Algebra 2 EOC Polynomial Functions

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

•  $18k^3+51k^2+22k+5$  

•  $18k^3+51k^2-22k+5$  

•  $18k^3-51k^2-22k-5$  

•  $18k^3-51k^2-22k+5$  

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operations on polynomials

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

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

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

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

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

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finding zeros of a polynomial

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

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

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

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

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

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end behavior of polynomial functions

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

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

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

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

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

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end behavior of polynomial functions

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

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

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

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

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

Tags

zeros of functions

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

•  $x^2+7x-3$  

•  $x^3-7x-3$  

•  $x^2-7x+3$  

•  $x^3+7x-3$  

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operations on polynomials

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

•  $2x^6y^{12}$  

•  $2x^5y^7$  

•  $8x^6y^{12}$  

•  $8x^5y^7$  

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Rules of Exponents

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

• add

• subtract

• multiply

• divide

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Rules of Exponents

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

• $2a^2b^6$

• $\frac{1}{2}a^2b^6$

• $\frac{b^6}{2a^2}$

• $\frac{2b^6}{a^2}$

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Rules of Exponents

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

•  $2x^3-x^2+x+9$  

•  $2x^2-x+1$  

•  $2x^2-x+1+\frac{9}{x-2}$  

•  $2x^2-9x-15-\frac{23}{x-2}$  

Tags

operations on polynomials