Question

Use the remainder theorem to determine whether x + 2 is a factor of
f(x) = 3x3 - 2x2 - 6x - 2

Answer 1

Use synthetic division
So the answer is 3x^2-8x+10-22/x+2

Sorry for bad writing I’m in a car

Answer 2

(x + 2) is not a factor of f(x).

Explanation:

The given function is

`f(x)=3x^3-2x^2-6x-2`

Remainder theorem: If a polynomial P(x) is divided by (x-c), then the remainder is defined by f(c).

If x + 2 is a factor of f(x), then the remainder is 0 when we divide the polynomial by (x+2).

`(x+2)=(x-c)`

On comparing both sides we get

`c=-2`

If f(-2) is 0, then by remainder theorem (x+2) is a factor of f(x).

Substitute x=-2 in the given polynomial.

`f(-2)=3(-2)^3-2(-2)^2-6(-2)-2`

`f(-2)=3(-8)-2(4)+12-2`

`f(-2)=-24-8+12-2`

`f(-2)=-22\\eq 0`

Therefore, (x + 2) is not a factor of f(x).