Chapter 1.3, Problem 62E

To determine

To calculate: The common factor of the expression $2x^4+4x^3-14x^2$ .

Answer to Problem 62E

The common factor of the expression $2x^4+4x^3-14x^2$ is $2x^2\left(x^2+2x-7\right)$ .

Explanation of Solution

Given information:

The expression $2x^4+4x^3-14x^2$ .

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 $2x^4+4x^3-14x^2$ .

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 2,4 and 14 is 2.

The greatest common factor of $x^4,x^3\text{ and }{x}^2$ is $x^2$ .

So, $2x^4+4x^3-14x^2$ can be written in simplified form as,

  $2x^4+4x^3-14x^2=2x^2\left(x^2+2x-7\right)$

Thus, the common factor of the expression $2x^4+4x^3-14x^2$ is $2x^2\left(x^2+2x-7\right)$ .