Question

check whether q(x) is a factor of p(x): p(x)=x^3-6x^2+11x-6, q(x)=x-3

Answer 1

Heya..

I'm here for ur help..

According to factor theorem, if x-a is a factor of p(x) then p(a) = 0..

Let x^3-6x^2+11x-6 be p(x)..

To check x-3 is a factor of p(x) or not..

If it is a factor then p(3) = 0

=) p(3) = 3^3 - 6*3^2 + 11*3 - 6

= 27 - 54 + 33 - 6

= 0

Hence x-3 is a factor of x^3-6x^2+11x-6.

Hope it's helpful to u.

Answer 2

x=3
x^3-6x^2+11x-6=0
(3)^3-6(3)^2+11 (3)-6=0
27-54+33-6=0
27+33-54-6=0
60-60=0
then we conclude that q(x) is a factor of p(x)