Question

in exercises 11–18, solve the equation. example 2

1. $(h - 8)(h - 8) = 0$ 12. $(5m + 4)^2 = 0$
2. $(r - 4)^2(r + 8) = 0$ 14. $w(w - 6)(w - 6) = 0$
3. $z(z + 2)(z - 1) = 0$ 16. $5p(2p - 3)(p + 7) = 0$
4. $(15 - 5c)(5c + 5)(-c + 6) = 0$
5. $(2 - n)\left(6 + \frac{2}{3}n\

ight)(n - 2) = 0$

in exercises 19 and 20, find the $x$-intercepts of the graph.

1. $y = (x - 8)(x + 8)$ 20. $y = -(x - 14)(x - 5)$

in exercises 21–26, factor the polynomial. example 3

1. $5z^2 + 45z$ 22. $6d^2 - 21d$
2. $3y^3 - 9y^2$ 24. $20x^3 + 30x^2$
3. (partially visible) 26. $12a^4 + 8a$

Explanation:

Step1: Solve 11: Set factors to 0

$h-8=0$

Step2: Solve for h

$h=8$ (repeated root)

Step3: Solve 12: Set base to 0

$5m+4=0$

Step4: Solve for m

$m=-\frac{4}{5}$ (repeated root)

Step5: Solve 13: Set each factor to 0

$r-4=0$; $r+8=0$

Step6: Solve for r

$r=4$ (repeated), $r=-8$

Step7: Solve 14: Set each factor to 0

$w=0$; $w-6=0$

Step8: Solve for w

$w=0$, $w=6$ (repeated)

Step9: Solve 15: Set each factor to 0

$z=0$; $z+2=0$; $z-1=0$

Step10: Solve for z

$z=0$, $z=-2$, $z=1$

Step11: Solve 16: Set each factor to 0

$5p=0$; $2p-3=0$; $p+7=0$

Step12: Solve for p

$p=0$, $p=\frac{3}{2}$, $p=-7$

Step13: Solve 17: Set each factor to 0

$15-5c=0$; $5c+5=0$; $-c+6=0$

Step14: Solve for c

$c=3$, $c=-1$, $c=6$

Step15: Solve 18: Set each factor to 0

$2-n=0$; $6+\frac{2}{3}n=0$; $n-2=0$

Step16: Solve for n

$n=2$ (repeated), $n=-9$

Step17: Solve 19: Set y=0, solve factors

$x-8=0$; $x+8=0$

Step18: Find x-intercepts

$x=8$, $x=-8$ → $(8,0), (-8,0)$

Step19: Solve 20: Set y=0, solve factors

$x-14=0$; $x-5=0$

Step20: Find x-intercepts

$x=14$, $x=5$ → $(14,0), (5,0)$

Step21: Factor 21: Factor out GCF

$5z(z+9)$

Step22: Factor 22: Factor out GCF

$3d(2d-7)$

Answer:

1. $\boldsymbol{h=8}$
2. $\boldsymbol{m=-\frac{4}{5}}$
3. $\boldsymbol{r=4, \, r=-8}$
4. $\boldsymbol{w=0, \, w=6}$
5. $\boldsymbol{z=0, \, z=-2, \, z=1}$
6. $\boldsymbol{p=0, \, p=\frac{3}{2}, \, p=-7}$
7. $\boldsymbol{c=3, \, c=-1, \, c=6}$
8. $\boldsymbol{n=2, \, n=-9}$
9. $\boldsymbol{(8,0) \text{ and } (-8,0)}$
10. $\boldsymbol{(14,0) \text{ and } (5,0)}$
11. $\boldsymbol{5z(z+9)}$
12. $\boldsymbol{3d(2d-7)}$