Question

What is the remainder when (x3 − 4x2 − 12x + 9) is divided by (x + 2)

Answer 1

Hello,

x^3-4x²-12x+9=x^3+2x²-6x²-12x+9
=x²(x+2)-6x(x+2)+9
=(x+2)(x²-6x)+9

Remainder is 9

Answer 2

9

Explanation:

This is a straightforward application of the Remainder Theorem, which states that any polynomial
`p(x)` , when divided by a linear factor
`(x-a)` will have a remainder equal to evaluating the function
`p(x)` at
`x=a`

To find the remainder of
`x^(3)-4x^(2)-12x+9` when divided by
`(x+2)` , we have to evaluate the polynomial at
`x=-2`

Let's do it.

`(-2)^(3)-4(-2)^(2)-12(-2)+9\\=9`

Hence, 9 is the remainder.