Q. 136E - Intermediate Algebra

Question

In the following exercises, factor each expression using any method $x^2-14x-32$

Step-by-Step Solution

Answer

The factors are $\left(x-16\right)\left(x+2\right)$

Step 1. Given Information

The trinomial is $x^2-14x-32$

Find factors by splitting middle term 

Step 2. Factor the trinomial

Split the middle term of trinomial to find factors

Find two numbers such as their product is $-32$and sum is $-14$.

The numbers are $-16 and +2$

$$\begin{gathered} x^2-14x-32 \\ {x}^2-16x+2x-32 \end{gathered}$$

Factor it

$$\begin{gathered} x\left(x-16\right)+2\left(x-16\right) \\ \left(x-16\right)\left(x+2\right) \end{gathered}$$

Step 3. Check

Multiply the factors$\left(x-16\right)\left(x+2\right)$

$$\begin{gathered} x^2-16x+2x-32 \\ {x}^2-14x-32 \end{gathered}$$