Question

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

Answer 1

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

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)`