show that (x+1)(x+3)(x+5) can be written in the form ax^3 + bx^2 + cx+ d where a, b,c and d are all positive integers.

x³ + 9x² + 23x + 15

Step-by-step explanation:

Given

(x + 1)(x + 3)(x + 5) ← expand the first pair of factors using FOIL

= (x² + 4x + 3)(x + 5)

Each of the terms in the second factor is multiplied by each of the terms in the first factor, that is

x²(x + 5) + 4x(x + 5) + 3(x + 5) ← distribute the 3 parenthesis

= x³ + 5x² + 4x² + 20x + 3x + 15 ← collect like terms

= x³ + 9x² + 23x + 15 ← in the form ax³ + bx² + cx + d