| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Single polynomial, two remainder/factor conditions |
| Difficulty | Moderate -0.8 This is a straightforward application of the remainder theorem and factor theorem with simultaneous equations. Part (a) requires simple substitution of x=1, and part (b) adds one more equation from x=-2, then solving two linear equations in two unknowns. The techniques are standard C2 content with no conceptual challenges or multi-step reasoning required. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
f(x) = ax³ + bx² - 7x + 14, where a and b are constants.
Given that when f(x) is divided by (x - 1) the remainder is 9.
(a) write down an equation connecting a and b. [2 marks]
Given also that (x + 2) is a factor of f(x),
(b) find the values of a and b. [4 marks]
\hfill \mbox{\textit{Edexcel C2 Q1 [6]}}