Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x)
f(x) = x3−6x2 + 11x - 6, g(x) = x2 -3x + 2
g(x) = x2 -3x + 2
=x2-x-2x+2
=x(x-1)-2(x-1)
=(x-1)(x-2)
If x -1 = 0, then x = 1
∴f(1)=(1)3−6(1)2+11(1)−6
=1-6+11-6=12-12=0
∴ Remainder is zero
∴ x - 1 is a factor of f(x)
and if x - 2 = 0, then x = 2
∴f(2)=(2)3−6(2)2+11(2)−6
=8-24+22-6=30-30=0
∴ Remainder k= 0
∴ x - 2 is also a factor of f(x)