Question

value: 4
find f(x) - g(x)
f(x) = -8x³ + 8x - 1
g(x) = 2x³ + 6x + 7
a. -10x³ + 2x - 8
b. -10x³ + 2x - 14
c. -3x³ + 2x - 6
d. -3x³ + 2x - 14

Explanation:

Step1: Substitute functions into expression

$f(x)-g(x) = (-8x^3 + 8x - 1) - (2x^3 + 6x + 7)$

Step2: Distribute the negative sign

$f(x)-g(x) = -8x^3 + 8x - 1 - 2x^3 - 6x - 7$

Step3: Combine like $x^3$ terms

$f(x)-g(x) = (-8x^3 - 2x^3) + 8x - 1 - 6x - 7 = -10x^3 + 8x - 1 - 6x - 7$

Step4: Combine like $x$ terms

$f(x)-g(x) = -10x^3 + (8x - 6x) - 1 - 7 = -10x^3 + 2x - 1 - 7$

Step5: Combine constant terms

$f(x)-g(x) = -10x^3 + 2x + (-1 - 7) = -10x^3 + 2x - 8$

Answer:

a. $-10x^3 + 2x - 8$