Question

Show that (x - 5) is a factor of (x⁴ - 3x³ - 19x² + 27x + 90).

 

Answer 1

Given polynomial x^4-3x^3-19x^2+27x+90

x = 5

x^4-3x^3-19x^2+27x+90 = (5)^4-3(5)^3-19(5)^2+27(5)+90

= 625-375-475+135+90

= 0

By the factor therom if f(c) = 0 then (x-c) is a factor.

So (x-5) is a factor of x^4-3x^3-19x^2+27x+90.