18M.1.AHL.TZ1.H_1

pestleMathematicsAAHLPaper 118M· ahl-2-12-factor-and-remainder-theorems-sum-and-product-of-rootssource ↗

Let f(x) = x⁴ + px³ + qx + 5 where p, q are constants.

The remainder when f(x) is divided by (x + 1) is 7, and the remainder when f(x) is divided by (x − 2) is 1. Find the value of p and the value of q.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt to substitute x = −1 or x = 2 or to divide polynomials (M1)

1 − p − q + 5 = 7, 16 + 8p + 2q + 5 = 1 or equivalent A1A1

attempt to solve their two equations M1

p = −3, q = 2 A1

[5 marks]

Examiners’ report

[N/A]