Question

If p(x)= 2x^2 -4x and q(c) = x-3, what is (p•q)(x)

Answer 1

2x^3 - 10x^2 +12x

Explanation:

p(x)= 2x^2 -4x

q(x) = x-3

(p•q)(x) = (2x^2 -4x) * ( x-3)

FOIL

first 2x^2 *x = 2x^3

outer 2x^2 *-3 = -6x^2

inner -4x *x = -4x^2

last -4x*-3 = 12x

Add together

2x^3 -6x^2 -4x^2 +12x

Combine like terms

2x^3 - 10x^2 +12x

Answer 2

(p•q)(x) = 2x² - 16x + 30

Explanation:

p(x) =2x² - 4x

q(x) = x - 3

In order to find (p•q)(x) substitute q(x) into p(x) that's replace every x in p(x) by q(x)

That's

(p•q)(x) = 2( x - 3)² - 4( x - 3)

Expand the terms

That's

(p•q)(x) = 2( x² - 6x + 9) - 4x + 12

= 2x² - 12x + 18 - 4x + 12

Group like terms

(p•q)(x) = 2x² - 12x - 4x + 18 + 12

Simplify

We have the final answer as

(p•q)(x) = 2x² - 16x + 30

Hope this helps you