Q. 420 - Intermediate Algebra

Question

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

$60x^{2}y-75x+30y$

Step-by-Step Solution

Answer

The factors of the given expression are $15(4x^{2}y-5x+2y)$.

Step 1. Given and explanation.

We have $60x^{2}y-75x+30y$.

We will take the common factor out, if any. The we will further factor out the expression if posisble.

Step 2. Taking common factor out and simplifying.

We have $60x^{2}y-75x+30y$.

Taking $15$ common will give us,

$15(4x^{2}y-5x+6y)$.

This cannot be further factored as it is prime.

This shows tat the factors of the expression are $15(4x^{2}y-5x+6y)$

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,

$$\begin{gathered} =15(4x^{2}y-5x+6y) \\ =60x^{2}y-75x+60y \end{gathered}$$

Thus our calculations are right.