Math 3 DCA #2 Review

Find the intervals of increase and decrease for the function

y = x³+2x² – 5x – 6

• Increase: $\left(-\infty,\ 4.06\right)\cup\left(-8.21,\ \infty\right)$ Decrease: $\left(-8.21,\ 4.06\right)$

• Increase: $\left(-2.12,\ 0.79\right)$ Decrease: $\left(-\infty,-2.12\right)\cup\left(0.79,\infty\right)$

• Increase: $\left(-\infty,-2.12\right)\cup\left(0.79,\infty\right)$ Decrease: $\left(-2.12,\ 0.79\right)$

• Increase: $\left(-\infty,\ -8.21\right)\cup\left(4.06,\ \infty\right)$ Decrease: $\left(-8.21,\ 4.06\right)$

Find the zeros for the function

y = x³+2x² – 5x – 6

• x = -3

• x = 1

• x = -1

• x = 0

• x = 2

Find the end behavior for the function

y = x³+2x² – 5x – 6

What is the distance between the two zeros that are the closest to each other for the function below:

y = x³+2x² – 5x – 6

• 1 unit

• 2 units

• 3 units

• 5 units

Divide using long or synthetic division.

 $\left(4x^2-10x+4\right)\div\left(2x-1\right)$  

• $4x-6-\frac{2}{2x-1}$

• $2x-6$

• $2x-4$
  

• $2x-1+\frac{1}{2x-1}$

Divide.

 $\left(x^3+2x^2-11x+12\right)\div\left(x^2+3\right)$  

•  $x+2+\frac{-14x+6}{x^2+3}$ 

•  $x+2$ 

•  $x-14$ 
  

•  $x+2+\frac{14x+18}{x^2+3}$ 

Is (x – 2) a factor of the polynomial P(x) = 2x⁴ – 3x³ + 6?

Explain why or why not.

• no, because the remainder is zero

• no, because the remainder is not zero

• yes, because the remainder is not zero

• yes, because the remainder is zero

Given the function P(x) = x³ + kx² + x – 4 , for what value of k is (x – 4) a factor of P(x)?

The expression  $V\left(x\right)=x^3-13x+12$   represents the volume of a rectangular safe in cubic feet. The length of the safe is x + 4. What expression would represent the area of the base of the safe?  

•  $x-4$  

•  $x^2-4x+3$  

•  $x^2-17x+80$  

•  $x^2+4x-9$  

Write a polynomial with the given zeros.

P(4) = 0, P(-2) = 0, P(1) = 0

• $P\left(x\right)=-x^3-3x^2+6x-8$

• $P\left(x\right)=x^3-2x^2-6x+8$

• $P\left(x\right)=x^3+3x^2-6x-8$

• $P\left(x\right)=x^3-3x^2-6x+8$