Chapter 1.3, Problem 96E

To determine

To calculate: The common factor of the expression $30x^3+15x^4$ .

Answer to Problem 96E

The common factor of the expression $30x^3+15x^4$ is $15x^3\left(x+2\right)$ .

Explanation of Solution

Given information:

The expression $30x^3+15x^4$ .

Formula used:

To factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.

Calculation:

Consider the given expression $30x^3+15x^4$ .

Recall that to factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.

Here, the greatest common factor of the terms $30x^3$ and $15x^4$ is $15x^3$ ,

So, $30x^3+15x^4$ can be written in simplified form as,

  $\begin{array}{c}30x^3+15x^4=15x^3\left(2+x\right)\\ =15x^3\left(x+2\right)\end{array}$

Thus, the common factor of the expression $30x^3+15x^4$ is $15x^3\left(x+2\right)$ .