PC: 5.2 Review #2

What are the critical numbers for this polynomial inequality?

 $\left(x+1\right)\left(x-3\right)\left(x+4\right)>0$  

• 0, -1, 3, -4

• 1, 3, -4

• -1, 3, -4

What are the critical numbers for this rational inequality?

 $\frac{x^2-4}{x+7}<0$  

• 2, -2

• 2, -7

• 2, -2, -7

Identify the equation(s) that find the real zeros of:

 $\frac{x^2-81}{x+5}\le0$  

•  $x+5=0$  

•  $x^2-81=0$  

• Both:  $x+5=0$  and  $x^2-81=0$  

Analyze the following student work for solving the polynomial inequality. Based on the table, what is the final solution?

• $\left(-\infty,\ -7\right)$

• $\left(-7,\ 7\right)$

• $\left(-\infty,\ -7\right)\cup\left(7,\ \infty\right)$

When solving this rational inequality, you must first set the inequality equal to zero and then express as a single fraction. What is the inequality expressed as a single fraction?

• $\frac{-3x}{x+3}>0$

• $\frac{3x}{x+3}>0$

• $\frac{-3x+18}{x+3}$

Express the shaded region in interval notation.

• $\left[-4,\ \infty\right)$

• $\left(-4,\ \infty\right)$

• $\left(-\infty,\ -4\right)$

Express the shaded region in interval notation.

• $\left(1,\ 9\right)$

• $\left[1,\ 9\right]$

• $\left[1,\ 9\right)$

• $\left(1,\ 9\right]$

When solving the rational inequality, what are the regions you will test?

 $\frac{x+6}{x-5}\le0$  

*Select 3 regions

•  $\left(-\infty,\ -6\right]$  

•  $\left[-6,\ 5\right]$  

•  $\left[-6,\ 5\right)$  

•  $\left[5,\ \infty\right)$  

•  $\left(5,\ \infty\right)$  

 $3x^3+5x^2-2x$  

Factor completely:

*GCF first

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

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

•  $x\left(x+6\right)\left(x-1\right)$  

Based on the work provided and the completed table, what is the final solution set for

 $\frac{x-3}{x+4}\ge0$  

•  $\left(-\infty,\ -4\right)\cup\left[3,\ \infty\right)$  

•  $\left(-4,\ 3\right]$  

• all real numbers

• no solution