Question

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x).

f(x) = $x^3-6x^2$ + 11x - 6; g(x) = x - 3

Answer 1

We know that if g(x) is a factor of p(x) then the remainder will be zero. Now,

f(x) = $x^3-6x^2$ + 11x - 6; g(x) = x - 3

Let x - 3 = 0, then x = 3

$\therefore$ Remainder = f(3)

$=(3{)}^3-6(3{)}^2+11\times$ 3 - 6

= 27- 54 + 33 - 6

= 60 - 60 = 0

$\therefore$ Remainder is zero,

$\therefore$ x - 3 is a factor of f(x)