Problem 31 - 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. $$8 x^{2}-4 x^{4}$$

Step-by-Step Solution

Answer

Therefore, the factored form of the polynomial \(8x^{2}-4x^{4}\) using the greatest common factor is \(4x^{2}(2 - x^{2})\).

Step 1: Identify the GCF

Identify the greatest common factor (GCF) from each term in the given polynomial. The GCF of \(8x^{2}\) and \(-4x^{4}\) is \(4x^{2}\).

Step 2: Factor out the GCF

Factor out the greatest common factor from the given polynomial to obtain an equivalent expression. In this case, factoring out \(4x^{2}\) from \(8x^{2}-4x^{4}\) we get \(4x^{2}(2 - x^{2})\)

Step 3: Check the Solution

Check if the factored form can be simplified further. Here \(2 - x^{2}\) cannot be factored further, so the answer is left as it is.