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

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