14. classify $-2x^4 - x^3 + 8x^2 + 12$ by degree.
a. quartic c. quadratic
b. quintic d. cubic
15. classify $8x^4 + 7x^3 + 5x^2 + 8$ by number of terms.
a. trinomial c. polynomial of 5 terms
b. binomial d. polynomial of 4 terms
write the polynomial in standard form. then name the polynomial based on its degree and number of terms.
16. $3x + 2x^2 - 6$
a. $3x - 6 + 2x^2$; not a polynomial
b. $3x + 2x^2 - 6$; cubic monomial
c. $2x^2 + 3x - 6$; quadratic trinomial
d. $2x^2 + 3x - 6$; fourth - degree binomial
what is the relative maximum and minimum of the function?
17. $f(x) = 2x^3 + x^2 - 11x$
a. the relative maximum is at $(-1.53, 8.3)$ and the relative minimum is at $(1.2, -12.01)$.
b. the relative maximum is at $(-1.53, 12.01)$ and the relative minimum is at $(1.2, -8.3)$.
c. the relative maximum is at $(-1.2, 8.3)$ and the relative minimum is at $(1.53, -12.01)$.
d. the relative maximum is at $(-1.2, 12.01)$ and the relative minimum is at $(1.53, -8.3)$.
consider the leading term of each polynomial function. what is the end behavior of the graph?
18. $-3x^3 - x$
a. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is down and down.
b. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is up and up.
c. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is up and down.
d. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is down and up.

Question

14. classify $-2x^4 - x^3 + 8x^2 + 12$ by degree.
   a. quartic  c. quadratic
   b. quintic  d. cubic
15. classify $8x^4 + 7x^3 + 5x^2 + 8$ by number of terms.
   a. trinomial  c. polynomial of 5 terms
   b. binomial  d. polynomial of 4 terms
write the polynomial in standard form. then name the polynomial based on its degree and number of terms.
16. $3x + 2x^2 - 6$
   a. $3x - 6 + 2x^2$; not a polynomial
   b. $3x + 2x^2 - 6$; cubic monomial
   c. $2x^2 + 3x - 6$; quadratic trinomial
   d. $2x^2 + 3x - 6$; fourth - degree binomial
what is the relative maximum and minimum of the function?
17. $f(x) = 2x^3 + x^2 - 11x$
   a. the relative maximum is at $(-1.53, 8.3)$ and the relative minimum is at $(1.2, -12.01)$.
   b. the relative maximum is at $(-1.53, 12.01)$ and the relative minimum is at $(1.2, -8.3)$.
   c. the relative maximum is at $(-1.2, 8.3)$ and the relative minimum is at $(1.53, -12.01)$.
   d. the relative maximum is at $(-1.2, 12.01)$ and the relative minimum is at $(1.53, -8.3)$.
consider the leading term of each polynomial function. what is the end behavior of the graph?
18. $-3x^3 - x$
   a. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is down and down.
   b. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is up and up.
   c. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is up and down.
   d. the leading term is $-3x^3$. since $n$ is odd and $a$ is negative, the end behavior is down and up.

