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:

$3x^2 + 18x + 4$