Q. 346 - Intermediate Algebra

Question

In the following exercises, factor the greatest common factor from each polynomial.

$-3x + 24$

Step-by-Step Solution

Answer

The factored form of the polynomial is,

$3(-x+8)$.

Step 1. Given Information

We are given a polynomial, 

$-3x + 24$

Step 2. Finding the greatest common factor

Factoring the polynomial, 

$$\begin{gathered} -3x=-3\times x \\ 24=2\times 2\times 2\times 3 \end{gathered}$$

The greatest common factor is $3$,

$-3x+24=3(-x+8)$

Step 3. Checking the factorization

Multiplying the factors, 

$$\begin{gathered} 3(-x+8)=-3x+24 \\ -3\times x+3\times 8=-3x+24 \\ -3x+24=-3x+24 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.