Problem 16 - 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. $$5 y-5$$

Step-by-Step Solution

Answer

The factorized form of the polynomial \(5y - 5\) is \(5(y - 1)\).

Step 1: Identify common factors

The first step in factorizing a polynomial is to identify if the terms have any common factors. Inspecting the given polynomial \(5y - 5\), both terms are divisible by 5.

Step 2: Factor out the GCF

Once we've identified the greatest common factor, we factor it out. The greatest common factor of the given polynomial is 5, so we factor 5 out of each term in the polynomial: \(5y - 5 = 5(y - 1)\).

Step 3: Verify the solution

To verify that the solution is correct, you can distribute the factor back into the parentheses. If you obtain the original expression, your solution is correct: \(5(y - 1) = 5y - 5\). Hence, the factorized form of the polynomial is indeed \(5(y - 1)\).