# Math Help - Polynomials

1. ## Polynomials

1, Find the values of a and b so that the polynomials x^3 + ax^2 + bx + 6 has x -2 as a factor and leaves a reminder 3 when divided by x-3

2, If ax^3 + bx^2 + x -b has x+2 as a factor and leaves a reminder 4 when divided by x-2 , find the values of a and b

2. ## Re: Polynomials

These are applications of the remainder and factor theorems. If a polynomial \displaystyle \begin{align*} P(x) \end{align*} is divided by \displaystyle \begin{align*} (x - \alpha ) \end{align*}, then the remainder is equal to \displaystyle \begin{align*} P \left( \alpha \right) \end{align*}.