2} \) to find another point: from \( (0,3) \), move right 2 units and up …
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problem. 5 : determine if the limit approaches a finite number, $\\inft…
\(\frac{3}{10}\) ### Problem 6
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problem. 3 : determine if the limit approaches a finite number, \\(\\in…
\(0\) ### Problem 4
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graph the system of equations, and determine the solutio $y = -dfrac{3}…
The system has no solution, as the two lines are parallel and never intersect.
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graph the equation $y = \\frac{1}{3}x - 2$. slope: $\\frac{1}{3}$ use t…
To plot another point on the line \( y = \frac{1}{3}x-2 \) using the slope \( \frac{1}{3}=\frac{\text{rise}}{\text{run}} \): 1. Start from the y - intercept point \( (0,-2) \). 2.…
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abstract. practice problems for lecture problem. 1 : determine if the l…
1. $18$ 2. $-1$ 3. $\frac{33}{13}$ 4. $-2$
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graph and determine the solution of the system y = 6x - 3 \\(\\frac{1}{…
The system has infinitely many solutions, represented by all points on the line $y = 6x - 3$.
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solve the following. $(4.78 \\times 10^9) \\times (7.24 \\times 10^3)$ …
a. $3.4607 \times 10^{13}$
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graph each equation. estimate the solution of the system of equa y = 2x…
The solution of the system is $x=-2.5$, $y=-1$ (or the point $(-2.5, -1)$)
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question 16 (4 points) solve the following system graphically or algebr…
The solutions are $(2, 0)$ and $(3, 1)$
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graph the system of equations to determine the solution. $y = \\frac{2}…
The solution is $(3, 3)$ (this is the intersection point of the two lines when graphed)
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n identify its domain 5. $f(x) = \\sqrt3{x + 2}$
The domain of \( f(x)=\sqrt[3]{x + 2} \) is all real numbers, which can be written in interval notation as \( (-\infty, \infty) \) or in set - builder notation as \( \{x|x\in\math…
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consider the following. \\(\\lim\\limits_{x \\to 0} \\frac{\\sin(2x)}{x…
### Completed Table: | $x$ | $f(x)$ | |-------|--------| | $-0.1$| 1.9867 | | $-0.01$| 1.9999 | | $-0.001$| 2.0000 | | $0.001$| 2.0000 | | $0.01$| 1.9999 | | $0.1$| 1.9867 | $\lim…
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match each expression to a reasonable estimate. 186 ÷ 6 98 ÷ 2 43 ÷ 4 a…
- \(186 \div 6\) matches \(30\) - \(98 \div 2\) matches \(50\) - \(43 \div 4\) matches \(10\)
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41. 80 + (-60) - 80 + 70
$10$
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rewrite each expression using the then compute.) 2. 9 - 9
$0$
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27. 23 - |11|
12
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decide whether the following problem can be solved using precalculus or…
0.4 miles per mile (the rate of change of elevation at $x=1$ is 0.4)
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28. |15| - 7
8
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26. 12 - |8| 29. |108| - 67
$12 - |8| = 4$ $|108| - 67 = 41$
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graph the system of equations to determine the solution. $y = \\frac{2}…
The solution is the point $(3, 3)$
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write each expression using th then compute.) 2. 9 - 9 5. 17 - 28
$29 - 9 = 20$ $17 - 28 = -11$
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6. 38 - 56
$-18$
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graph the system of equations to determine the solution. $y = \\frac{1}…
All points on the line $y = \frac{1}{2}x + 3$ are solutions; the system has infinitely many solutions.
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does this graph represent a function? why or why not? a. no, because it…
D. Yes, because it passes the vertical line test.
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graph the system of equations to deter $y = \\frac{1}{2}x + 3$ $2y = x …
Plot the point $(2,4)$ (or any other valid point on the line $y=\frac{1}{2}x+3$, such as $(4,5)$ or $(-2,2)$) to complete the line. The system has infinitely many solutions since …
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the table below represents a linear function. | x | y | |----|----| | -…
B. $y=-\frac{3}{4}x - 5$
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which of the relationships below represents a function with the same ra…
C
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which graph shows the polynomial function $g(x) = -x^4 + x + 2$?
The top-left graph (the one with downward opening, y-intercept at (0,2), and passing through (1,2))
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the graph of a function is shown on the coordinate plane below. which r…
C. $y=-\frac{5}{2}x+3$
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the table below represents a linear function. | x | y | |----|----| | 4…
D (the graph with slope -5)
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question 11 (4 points) a ball is thrown vertically upward with an initi…
The ball is more than 128 feet above the ground when $2 < t < 4$ seconds.
