Question

In the following exercises, factor the greatest common factor from each polynomial.

$-6a^{3}b-12a^2{b}^2+18a{b}^2$

Short answer

The given polynomial is factored as$-6a^{3}b-12a^2{b}^2+18a{b}^2=-6ab(a^2+2ab-3b)$

Step-by-step solution

Step 1. Given Information

Consider a polynomial $-6a^{3}b-12a^2{b}^2+18a{b}^2$.

The objective is to factor the polynomial by factoring the greatest common factor.

Step 2. Factor the GCF

The GCF of three terms of the polynomial $-6a^{3}b,-12a^2{b}^2,18a{b}^2$is $-6ab$. So rewriting the polynomial terms with the product of GCF and then using the distributive property we get

$\begin{array}{rcl}-6a^{3}b-12a^2{b}^2+18a{b}^2& =& -6ab·a^2-6ab·2ab+(-6ab)(-3b)\\ & =& -6ab(a^2+2ab-3b)\end{array}$

Step 3. Check

To check we multiply the factors and we get

$\begin{array}{rcl}-6ab(a^2+2ab-3b)& =& -6ab·a^2+(-6ab)·2ab+(-6ab)(-3b)\\ & =& -6a^{3}b-12a^2{b}^2+18a{b}^2\end{array}$

And we get the given polynomial. So the factor is done correctly.