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

Answer:

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:

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