Factor $$ x^{2}-8 x+16 $$ $$ (x-4)^{2} $$ $$ (x+4)^{2} $$ $$ (x-4)(x+4) $$ $$ (x-2)(x-8) $$

Question

UpStudy AI · Accepted Answer

Consider the quadratic:

$$
x^{2} - 8x + 16
$$

We want to factor it into the form:

$$
(x - a)^2 = x^2 - 2ax + a^2
$$

By comparing coefficients:

1. The coefficient of $$ x $$ is $$-2a$$ so that:

$$
-2a = -8 \quad \Longrightarrow \quad a = 4
$$

2. The constant term is $$ a^2 $$:

$$
a^2 = 4^2 = 16
$$

Since both conditions match, the factored form is:

$$
(x-4)^2
$$
$$ (x-4)^2 $$

Factor \( x^{2}-8 x+16 \) \( (x-4)^{2} \) \( (x+4)^{2} \) \( (x-4)(x+4) \) \( (x-2)(x-8) \)