Question 8(Multiple Choice Worth 4 points) (07.01, 07.02 MC) Factor the greatest common factor: 28a^3b^4+20a^2b^2-16ab^3 4ab(7a^2b+5a-4b^2) 4ab^2(7a^2b+5a-4b) 4ab^2(7a^2b^2+5a-4b) 4ab(7a^2b^3+5a-4b)

## Step 1<br />The problem asks us to factor the greatest common factor (GCF) from the given expression. The GCF is the largest number or term that can be divided evenly into all terms of the expression.<br /><br />## Step 2<br />The given expression is \(28a^{3}b^{4}+20a^{2}b^{2}-16ab^{3}\). We need to find the GCF of the coefficients and the variables.<br /><br />## Step 3<br />The GCF of the coefficients (28, 20, and 16) is 4. This is because 4 is the largest number that can divide all three numbers evenly.<br /><br />## Step 4<br />The GCF of the variables is \(ab\). This is because \(a\) and \(b\) are the smallest powers of \(a\) and \(b\) that appear in all three terms.<br /><br />## Step 5<br />Therefore, the GCF of the entire expression is \(4ab\).<br /><br />## Step 6<br />Next, we divide each term of the expression by the GCF to get the remaining factors.<br /><br />## Step 7<br />The first term \(28a^{3}b^{4}\) divided by \(4ab\) gives \(7a^{2}b^{3}\).<br /><br />## Step 8<br />The second term \(20a^{2}b^{2}\) divided by \(4ab\) gives \(5a\).<br /><br />## Step 9<br />The third term \(-16ab^{3}\) divided by \(4ab\) gives \(-4b^{2}\).<br /><br />## Step 10<br />Therefore, the factored form of the expression is \(4ab(7a^{2}b^{3}+5a-4b^{2})\).