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find the zeros of the given function $f(x)=x^{4}-4x^{3}-x^{2}+14x + 10$…
$-1, 3+i, 3-i$
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3. $7\\times12 = 7\\times(\\underline{\\quad} + 2)$ $\\quad\\quad\\quad…
Para completar: \( 7\times12 = 7\times(\boldsymbol{10}+ 2) \) \(=(7\times\boldsymbol{10})+(7\times2) \) \(=\boldsymbol{70}+\boldsymbol{14} \) Área: \(\boldsymbol{84}\)
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4. $6\\times14 = 6\\times(\\underline{quadquad}+\\underline{quadquad})$…
\( 6 \times 14 = 6 \times (\underline{10} + \underline{4}) \) \( = (6 \times \underline{10}) + (6 \times \underline{4}) \) \( = \underline{60} + \underline{24} \) Área: \(\underli…
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select the correct answer. each statement describes a transformation of…
C. It is the graph of \( f(x) \) reflected about the \( y \)-axis and shrunk or compressed horizontally by a factor of 10.
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determine the domain on which the following graph of $f(x)$ is positive.
$-4 < x < 0$ (or in interval notation: $(-4, 0)$)
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select the correct answer. consider the graph of function f below. grap…
B. \( g(x) = f(x) + 4 \)
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question 9 of 10 which of the following is a good way to save money if …
C. Check Web sites for student discounts
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which expression is 5 times the sum of 4,215 and 1,172? a 5 × (4,215 + …
A. $5 \times (4,215 + 1,172)$
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question 8 of 10 when taking into consideration a colleges tuition cost…
C. be open to lesser-known, cheaper colleges.
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lesson check you know how? graphing, determine whether the function exp…
s: - 26a: $\$2249.73$ - 18: Exponential growth, y - intercept = 129 - 19: Exponential decay, y - intercept = 2 - 27: $143511.36$ (population after 15 years) - 29a: $h(n)=72(0.5)^{…
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select the correct answer. consider the graph of f(x) given below. the …
A. \( g(x)=f(x)+4 \)
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select the correct answer. in which direction must the graph of f(x) = …
C. down
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$f(x)=\frac{3x^2 + 4x - 3}{x + 1}$ start by drawing the asymptotes. the…
1. Vertical Asymptote: $x=-1$ (dashed vertical line) 2. Slant Asymptote: $y=3x+1$ (dashed line) 3. Points on left segment: $(-3, -6)$, $(-2, -1)$ 4. Points on right segment: $(0, …
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which graph represents the function ( f(x) = \frac{1}{4}x - 6 )? option…
A (the graph with positive slope, crossing the y - axis at a negative value)
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find all the zeros of the function (enter your answers as a comma - sep…
Zeros: $-3, -3, i, -i$ Product of linear factors: $h(x)=(x+3)^2(x-i)(x+i)$
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solve each expression and match them with their appropriate result. (-8…
$(-841) \times (-11) = 9251$ $-661 \times 9 = -5949$ $202 \times (-10) = -2020$ $3871 \times 6 = 23226$
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12 divide. 927 ÷ (-9) =
-103
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f(x) = \\frac{-3x^{2} + 15x}{x^{2} - 7x + 10} start by drawing the asym…
1. Draw vertical dashed asymptote at $x=2$, horizontal dashed asymptote at $y=-3$ 2. Plot hollow dot at $(5, -5)$ 3. Plot solid points: $(0,0)$, $(1,3)$ (left of $x=2$); $(3,-9)$,…
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move at least one of the 3 guide points below to complete the graph of …
To complete the graph of \( y=\frac{5}{2}\sqrt{x - 4} \): 1. Move the blue vertex point from \( (0,0) \) to \( (4,0) \) (horizontal shift right 4 units). 2. Move the red points to…
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use the drawing tool(s) to form the correct answer on the provided grap…
The transformed points for \( g \) are \((-3, -2)\), \((-2, -1)\), \((-1, 0)\), \((0, 1)\), \((1, 2)\). To plot, use these coordinates.
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f(x) = \\frac{-7}{x + 1} start by drawing the vertical and horizontal a…
Vertical asymptote: $x=-1$ (dashed line) Horizontal asymptote: $y=0$ (dashed line) Points on left of asymptote: $(-2,7)$, $(-8,1)$ Points on right of asymptote: $(0,-7)$, $(6,-1)$…
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7. some banks charge a(n) maintenance fee each month just to keep your …
Mobile Check Deposit ### Question 11
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select the correct answer. what is the range of the function shown on t…
A. \(-9\leq y\leq8\)
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select the correct answer from each drop - down menu. let d(t) be the t…
For \( d(4) \), the value is 68. The first drop - down (for \( d(4) \)) should be 68. The second drop - down (the time) should be "4 hours", and the third drop - down (what it mea…
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consider the following. $f(x) = x^3 - 4x^2 - 4x + 16$ find all the zero…
$x = -2, 2, 4$ ---
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step 3 use synthetic division again to divide the second known zero (th…
The factor is $(x + \boldsymbol{1})$. The zero of this factor is $x = \boldsymbol{-1}$
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simplify the following expression. assume any factors you cancel are no…
$\frac{7t + 6s}{s^2t^2}$