# Given #P(x) = 2x^2-x+2# and #Q(x) = 2x-1#, what is #P(Q(x))# ?

##### 2 Answers

#### Explanation:

Note that changing the variable name does not really affect what the polynomial is. So we can write:

#P(t) = 2t^2-t+2#

Then, substituting

#P(Q(x)) = 2(Q(x))^2-Q(x)+2#

#color(white)(P(Q(x))) = 2(2x-1)^2-(2x-1)+2#

#color(white)(P(Q(x))) = 2(4x^2-4x+1)-(2x-1)+2#

#color(white)(P(Q(x))) = (8x^2-8x+2)-(2x-1)+2#

#color(white)(P(Q(x))) = 8x^2-10x+5#

Answer:

#### Explanation:

This is a composition of functions problem. Note that

Therefore, given

We can continue simplifying by noting that

So: