Question

which of the following best describes the relationship between (x+1) and the polynomial -3x^3-2x^2+1 a) (x+1) is a factor b) (x+1) is not a factor c) it is impossible to tell whether (x+1) is a factor

Answer 1

Hello,

3x^3+2x²-1=(x-1)(3x²-x+1)+2
remainder is 2
(x+1) is not a factor of 3x^3+2x²-1 nor of -(3x^3+2x²-1)= -3x²-2x²+1.

Answer B

Answer 2

I will solve this problem by factor theorem.

If , (x+1) is a factor of the polynomial ,
`f(x)=-3 x^3-2 x^2 +1` then ,if we substitute,x= -1 in f(x), then, f(-1)=0.

Now,

`f(-1)= -3* (-1)^3-2 * (-1)^2+1\\\\ f(-1)=-3 * (-1)-2 * 1+1\\\\ f(-1)=3 -2+1\\\\ f(-1)=2`

As, f(-1)≠ 0

Option B: (x+1) is not a factor of the polynomial ,
`f(x)=-3 x^3-2 x^2 +1`.