when 3x^3 + 2x^2 + ax +b is divided by x-1 the remainder is 5. when divided by 3x-1 the remainder is -1/3. find values of a and b
thanks everyone
Use the remainder theorem:
When a polynomial P(x) is divided by $\displaystyle (\alpha x - \beta)$ the remainder is $\displaystyle P\left( \frac{\beta}{\alpha}\right)$.
Let $\displaystyle P(x) = 3x^3 + 2x^2 + ax + b$. Then:
$\displaystyle P(1) = 5 \Rightarrow 3 + 2 + a + b = 5 \Rightarrow a + b = 0$ .... (1)
$\displaystyle P\left( \frac{1}{3}\right) = - \frac{1}{3} \Rightarrow ....$ .... (2)
Solve equations (1) and (2) simultaneously for a and b.