Question

Given that f(x) = 3x^2 + 2x, find f(x + h)
I know how to multiply multi-term polynomials but I'm not sure what are the steps to take with this function.
Can someone please solve it step by step so I know what I'm getting wrong :( thank you.

Answer 1

\[f(x+h)=3(x+h)^2+2(x+h)\]

Answer 2

So with f(x) defined, and you have f(x+h), you plug (x+h) for the FUNCTION X

f(x+h) = 3(x+h)^2 + 2(x+h)
= 3(x^2+2xh+h^2) + 2x + 2h
= 3x^2 + 6xh + 3h^2 + 2x + 2h

Answer 3

Yes but how do you get 2xh term on the second line?

Answer 4

because what i get is 3(x^2 + h^2) and I know im doing it wrong but I dont understand it T-T

Answer 5

\[(a+b)^2=a^2+2ab+b^2 \]
\[(a+b)^2=(a+b)(a+b)=a(a+b)+b(a+b)=a^2+ab+ba+b^2\]
\[=a^2+ab+ab+b^2=a^2+2ab+b^2\]

Answer 6

Ohh I get it thanks.