## College Algebra (6th Edition)

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