Q. 6.6 - Intermediate Algebra

Question

Factor: $6y^3-15y^2$

Step-by-Step Solution

Answer

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

Step 1. Given Information

The given expression is $6y^3-15y^2$.

Step 2. Find GCF of the terms

• Factor each of the terms in the given expression.

$$\begin{gathered} 6y^3=2·3·y·y·y \\ 15y^2=3·5·y·y \end{gathered}$$

• From the obtained factors, it is observed that the common factors are $3,y,y$.
• Multiply the common factors to determine the GCF of the terms of the given expression.

$3·y·y=3y^2$

• So, the GCF of the terms of the given expression is $3y^2$.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, $3y^2$.

$3y^2·2y-3y^2·5$

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

$3y^2·2y-3y^2·5=3y^2(2y-5)$

Step 4. Check

• Multiply the obtained factors.

$\begin{array}{rcl}3y^2(2y-5)& =& 3y^2·2y-3y^2·5\\ & =& 6y^3-15y^2\end{array}$

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