17. Thealgebra teache asks Kashvi to factor 20x^3y-15x^2y^2-35x^4y^2 using the GCE What is the answer? 5x^2y(4x-3y-7x^2y) This polynomial does not factor using the GCR 5x^3y^2(4xy-3xy-7x^2y^2) 5(4x^3y-3x^2y^2-7x^4y^2)

## Step 1<br />The problem asks us to factor the given polynomial using the Greatest Common Factor (GCF). The GCF is the largest number or term that can divide each term of the polynomial without leaving a remainder.<br /><br />## Step 2<br />The given polynomial is \(20x^{3}y-15x^{2}y^{2}-35x^{4}y^{2}\). We need to find the GCF of the coefficients and the variables.<br /><br />## Step 3<br />The GCF of the coefficients (20, 15, and 35) is 5. The GCF of the variables \(x^{3}\), \(x^{2}\), and \(x^{4}\) is \(x^{2}\). The GCF of the variables \(y\), \(y^{2}\), and \(y^{2}\) is \(y\).<br /><br />## Step 4<br />Therefore, the GCF of the given polynomial is \(5x^{2}y\).<br /><br />## Step 5<br />Next, we divide each term of the polynomial by the GCF to get the remaining factors.<br /><br />## Step 6<br />The polynomial \(20x^{3}y\) divided by \(5x^{2}y\) gives \(4x\).<br /><br />## Step 7<br />The polynomial \(-15x^{2}y^{2}\) divided by \(5x^{2}y\) gives \(-3y\).<br /><br />## Step 8<br />The polynomial \(-35x^{4}y^{2}\) divided by \(5x^{2}y\) gives \(-7x^{2}y\).<br /><br />## Step 9<br />Therefore, the factored form of the given polynomial is \(5x^{2}y(4x-3y-7x^{2}y)\).