Question

If c(x) = 4x-2 and d(x) = x^2 + 5x is is (c•d) (x)

Answer 1

Answer: (c * d)(x) = 4x^3 + 18x^2 - 10x

Work Shown:

I'm assuming the dot means multiplication. If so, then,

(c * d)(x) = c(x)*d(x)

(c * d)(x) = [ c(x) ] * [ d(x) ]

(c * d)(x) = (4x-2)(x^2+5x) .... substitution

(c * d)(x) = 4x(x^2+5x) - 2(x^2+5x) ... distribute

(c * d)(x) = 4x(x^2)+4x(5x) - 2(x^2)-2(5x) ... distribute again

(c * d)(x) = 4x^3 + 20x^2 - 2x^2 - 10x

(c * d)(x) = 4x^3 + 18x^2 - 10x