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) = $x^2$ -3x + 2

Answer 1

g(x) = $x^2$ -3x + 2

=$x^2$-x-2x+2

=x(x-1)-2(x-1)

=(x-1)(x-2)

If x -1 = 0, then x = 1

$\therefore f\left(1\right)=(1{)}^3-6(1{)}^2+11\left(1\right)-6$

=1-6+11-6=12-12=0

$\therefore$ Remainder is zero

$\therefore$ x - 1 is a factor of f(x)

and if x - 2 = 0, then x = 2

$\therefore f\left(2\right)=(2{)}^3-6(2{)}^2+11\left(2\right)-6$

=8-24+22-6=30-30=0

$\therefore$ Remainder k= 0

$\therefore$ x - 2 is also a factor of f(x)