Problem 34 - 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. $$15 y^{2}-3 y+9$$

Step-by-Step Solution

Answer

The factored form of the polynomial \(15 y^{2}-3 y+9\) is \(3(5y^2 - y + 3)\).

Step 1: Find the GCF

Identify the largest number that each coefficient in the polynomial has in common. In this case, the coefficients are 15, -3, and 9. The greatest common factor of these numbers is 3.

Step 2: Rewrite the polynomial

Write each term as a product of the GCF and the remaining factor. We get the following:\[3(5y^2 - y + 3)\]

Step 3: Check the result

Check if the expression can be factored further. In this case, \(5y^2 - y + 3\) can't be factored further, so we're done.