Math 3 EOC Review - Polynomials

Determine the end behavior of  $f\left(x\right)=-x^{12}+6x^6-36$  

• As  $x\rightarrow-\infty$ ,  $f\left(x\right)\rightarrow-\infty$   and as  $x\rightarrow+\infty$ ,  $f\left(x\right)\rightarrow+\infty$ .

• As  $x\rightarrow-\infty$ ,  $f\left(x\right)\rightarrow+\infty$   and as  $x\rightarrow+\infty$ ,  $f\left(x\right)\rightarrow-\infty$ .

• As  $x\rightarrow\pm\infty$  ,  $f\left(x\right)\rightarrow-\infty$ .

• As  $x\rightarrow\pm\infty$  ,  $f\left(x\right)\rightarrow+\infty$  .

Which expression is equivalent to  $\left(x^3-3x^2+x-6\right)\div\left(x^2+2\right)$ ?

•  $x-3-\frac{x}{x^2+2}$  

•  $x-8+\frac{x+1}{x^2+2}$  

•  $x-5+\frac{x+4}{x^2+2}$  

•  $x+3+\frac{12}{x^2+2}$  

The expression  $\left(x+4\right)$  is a factor of  $x^2+kx-20$ .
What is the value of  $k$ ?

Let  $p\left(x\right)=x^5-x^4+8x^2-9x+30$ .  Evaluate  $p\left(-2\right)$ .  What does the solution tell you about the factors of  $p$ ?

•  $p\left(-2\right)=32$ .    $\left(x+2\right)$  is not a factor of  $p$ .

•  $p\left(-2\right)=32$ .    $\left(x-2\right)$  is not a factor of  $p$ .

•  $p\left(-2\right)=0$ .    $\left(x+2\right)$  is a factor of  $p$ .

•  $p\left(-2\right)=0$ .    $\left(x-2\right)$  is a factor of  $p$ .

What is the value of  $a$ if  $\left(x-2\right)$  is a factor of  $x^4-3x^3+ax^2-6x+14$ ? 

•  $a=1.5$  

•  $a=0.\overline{6}$  

•  $a=2$  

•  $a=3$  

Describe the roots of the polynomial function below (real/imaginary): $f\left(x\right)=x^4-10x^2-21x-12$  

• 4 real, 0 imaginary roots

• 0 real, 4 imaginary roots

• 2 real, 2 imaginary roots

• 3 real, 1 imaginary roots

Which expression is equivalent to  $2x^2-3x^2-3+2x$ ? 

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

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

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

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

Does the polynomial function have any root with a multiplicity of 2 (a double root)?  $f\left(x\right)=x^5-3x^4-27x^3+19x^2+114x-72$  

If so, type in the root.  If not, type "none"

What are the two non-rational solutions to the equation below?  $0=\left(x-5\right)\left(3x+5\right)\left(x^2-7x+15\right)$  

•  $x=\frac{7\pm i\sqrt{11}}{2}$  

•  $x=\frac{7\pm\sqrt{109}}{2}$  

•  $x=\frac{7\pm i\sqrt{46}}{2}$  

•  $x=\frac{7\pm\sqrt{74}}{2}$