#7 PC Polynomial Inequalities

Choose the behavior of the polynomial graph at the x-intercept whose factor has an ODD multiplicity.

• Touches or bounces at the x intercept.

• Crosses or passes through at the x intercept.

What are the zeros and their multiplicities of the polynomial graphed?

• -4 (multiplicity of 1)

  -1 (multiplicity of 2)

  1 (multiplicity of 1)

  2 (multiplicity of 1)

• -4 (multiplicity of 1)

  -1 (multiplicity of 1)

  1 (multiplicity of 2)

  2 (multiplicity of 1)

• -4 (multiplicity of 1)

  -1 (multiplicity of 2)

  1 (multiplicity of 3)

  2 (multiplicity of 1)

• -4 (multiplicity of 1)

  -1 (multiplicity of 3)

  1 (multiplicity of 2)

  2 (multiplicity of 1)

Choose the sentence that best describes what you would inspect to be able to declare the end behavior of this polynomial graph.

• A polynomial equation of an odd degree and a negative leading coefficient.

• A polynomial equation of an odd degree and a positive leading coefficient.

• A polynomial equation of an even degree and a negative leading coefficient.

• A polynomial equation of an even degree and a positive leading coefficient.

Given the graph of the polynomial function, determine where f(x) < 0.

• (-oo, 4)

• (-oo, 4]

• (-oo, 2) U (2, 4)

• (-oo, 2) U (2, 4]

Without graphing, solve the inequality.

(x - 2) (x + 3)² (x² + 4) ≥ 0

• (2,∞)

• [2,∞)

• ( -3) U (2,∞)

• [-3] U [2,∞)

Given the graph of the polynomial function, determine where f(x) ≤ 0.

•  $\left(-\infty,\ 4\right)$ 

•  $\left(-\infty,\ 4\right]$ 

•  $\left(-\infty,2\right]\cup\left[2,4\right)$  

• $\left(-\infty,2\right)\cup\left(2,4\right)$

What are the solutions for the polynomial inequality?
 $x^2-x\le6$  

•  $\left(-2,3\right)$  

•  $\left[-2,3\right]$  

•  $\left(-\infty,-2\right)\cup\left(3,\ \infty\right)$  

•  $\left(-\infty,-2\right]\cup\left[3,\ \infty\right)$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.4

What are the solutions for the polynomial inequality?
 $-2x^3+2x^2+4x<0$  

•  $\left(-1,\ 0\right)\cup\left(2,\ \infty\right)$  

•  $\left(-\infty,\ -1\right)\cup\left(0,\ 2\right)$  

•  $\left(2,\ \infty\right)$  

•  $\left(-1,\ 2\right)\cup\left(2,\ \infty\right)$  

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

What are the solutions for the polynomial inequality? $-2\left(x+5\right)\left(x-2\right)\left(x-3\right)\le0$  
  

•   $\left(-5,2\right)\cup\left(3,\infty\right)$  

•  $\left[-5,2\right]\cup\left[3,\infty\right)$  

•  $\left(-\infty,5\right)\cup\left(2,3\right)$  

•  $\left(-\infty,5\right]\cup\left[2,3\right]$  

Choose the behavior of the polynomial graph at the x-intercept whose factor has an EVEN multiplicity.

• Touches or bounces at the x intercept.

• Crosses or passes through at the x intercept.