Q. 341 - Intermediate Algebra

Question

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

$35y+84$

Step-by-Step Solution

Answer

The factored form of the polynomial is $7\left(5y+12\right)$.

Step 1. Given information.

The polynomial is,

$35y+84$ 

Step 2. Finding the greatest common factor.

Now, the greatest common factor for the given polynomial will be

$$\begin{gathered} 35y+84 \\ \Rightarrow 35y=5\times 7\times y \\ \Rightarrow 84=2\times 2\times 3\times 7 \end{gathered}$$

Then the greatest common factor is $7$.

Step 3. Factoring the polynomial.

Now using distributive property factor the polynomial.

$$\begin{gathered} 35y+84=7\times 5y+7\times 12 \\ =7\left(5y+12\right) \end{gathered}$$

Hence, the simplified polynomial is $7\left(5y+12\right)$.

Step 4. Checking the result.

Multiplying the factors we get,

$7\left(5y+12\right)=35y+84$.