Question

Simplify (p – 2)(p + 1)(p – 4)

Answer 1

(p – 2)(p + 1)(p – 4) = (p + (– 2))(p + 1)(p + (– 4))

Comparing (p – 2)(p + 1)(p – 4) with (x + a)(x + b)(x + c) we have x = p, a = – 2, b = 1, c = – 4.

(x + a)(x + b)(x + c) = x² + (a + b + c)x² + (ab + bc + ca)x + abc

= p³ + (– 2 + 1 + (– 4))p² + (– 2)(1) + (1)(– 4) + (– 4)(– 2))p + (– 2)(1)(– 4)

= p³ + (– 5)p² + (– 2 + (– 4) + 8)p + 8

= p² – 5p² + 2p + 8