Question

directions: choose 10 of the following questions to answer. you do not need to do all 20! but if you choose to do more, that will prepare you for the midterm.
1
when $6x^3 - 2x + 8$ is subtracted from $5x^3 + 3x - 4$, the result is
(1) $x^3 - 5x + 12$
(3) $-x^3 + 5x - 12$
(2) $x^3 + x + 4$
(4) $-x^3 + x + 4$
unit 1
2
which trinomial is written in standard form and has a constant term of five?
(1) $x^5 - 4x^2 + 10$
(3) $5x^4 - 3x^2 + 1$
(2) $2x^2 + 6x^4 + 5$
(4) $4x^5 - 8x^2 + 5$
unit 1
3
the tables below show the values of four different functions for given values of $x$.

x	f(x)		x	g(x)		x	h(x)		x	k(x)
1	12		1	-1		1	9		1	-2
2	19		2	1		2	12		2	4
3	26		3	5		3	17		3	14
4	33		4	13		4	24		4	28

which table represents a linear function?
(1) $f(x)$
(3) $h(x)$
(2) $g(x)$
(4) $k(x)$
unit 4
4
stephanie is solving the equation $x^2 - 12 = 7x - 8$. her first step is shown below.
given: $x^2 - 12 = 7x - 8$
step 1: $x^2 - 4 = 7x$
which property justifies her first step?
(1) associative property
(3) distributive property
(2) commutative property
(4) addition property of equality
unit

Explanation:

Step1: Set up subtraction expression

$(5x^3 + 3x - 4) - (6x^3 - 2x + 8)$

Step2: Distribute the negative sign

$5x^3 + 3x - 4 - 6x^3 + 2x - 8$

Step3: Combine like terms

$(5x^3 - 6x^3) + (3x + 2x) + (-4 - 8) = -x^3 + 5x - 12$

Step1: Recall standard polynomial form

Standard form orders terms by descending exponents, with constant term last.

Step2: Evaluate each option

1. Constant term is 10, not 5.
2. Not in standard form (exponents not descending).
3. Constant term is 1, not 5.
4. In standard form, constant term is 5.

Step1: Define linear function slope

Linear functions have constant slope: $\frac{\Delta y}{\Delta x} = \text{constant}$

Step2: Calculate slope for $f(x)$

$\frac{19-12}{2-1}=7$, $\frac{26-19}{3-2}=7$, $\frac{33-26}{4-3}=7$ (constant)

Step3: Verify other functions

• $g(x)$: $\frac{1-(-1)}{2-1}=2$, $\frac{5-1}{3-2}=4$ (not constant)
• $h(x)$: $\frac{12-9}{2-1}=3$, $\frac{17-12}{3-2}=5$ (not constant)
• $k(x)$: $\frac{4-(-2)}{2-1}=6$, $\frac{14-4}{3-2}=10$ (not constant)

Step1: Analyze the first step

Original: $x^2 - 12 = 7x - 8$; Step1: $x^2 - 4 = 7x$

Step2: Identify the operation

8 was added to both sides: $x^2 - 12 + 8 = 7x - 8 + 8$

Step3: Match to equality property

Adding the same value to both sides uses the addition property of equality.

Answer:

(3) $-x^3 + 5x - 12$

---