Q. 418 - Intermediate Algebra

Question

Recognize and Use the Appropriate Method to Factor a Polynomial Completely.

$4u^{5}v+4u^2{v}^3$

Step-by-Step Solution

Answer

The factors of the given expression are $4u^{2}v(u^3+v^2)$.

Step 1. Given and explanation.

We have $4u^{5}v+4u^2{v}^3$.

We will firstly take out the common factors, if any, from the equation. Then we will proceed further for factorizing it, if possible.

Step 2. Taking common factor out.

We have $4u^{5}v+4u^2{v}^3$.

We can take $4u^{2}v$ common from the equation and it will give us,

$$\begin{gathered} =4u^{5}v+4u^2{v}^3 \\ =4u^{2}v(u^3+v^2) \end{gathered}$$

This cannot be further factorized so the factors of the given equation are $4u^{2}v(u^3+v^2)$.

Step 3. Check the solution.

We will check the solution by simply multiplying the factors. If we get the given equation as the product, our answer is right.

So,

$$\begin{gathered} =4u^{2}v(u^3+v^2) \\ =4u^{5}v+4u^2{v}^3 \end{gathered}$$

Thus our calculations are right.