Q. 343 - Intermediate Algebra

Question

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

$18x^3-15x$

Step-by-Step Solution

Answer

The factored form of the polynomial is $3x\left(6x^2-5\right)$. 

Step 1. Given information.

The polynomial is, 

$18x^3-15x$.

Step 2. Finding the greatest common factor.

Now, the greatest common factor for the given polynomial will be 

$$\begin{gathered} 18x^3-15x \\ \Rightarrow 18x^3=2\times 3\times 3\times x\times x\times x \\ \Rightarrow 15x=3\times 5\times x \end{gathered}$$

Then the greatest common factor is 

$3\times x=3x$

Step 3. Factoring the polynomial.

Now using distributive property factor the polynomial. 

$$\begin{gathered} 18x^3-15x=3x\times 6x^2-3x\times 5 \\ =3x\left(6x^2-5\right) \end{gathered}$$

Hence, the simplified polynomial is $3x\left(6x^2-5\right)$.

Step 4. Checking the result.

Multiplying the factors we get, 

$3x\left(6x^2-5\right)=18x^3-15x$