Q. 348 - Intermediate Algebra

Question

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

$3x(x - 1) + 5(x - 1)$

Step-by-Step Solution

Answer

The factored form of the polynomial is, 

$(x-1)(3x+5)$.

Step 1. Given Information

 We are given a polynomial, 

$3x(x - 1) + 5(x - 1)$

Step 2. Factorizing the polynomial

It can be seen that the greatest common factor of given polynomial is $x-1$, so

$3x(x - 1) + 5(x - 1)=(x-1)(3x+5)$

Step 3. Checking the factorization

 Multiplying the factors,

$$\begin{gathered} (x-1)(3x+5)=3x(x - 1) + 5(x - 1) \\ 3x(x - 1) + 5(x - 1)=3x(x - 1) + 5(x - 1) \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.