College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.6 - Page 420: 7


Solution set: $(-\infty, -4)\cup(-1,\infty)$

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. $f(x)= x^{2}+5x+4>0$ factor the trinomial... find factors of $4$ that add to $5:$ $f(x)=(x+1)(x+4)>0$ 2. Solve the equation $f(x)=0$. The real solutions are the boundary points. $(x+1)(x+4)=0$ $x=-1$ or $x=-4$ 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, $\begin{array}{llll} Intervals: & (-\infty, -4) & (-4,-1) & (-1,\infty)\\ a=test.val. & -10 & -2 & 0\\ f(a) & (-9)(-6) & (-1)(2) & (1)(4)\\ f(a) > 0 ? & T & F & T \end{array}$ 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: $(-\infty, -4)\cup(-1,\infty)$
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