Question

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

$24y^3-18y^2-30y$

Short answer

The factored form is$\begin{array}{rcl}& & 6y(4y^2-3y-5)\end{array}$.

Step-by-step solution

Step 1. Given Information

The given polynomial is$24y^3-18y^2-30y$.

Step 2. Find the GCF of the terms   

• Factor each of the terms in the given expression.

$$\begin{gathered} 24y^3=2·2·2·3·y·y·y \\ 18y^2=2·3·3·y·y \\ 30y=2·3·5·y \end{gathered}$$

• From the obtained factors, it is observed that the common factors are $2,3,y$.
• Multiply the common factors.

$2·3·y=6y$

• So, the GCF of the terms of the given expression is $6y$.

Step 3. Rewrite the given expression       

• Express each of the term of the given expression as a product of GCF, $6y$.

$6y·4y^2-6y·3y-6y·5$

• Use the reverse distributive property, $ab+ac=a(b+c)$to rewrite the obtained expression.

role="math" localid="1644582515017" $6y·4y^2-6y·3y-6y·5=6y(4y^2-3y-5)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}6y(4y^2-3y-5)& =& 6y·4y^2-6y·3y-6y·5\\ & =& 24y^3-18y^2-30y\end{array}$

• Since the obtained expression is the same as the given expression, the obtained factors are verified.