Question

How do you find the remainder when `1.f(x)=x^3+2x^2-6x+8; x+4`?

Answer 1

The remainder is `0`

Explanation:

The remainder theorem tell us that if we divide a polynomial `f(x)` by a linear factor `(x-a)` then the remainder is `f(a)`

Thus the remainder we seek for:

`f(x) = x^3+2x^2-6x+8`

divided by `(x+4)` is given by:

`f(-4) = (-4)^3+ 2(-4)^2-6(-4)+8`
`\ \ \ \ \ \ \ \ \ \ \ = -64+ 32+24+8`
`\ \ \ \ \ \ \ \ \ \ \ = 0`

And we can conclude that `x+4` is a factor