Theory question 101
PolynomialsThe polynomial f(x) = 2x3 + px2 + qx − 5 has (x − 1) as a factor and a remainder of 27 when divided by (x + 2), where p and q are constants. Find the values of p and q.
Show the model answer
Model answer
f(1) = 0: 2 + p + q − 5 = 0, so p + q = 3.
f(−2) = 27: −16 + 4p − 2q − 5 = 27, so 2p − q = 24.
Adding: 3p = 27, p = 9 and q = −6.
Explanation
Use the factor theorem and remainder theorem to get two equations.