Question

Check whether (x-1) is a factor of the polynomial x3-27x2+8x+18

Answer 1

To check if (x-1) is a factor of the equation, put x=1 as value of x in the above polynomial....putting x = 1
we get,

= x3-27x2+8x+18
= (1)3-27 (1)2+8 (1)+18
= 1-27+8+18
= 0

If we get zero, then
(x-1) IS A factor of the given polynomial...

Answer 2

Let p (x)=x^3-27x^2+8x+18

divided by x-1

By remainder theorem

Remainder =p (a)

=p (1)

=x^3-27x^2+8x+18

=(1)^3-27 (1)^2+8 (1)+18

=1-27+8+18

= -27+27

=0

Remainder is equal to 0.

(x-1)is a factor of p (x).