Q. 344 - Intermediate Algebra

Question

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

$15m^4+6m^{2}n$

Step-by-Step Solution

Answer

The factored form of the polynomial is $3m^2\left(5m^2+2n\right)$.

Step 1. Given information.

The polynomial is, 

$15m^4+6m^{2}n$.

Step 2. Finding the greatest common factor.

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

$$\begin{gathered} 15m^4+6m^{2}n \\ \Rightarrow 15m^4=3\times 5\times m\times m\times m\times m \\ \Rightarrow 6m^{2}n=2\times 3\times m\times m\times n \end{gathered}$$

Then the greatest common factor is 

$3\times m\times m=3m^2$.

Step 3. Factoring the polynomial.

Now using distributive property factor the polynomial. 

$$\begin{gathered} 15m^4+6m^{2}n=3m^2\times 5m^2+3m^2\times 2n \\ =3m^2\left(5m^2+2n\right) \end{gathered}$$

Hence, the simplified polynomial is $3m^2\left(5m^2+2n\right)$.

Step 4. Checking the result.

Multiplying the factors we get, 

$3m^2\left(5m^2+2n\right)=15m^4+6m^{2}n$.