Q 71E - Intermediate Algebra

Question

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

$x^2-8x+7$

Step-by-Step Solution

Answer

The factorization is $(x-1)(x-7)$.

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 $7$ and sum is $-8$.

Since we know that $7$ is a prime number, $-1$ and $-7$ are the only negative factors and their sum is $-8$.

Hence, the factorization is $(x-1)(x-7)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (x-1)(x-7)=x^2-7x-x+7 \\ (x-1)(x-7)=x^2-8x+7 \end{gathered}$$

Thus, the obtained factorization is correct.