Chapter 14, Problem 48SGR

To determine

To solve: Factorize the polynomial by the Greatest Common Factor $\left(\text{G}.\text{C}.\text{F}.\right)$ .

Answer to Problem 48SGR

The factored polynomial is $3r^3{s}^3\left(-5r+1+2s\right)$ .

Explanation of Solution

Given information:

The polynomial equation mentioned in the problem is $-15r^4{s}^3+3r^3{s}^3+6r^3{s}^4$ .

Formula:

For factorize the polynomial we will divide it by the term which is common to polynomial.

Consider the statement polynomial equation mentioned in the problem is $-15r^4{s}^3+3r^3{s}^3+6r^3{s}^4$ .

Recall that for factorize the polynomial we will divide it by the term which is common to polynomial.

Therefore the common term is $3r^3{s}^3$ .

Now we will divide the polynomial $-15r^4{s}^3+3r^3{s}^3+6r^3{s}^4$ by $3r^3{s}^3$ with the help of Greatest Common Factor.

On divide we will get the quotient as $-5r+1+2s$ .

Therefore factored polynomial is $3r^3{s}^3\left(-5r+1+2s\right)$ .