Question

check whether(x+1) is a factor of the polynomial p(x)= 6x^3+3x^2.

b) what is the first degree polynomial added to p(x) gives a polynomial for which (x^2-1) is a factor?

Answer 1

Using remainder theorem

6x^3 + 3x^2

= 6 ( -1 )^3 + 3 ( -1 )^2

= -6 -3

= - 9

remainder is not equal to 0 so ( x + 1 ) is not a factor of 6x^3 + 3x^2

Answer 2

We are given 6x^3+3x^2
If x+1 is a factor of above polynomial then bye putting x= -1 result will be 0.

so, 6(-1)^3+3(-1)^2= 6*-1+3*1= 3-6= -3≠0
So, x+1 is not a factor of above polynomial