Question

IMPORTANT, PLEASE HELP QUICKLY! 15 POINTS

Explain how to factor the expression q(x)=9x2−24x+16 to the expression q(x)=(3x−4)2 . You may show your work. Be sure to include a detailed explanation of your steps.

Answer 1

Given function:

`q(x)=9x^2-24x+16`

To factor a quadratic in the form
`ax^2+bx+c`, find two numbers that multiply to
`ac` and sum to
`b`:

`ac=9 \cdot 16=144`

Two numbers that multiply to 144 and sum to -24 are: -12 and -12

Rewrite
`b` as the sum of these two numbers:

`\implies q(x)=9x^2-12x-12x+16`

Factorize the first two terms and the last two terms separately:

`\implies q(x)=3x(3x-4)-4(3x-4)`

Factor out the common term
`(3x-4)`:

`\implies q(x)=(3x-4)(3x-4)`

Therefore:

`\implies q(x)=(3x-4)^2`