Question

two functions are defined as shown.
$q(x) = 8x - 10$
$p(x)=-3x^{2}-10x-14$
what is $q(x)-p(x)$?

Explanation:

Step1: Substitute the functions

$q(x)-p(x) = (8x - 10) - (-3x^2 - 10x - 14)$

Step2: Distribute the negative sign

$q(x)-p(x) = 8x - 10 + 3x^2 + 10x + 14$

Step3: Combine like terms

$q(x)-p(x) = 3x^2 + (8x + 10x) + (-10 + 14)$

Step4: Simplify the expression

$q(x)-p(x) = 3x^2 + 18x + 4$

Answer:

$3x^2 + 18x + 4$