Answer:
[tex](p - q)(x) = (x -1) (x - 4)[/tex]
Step-by-step explanation:
Given
[tex]p(x) = x^2 - 1[/tex]
[tex]q(x) = 5(x - 1)[/tex]
Required
(p - q)(x)
This is represented as:
[tex](p - q)(x) = p(x) - q(x)[/tex]
[tex](p - q)(x) = x^2 - 1 - 5(x - 1)[/tex]
[tex](p - q)(x) = x^2 - 1 - 5x + 5[/tex]
Collec like terms
[tex](p - q)(x) = x^2 - 5x + 5 - 1[/tex]
[tex](p - q)(x) = x^2 - 5x + 4[/tex]
Expand
[tex](p - q)(x) = x^2 -4x - x + 4[/tex]
Factorize
[tex](p - q)(x) = x(x -4) - 1(x - 4)[/tex]
[tex](p - q)(x) = (x -1) (x - 4)[/tex]
