The polynomial P(x)=x2+ax +b has a zero at x =2. When P(x)is divided by x +1, the remainder is 18.Find the values of a and b.
with working out please
You have $\displaystyle P(x) = x^2 + ax + b$.
By the Remainder and Factor Theorems:
If there is a root at $\displaystyle x = 2$, then $\displaystyle P(2) = 0$.
If, when you divide by $\displaystyle x + 1$ you get a remainder of $\displaystyle 18$, then $\displaystyle P(-1) = 18$.
So you have:
$\displaystyle 2^2 + 2a + b = 0$
$\displaystyle (-1)^2 - a + b = 18$.
Simplify and solve these equations simultaneously for $\displaystyle a$ and $\displaystyle b$.