Free Printable Algebra 2 EOC Polynomial Functions

1.

Simplify: $\left(3k^2-8k-5\right)\left(6k-1\right)$

a)

$18k^3+51k^2+22k+5$

b)

$18k^3+51k^2-22k+5$

c)

$18k^3-51k^2-22k-5$

d)

$18k^3-51k^2-22k+5$

2.

Find all the factors of $x^3-3x^2-4x+12$ given that $-2$ is a zero.

a)

$\left(x-2\right)\left(x+2\right)\left(x+3\right)$

b)

$\left(x-2\right)\left(x-2\right)\left(x+3\right)$

c)

$\left(x+2\right)\left(x+2\right)\left(x+3\right)$

d)

$\left(x-2\right)\left(x+2\right)\left(x-3\right)$

3.

Given the function above, choose the true statement with respect to its end behavior.

a)

As $\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$ ; as $\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

b)

As $\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$ ; as $\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

c)

As $\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$ ; as $\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$

d)

As $\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$ ; as $\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$

4.

Given the function $P\left(x\right)=4x^3-3x^2-12x\ +2$ , determine its end behavior.

a)

As $\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$ ; as $\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$

b)

As $x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$ ; as $\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

c)

As $\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$ ; as $x\rightarrow\infty,\ f\left(x\right)\rightarrow0$

d)

As $\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$ ; as $\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

5.

What is the factored form of a function if it has zeros of 2, 3 and -1?

a)

$f\left(x\right)=\left(x-2\right)\left(x-3\right)\left(x+1\right)$

b)

$f\left(x\right)=\left(x+1\right)\left(x+2\right)\left(x+3\right)$

c)

$f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+3\right)$

d)

$f\left(x\right)=\left(x-3\right)\left(x-2\right)\left(x-1\right)$

6.

Simplify: $\frac{2x^4-7x^3+14x^2-55x+21}{2x-7}$

a)

$x^2+7x-3$

b)

$x^3-7x-3$

c)

$x^2-7x+3$

d)

$x^3+7x-3$

7.

Simplify: $\left(2x^2y^4\right)^3$

a)

$2x^6y^{12}$

b)

$2x^5y^7$

c)

$8x^6y^{12}$

d)

$8x^5y^7$

8.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

9.

Simplify: $\frac{12a^2b^8}{24a^4b^2}$

a)

$2a^2b^6$

b)

$\frac{1}{2}a^2b^6$

c)

$\frac{b^6}{2a^2}$

d)

$\frac{2b^6}{a^2}$

10.

Simplify: $\left(2x^3-5x^2+3x+7\right)\div\left(x-2\right)$

a)

$2x^3-x^2+x+9$

b)

$2x^2-x+1$

c)

$2x^2-x+1+\frac{9}{x-2}$

d)

$2x^2-9x-15-\frac{23}{x-2}$

11.

Simplify: $\left(3x^3+5x-1\right)\div\left(x+1\right)$

a)

$3x^3-3x^2+8x-9$

b)

$3x^2-3x+8-\frac{9}{x+1}$

c)

$3x^2+3x+8+\frac{7}{x+1}$

d)

$3x^3+3x^2+8x+7$

12.

Simplify: $\frac{8x^4y^5x^{-6}y^{-7}}{4x^2y^3x^{-4}y^{-5}}$

a)

$\frac{2}{x^4y^4}$

b)

$\frac{2x^4}{y^4}$

c)

$2x^4y^4$

d)

$2$

13.

Factor completely:
$n^3-27$

a)

$\left(n-3\right)\left(n^2+9\right)$

b)

$\left(n+3\right)\left(n^2-9\right)$

c)

$\left(n+3\right)\left(n^2-3n+9\right)$

d)

$\left(n-3\right)\left(n^2+3n+9\right)$

14.

Factor completely:
$8x^3+27y^3$

a)

$\left(2x+3y\right)\left(4x^2-9y^2\right)$

b)

$\left(2x+3y\right)\left(4x^2-36xy+81y^2\right)$

c)

$\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)$

d)

$\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)$

Algebra 2 EOC Polynomial Functions

Total questions: 14

Worksheet time: 1hrs 10mins

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