Chapter 1.3, Problem 66E

To determine

To calculate: The common factor of the expression $-7x^4{y}^2+14x{y}^3+21x{y}^4$ .

Answer to Problem 66E

The common factor of the expression $-7x^4{y}^2+14x{y}^3+21x{y}^4$ is $-7x{y}^2\left(x^3-2y-3y^2\right)$ .

Explanation of Solution

Given information:

The expression $-7x^4{y}^2+14x{y}^3+21x{y}^4$ .

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 $-7x^4{y}^2+14x{y}^3+21x{y}^4$ .

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 $-7,14\text{ and }21$ is $-7$ .

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

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

So, $-7x^4{y}^2+14x{y}^3+21x{y}^4$ can be written in simplified form as,

  $-7x^4{y}^2+14x{y}^3+21x{y}^4=-7x{y}^2\left(x^3-2y-3y^2\right)$

Thus, the common factor of the expression $-7x^4{y}^2+14x{y}^3+21x{y}^4$ is $-7x{y}^2\left(x^3-2y-3y^2\right)$ .