Question

solve each equation. see example 1

1. $(x - 5)(x + 2) = 0$ 21. $(2x - 5)(7x + 2) = 0$
2. $3(x + 2)(x - 2) = 0$ 23. $(3x - 8)^2 = 0$

Explanation:

Step1: Apply Zero Product Property

For equation 20: $(x-5)(x+2)=0$, set each factor to 0:
$x-5=0$ or $x+2=0$

Step2: Solve for $x$

$x=5$ or $x=-2$

Step3: Apply Zero Product Property

For equation 21: $(2x-5)(7x+2)=0$, set each factor to 0:
$2x-5=0$ or $7x+2=0$

Step4: Solve for $x$

$2x=5 \implies x=\frac{5}{2}$; $7x=-2 \implies x=-\frac{2}{7}$

Step5: Apply Zero Product Property

For equation 22: $3(x+2)(x-2)=0$, ignore non-zero factor 3, set $(x+2)(x-2)=0$:
$x+2=0$ or $x-2=0$

Step6: Solve for $x$

$x=-2$ or $x=2$

Step7: Apply Zero Product Property

For equation 23: $(3x-8)^2=0$, set the repeated factor to 0:
$3x-8=0$

Step8: Solve for $x$

$3x=8 \implies x=\frac{8}{3}$ (double root)

Answer:

1. $x=5$ or $x=-2$
2. $x=\frac{5}{2}$ or $x=-\frac{2}{7}$
3. $x=-2$ or $x=2$
4. $x=\frac{8}{3}$