Q 67E - Intermediate Algebra

Question

In the following exercises, factor each trinomial of the form $x^2+bx+c$.

$x^2-8x+12$

Step-by-Step Solution

Answer

The factorization is $(x-2)(x-6)$.

Step 1. Writing the expression

Write the factors as two binomials with first terms $x$.

$(x )(x )$.

Step 2. Finding the factors

We need to find two numbers whose product is $12$ and sum is $-8$.

Factors of $12$	Sum
$-1, -12$	$-13$
$-2, -6$	$-8$
$-3, -4$	$-7$

Thus, $-2$ and $-6$ are the correct factors.

Hence, the factorization is $(x-2)(x-6)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (x-2)(x-6) = x^2-6x-2x+12 \\ (x-2)(x-6) = x^2-8x+12 \end{gathered}$$

Thus, the obtained factorization is correct.