Problem 53 - Introductory Algebra for College Students

Question

Factor each polynomial using the negative of the greatest common factor. $$-4 a^{3} b^{2}+6 a b$$

Step-by-Step Solution

Answer

The factored form of the polynomial \( -4a^{3}b^{2} + 6ab \) using the negative of the GCF is \( -2ab (2a^{2}b - 3) \).

Step 1: Identify the GCF

The given polynomial is \( -4a^{3}b^{2} + 6ab \). The greatest common factor (GCF) of these terms is \( 2ab \).

Step 2: Subtract the GCF

Factor out the negative of the GCF, which is \( -2ab \). After doing this, you'll get \( -2ab (2a^{2}b - 3) \). See that the polynomial is the product of the GCF and the resulting expression. Therefore, the factored form using the negative of the GCF is \( -2ab (2a^{2}b - 3) \).