Theory question 104
PolynomialsWhen f(x) = 2x3 + mx2 + nx + 11 is divided by x2 + 5x + 1, the quotient is 2x − 5 and the remainder is 30x + 16. Find the values of m and n.
Show the model answer
Model answer
f(x) = (x² + 5x + 1)(2x − 5) + 30x + 16 = 2x³ + 5x² − 23x − 5 + 30x + 16 = 2x³ + 5x² + 7x + 11.
m = 5, n = 7.
Explanation
Dividend = divisor × quotient + remainder.