Problem 56 - Introductory Algebra for College Students

Question

Factor each polynomial using the negative of the greatest common factor. $$-24 x^{3} y^{2}-32 x^{3} y+16 x^{2} y$$

Step-by-Step Solution

Answer

The factored form of the polynomial \(-24 x^{3} y^{2}-32 x^{3} y+16 x^{2} y\) using the negative of the greatest common factor is \(-8x^{2}y(3x^{2}y + 4x^{2} - 2x)\).

Step 1: Identify the Greatest Common Factor

Observe each term and identify the greatest common factor. In this case, \(8x^{2}y\) is the greatest common factor for all terms.

Step 2: Make the GCF Negative

Make the Greatest Common Factor (GCF) negative to get \(-8x^{2}y\), as the exercise demands.

Step 3: Apply the GCF to Each Term

Divide each term by the negative GCF. This gives the polynomial: \(3x^{2}y + 4x^{2} - 2x\).

Step 4: Write the Final Factored Form

Write the final factored form of the polynomial. Here, it will be \(-8x^{2}y(3x^{2}y + 4x^{2} - 2x)\).