Chapter 4.3, Problem 34PPS

To determine

To calculate: The factors of the polynomial $18x^2{y}^2-24x{y}^2+36y^2$ .

Answer to Problem 34PPS

The polynomial is factored as $6y^2\left(3x^2-4x+6\right)$ .

Explanation of Solution

Given information:

The polynomial $18x^2{y}^2-24x{y}^2+36y^2$ .

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the polynomial $18x^2{y}^2-24x{y}^2+36y^2$ .

Take out the common factor,

  $18x^2{y}^2-24x{y}^2+36y^2=6y^2\left(3x^2-4x+6\right)$

Recall that to factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

For the above polynomial there are no two numbers such that their sum is $-4$ and product is $-18$ .

Thus, the polynomial is factored as $6y^2\left(3x^2-4x+6\right)$ .