Find and simplify f (x + h).
-$$f ( x ) = x ^ { 3 } - 5 x + 8$$
A) $x ^ { 3 } + 3 x ^ { 2 } h + 3 x h ^ { 2 } + h ^ { 3 } - 5 x - 5 h + 8$
B) $x ^ { 3 } - 5 x + h + 8$
C) $x ^ { 3 } + h ^ { 3 } - 5 x - 5 h + 8$
D) $x ^ { 3 } - 5 x - 5 h + 8$

Question

Quizplus · Accepted Answer

To find $f(x + h)$, substitute $x + h$ for every $x$ in the original function $f(x) = x^3 - 5x + 8$. This gives $(x + h)^3 - 5(x + h) + 8$. Expanding $(x + h)^3$ gives $x^3 + 3x^2h + 3xh^2 + h^3$, and distributing $-5$ gives $-5x - 5h$. Adding $8$ at the end, the complete expression is $x^3 + 3x^2h + 3xh^2 + h^3 - 5x - 5h + 8$.

Find and Simplify F (X + H) f(x)=x3−5x+8f ( x ) = x ^ { 3 } - 5 x + 8f(x)=x3−5x+8

Find and Simplify F (X + H) $f ( x ) = x ^ { 3 } - 5 x + 8$