Question

What is the remainder when (3x4 + 2x3 – x2 + 2x – 19) ÷ (x + 2) ?

Answer 1

Do you know the polynomial remainder theorem?

Answer 2

no

Answer 3

If \(p(x)\) is divided by \(x - k\), then the remainder is \(p(k)\).

Answer 4

5

Answer 5

So, if \(f(x)\) is divided by \(x + 2\), then the remainder is \(p(-2)\).

Answer 6

p(x)*

Answer 7

Oh OK

Answer 8

\[p(x) = 3x^4 + 2x^3 - x^2 + 2x - 19 \Longrightarrow p(-2) = 3(-2)^4 + 2(-2)^3 - (-2)^2 + 2(-2) - 19 \]