Chapter 8.6, Problem 5CYU

To determine

To factor: The polynomial $4x^2-30x+36$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 5CYU

  $2\left(x-6\right)\left(2x-3\right)$

Explanation of Solution

Given:

  $4x^2-30x+36$

Calculation:

The given polynomial is $4x^2-30x+36$

Factor out the GCF

  $2\left(2x^2-15x+18\right)$

Rewrite the middle term as $-15x=-12x-3x$ . So, the polynomial becomes

  $2\left(2x^2-12x-3x+18\right)$

Make group as shown below

  $2\left(\left(2x^2-12x\right)+\left(-3x+18\right)\right)$

Factor out the GCF from each of the group

  $2\left(2x\left(x-6\right)-3\left(x-6\right)\right)$

Finally, factored out the common factor

  $2\left(x-6\right)\left(2x-3\right)$

Therefore, the factored form of the given polynomial is $2\left(x-6\right)\left(2x-3\right)$