Problem 24 - 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. $$20 y^{2}+15$$

Step-by-Step Solution

Answer

The polynomial \(20y^{2}+15\) factored using the greatest common factor is \(5(4y^{2}+3)\)

Step 1: Identify the GCF

The terms in the polynomial presented are 20 \(y^2\) and 15. To process, divide 20 and 15 by their Greatest Common Factor (GCF). The GCF of the coefficients 20 and 15 is 5.

Step 2: Factorize the polynomial

Divide both terms of the polynomial by the GCF to form a factored polynomial. Hence, the polynomial can be rewritten as \(5(4y^{2}+3)\)

Step 3: Check correctness

To make sure that the binomial is correctly factored, multiply back the factored forms and compare the result against the given polynomial. In this case, \(5 * 4y^2 + 5 * 3 = 20y^2 + 15\), which verifies the solution is correct.