Question

$f(x)=8x^{2}-2x+3$
$g(x)=12x^{2}+4x-3$
what is $h(x)=f(x)-g(x)$?
$\bigcirc$ $h(x)=20x^{2}+2x$
$\bigcirc$ $h(x)=-4x^{2}-6x$
$\bigcirc$ $h(x)=-4x^{2}-6x+6$
$\bigcirc$ $h(x)=-4x^{2}+2x$

Explanation:

Step1: Substitute functions into $h(x)$

$h(x) = (8x^2 - 2x + 3) - (12x^2 + 4x - 3)$

Step2: Distribute the negative sign

$h(x) = 8x^2 - 2x + 3 - 12x^2 - 4x + 3$

Step3: Combine like $x^2$ terms

$h(x) = (8x^2 - 12x^2) - 2x - 4x + 3 + 3 = -4x^2 - 2x - 4x + 3 + 3$

Step4: Combine like $x$ terms

$h(x) = -4x^2 + (-2x - 4x) + 3 + 3 = -4x^2 - 6x + 3 + 3$

Step5: Combine constant terms

$h(x) = -4x^2 - 6x + 6$

Answer:

C. $h(x) = -4x^2 - 6x + 6$