Question

How do you use the remainder theorem to find the remainder for the division `(10x^3-11x^2-47x+30)div(x+2)`?

Answer 1

The remainder states that when any polynomial `f(x)` is divided by `x - a`, the remainder is `f(a)`.

So, Letting `f(x) = 10x^3 - 11x^2 - 47x + 30`, we have:

`f(-2) = 10(-2)^3 - 11(-2)^2 - 47(-2) + 30`

`f(-2) = 10(-8) - 11(4) + 94 + 30`

`f(-2) = -80 - 44 + 94 + 30`

`f(-2)= 0`

The remainder is `0`. In other words, `x + 2` is a factor of `10x^3 - 11x^2 - 47x +30`.

Hopefully this helps!

Answer 2

This expression has a remainder of zero.
`(10x^3-11x^2-47x+30)/(x+2)` is equal to `(10x^2-31x+15)`, with no remainder.