Question

if p(x)=x*2-1 and q(x)=5(x-1),which expression is equivalent to (p-q)(x)?

Answer 1

Answer:

$(p - q)(x) = (x -1) (x - 4)$

Step-by-step explanation:

Given

$p(x) = x^2 - 1$

$q(x) = 5(x - 1)$

Required

(p - q)(x)

This is represented as:

$(p - q)(x) = p(x) - q(x)$

$(p - q)(x) = x^2 - 1 - 5(x - 1)$

$(p - q)(x) = x^2 - 1 - 5x + 5$

Collec like terms

$(p - q)(x) = x^2 - 5x + 5 - 1$

$(p - q)(x) = x^2 - 5x + 4$

Expand

$(p - q)(x) = x^2 -4x - x + 4$

Factorize

$(p - q)(x) = x(x -4) - 1(x - 4)$

$(p - q)(x) = (x -1) (x - 4)$