Question

1. $r^{2}+10r + 16 = 0$ 24) $x^{2}+8x - 48 = 0$

Explanation:

Step1: Factor quadratic 23

Find two numbers that multiply to 16 and add to 10: 2 and 8.
$r^2 + 10r + 16 = (r+2)(r+8) = 0$

Step2: Solve for r (23)

Set each factor equal to 0.
$r+2=0 \implies r=-2$; $r+8=0 \implies r=-8$

Step3: Factor quadratic 24

Find two numbers that multiply to -48 and add to 8: 12 and -4.
$x^2 + 8x - 48 = (x+12)(x-4) = 0$

Step4: Solve for x (24)

Set each factor equal to 0.
$x+12=0 \implies x=-12$; $x-4=0 \implies x=4$

Answer:

For $r^2 + 10r + 16 = 0$: $r=-2$ or $r=-8$
For $x^2 + 8x - 48 = 0$: $x=-12$ or $x=4$