## College Algebra (6th Edition)

Published by Pearson

# Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.6 - Page 420: 3

#### Answer

Solution set: $[-3,7]$

#### Work Step by Step

Follow the "Procedure for Solving Polynomial lnequalities",\ p.412: 1. Express the inequality in the form $f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$ where $f$ is a polynomial function. $f(x)=(x-7)(x+3)\leq 0$ 2. Solve the equation $f(x)=0$. The real solutions are the boundary points. $(x-7)(x+3)=0$ $x=-3$ or $x=7$ 3. Locate these boundary points on a number line, thereby dividing the number line into intervals. 4. Test each interval's sign of $f(x)$ with a test value, $\left[\begin{array}{llll} Intervals: & (-\infty, -3) & (-3,7) & (7,\infty)\\ a=test.val. & -10 & 0 & 10\\ f(a) & (-17)(-7) & (-7)(3) & (3)(15)\\ f(a) \leq 0 ? & F & T & F \end{array}\right]$ 5. Write the solution set, selecting the interval or intervals that satisfy the given inequality. If the inequality involves $\leq$ or $\geq$, include the boundary points. Solution set: $[-3,7]$

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