Question

1. (x^2 - 8x + 15 = 0)

Explanation:

Step1: Find factors of 15 that sum to -8

We need two numbers that multiply to $15$ and add to $-8$. These numbers are $-3$ and $-5$.

Step2: Factor the quadratic expression

Rewrite the quadratic using the found factors:
$x^2 -8x +15=(x-3)(x-5)$

Step3: Solve for x using zero product rule

Set each factor equal to 0:
$x-3=0$ or $x-5=0$

Answer:

$x=3$ and $x=5$