Problem 30 - 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. $$10 y^{4}+15 y^{6}$$

Step-by-Step Solution

Answer

The factored form of the polynomial \(10y^{4} + 15y^{6}\) is \(5y^{4}(2 + 3y^{2})\).

Step 1: Identify the Greatest Common Factor

The first stage is to identify the greatest common factor (GCF) of the terms in the polynomial. The GCF refers to the highest number or term that divides each term of the polynomial. In the polynomial \(10y^{4} + 15y^{6}\), the number 5 divides both coefficients and \(y^{4}\) can be factored from each term. Hence, the GCF is \(5y^{4}\).

Step 2: Factor the Polynomial

Factoring out the GCF from each term, this will leave \(2 + 3y^{2}\). So, the polynomial in factored form becomes \(5y^{4}(2 + 3y^{2})\).