Accepted Answer

### Question 14 # Explanation: ## Step1: Recall degree of polynomial The degree of a polynomial is the highest power of the variable. For $-2x^4 - x^3 + 8x^2 + 12$, the highest power of $x$ is $4$. ## Step2: Match with options - Quartic means degree 4, quintic is degree 5, quadratic is degree 2, cubic is degree 3. So the polynomial is quartic. # Answer: a. quartic ### Question 15 # Explanation: ## Step1: Count number of terms A term is a single number, variable, or product. For $8x^4 + 7x^3 + 5x^2 + 8$, the terms are $8x^4$, $7x^3$, $5x^2$, $8$ – that's 4 terms. ## Step2: Match with options - Trinomial has 3 terms, binomial 2, so it's a polynomial of 4 terms. # Answer: d. polynomial of 4 terms ### Question 16 # Explanation: ## Step1: Write in standard form Standard form is descending powers of $x$. For $3x + 2x^2 - 6$, that's $2x^2 + 3x - 6$. ## Step2: Determine degree and terms Degree is highest power ($2$, so quadratic), number of terms is 3 (trinomial). # Answer: c. $2x^2 + 3x - 6$; quadratic trinomial ### Question 17 # Explanation: ## Step1: Analyze the function $f(x)=2x^3 + x^2 - 11x$ To find relative max/min, we can use calculus (find derivative $f'(x)=6x^2 + 2x - 11$, set to zero, solve, then test or use graphing). Alternatively, recall typical cubic behavior. The critical points can be approximated. Solving $6x^2 + 2x - 11 = 0$ using quadratic formula $x=\frac{-2\pm\sqrt{4 + 264}}{12}=\frac{-2\pm\sqrt{268}}{12}\approx\frac{-2\pm16.37}{12}$. So $x\approx\frac{14.37}{12}\approx1.2$ or $x\approx\frac{-18.37}{12}\approx -1.53$. Then evaluate $f(x)$ at these points: $f(-1.53)\approx2(-1.53)^3+(-1.53)^2 - 11(-1.53)\approx -7.1 + 2.34 + 16.83\approx12.07$ (close to 12.01), $f(1.2)\approx2(1.728)+1.44 - 13.2\approx3.456 + 1.44 - 13.2\approx -8.304$ (close to -8.3). So relative max at $(-1.53,12.01)$, min at $(1.2, -8.3)$. # Answer: b. The relative maximum is at $(-1.53, 12.01)$ and the relative minimum is at $(1.2, -8.3)$. ### Question 18 # Explanation: ## Step1: Recall end - behavior rules For a polynomial $a_nx^n+\cdots+a_0$, if $n$ is odd: - If $a_n>0$, end behavior is down (as $x ightarrow-\infty$) and up (as $x ightarrow\infty$). - If $a_n<0$, end behavior is up (as $x ightarrow-\infty$) and down (as $x ightarrow\infty$)? Wait, no: Wait, for $y = ax^n$, $n$ odd: - If $a>0$: as $x ightarrow-\infty$, $y ightarrow-\infty$; as $x ightarrow\infty$, $y ightarrow\infty$ (down then up). - If $a<0$: as $x ightarrow-\infty$, $y ightarrow\infty$; as $x ightarrow\infty$, $y ightarrow-\infty$ (up then down). Wait, but the options: Let's re - check. The leading term is $-3x^3$, $n = 3$ (odd), $a=-3<0$. So as $x ightarrow-\infty$, $(-3)x^3 ightarrow - 3\times(-\infty)^3=\infty$ (up), as $x ightarrow\infty$, $(-3)x^3 ightarrow - 3\times\infty^3=-\infty$ (down). Wait, but option c says "up and down", option a says "down and down", option b "up and up", option d "down and up". Wait, maybe I mixed up. Wait, when $n$ is odd and $a<0$: - As $x ightarrow-\infty$: $x^3 ightarrow-\infty$, multiply by $-3$ (negative) gives $(-3)\times(-\infty)=\infty$ (so the graph goes up on the left). - As $x ightarrow\infty$: $x^3 ightarrow\infty$, multiply by $-3$ gives $-\infty$ (so the graph goes down on the right). So end behavior is up (as $x ightarrow-\infty$) and down (as $x ightarrow\infty$), which is option c. # Answer: c. The leading term is $-3x^3$. Since $n$ is odd and $a$ is negative, the end behavior is up and down.

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QUESTION IMAGE

Question

Explanation:

Question 14

Step1: Recall degree of polynomial

Step2: Match with options

Step1: Count number of terms

Step2: Match with options

Step1: Write in standard form

Step2: Determine degree and terms

Answer:

Question 15