# Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x), or not:

Question:

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x), or not:

$f(x)=x^{3}-6 x^{2}+11 x-6, g(x)=x-3$

Solution:

Here, $f(x)=x^{3}-6 x^{2}+11 x-6$

g(x) = x - 3

To prove that g(x) is the factor of f(x),

we should show ⟹ f(3) = 0

here, x - 3 = 0

⟹ x = 3

Substitute the value of x in f(x)

$f(3)=3^{3}-6 *(3)^{2}+11(3)-6$

= 27 - (6*9) + 33 - 6

= 27 - 54 + 33 - 6

= 60 - 60

= 0

Since, the result is 0 g(x) is the factor of f(x)