#### Answer

Solution set: $ (-\infty, 1)\cup(4,\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.
$f(x)=x^{2}-5x+4$
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)$