Problem 27 - Introductory Algebra for College Students

Question

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$13 y^{2}-25 y$$

Step-by-Step Solution

Answer

The factored form of the polynomial \(13 y^{2}-25 y\) is \(y(13y - 25)\).

Step 1: Identify the greatest common factor

Find the greatest common factor (GCF) present in both terms. In this case, \(y\) is common to both terms. So the GCF between \(13y^{2}\) and \(-25y\) is \(y\).

Step 2: Apply the GCF to each term

The application involves dividing each term by the GCF. Dividing \(13y^{2}\) by \(y\) gives \(13y\) and dividing \(-25y\) by \(y\) gives -25. Combined, we then get \(13y - 25\) as the result for this step.

Step 3: Express the factored polynomial

Express the factored form of the polynomial. It's done by writing the result of step 2 in parentheses, multiplied by the GCF. Therefore the factored form of the polynomial \(13 y^{2}-25 y\) is \(y(13y - 25)\).