OCR MEI C1 — Question 7 5 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFactor & Remainder Theorem
TypeFully specified polynomial: verify factor and solve
DifficultyModerate -0.8 This is a straightforward application of the factor theorem requiring students to verify f(2)=0, then perform polynomial division to find the quadratic factor, and finally solve by factoring or using the quadratic formula. It's a standard C1 textbook exercise with clear steps and no novel insight required, making it easier than average.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

7 Show that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 4 x + 4\).
Hence solve the equation \(x ^ { 3 } - x ^ { 2 } - 4 x + 4 = 0\).

Question 7:
AnswerMarks
\(f(2)=8-4-8+4=0 \Rightarrow (x-2)\) is a factorB1
\(f(x)=x^3-x^2-4x+4\)M1
\(=(x-2)(x^2+x-2)\)A1
\(=(x-2)(x+2)(x-1)\)A1
\(\Rightarrow f(x)=0 \Rightarrow x=1,2,-2\)B1
Total: 5
## Question 7:
$f(2)=8-4-8+4=0 \Rightarrow (x-2)$ is a factor | B1 |
$f(x)=x^3-x^2-4x+4$ | M1 |
$=(x-2)(x^2+x-2)$ | A1 |
$=(x-2)(x+2)(x-1)$ | A1 |
$\Rightarrow f(x)=0 \Rightarrow x=1,2,-2$ | B1 |
**Total: 5**

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7 Show that ( $x - 2$ ) is a factor of $\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 4 x + 4$.\\
Hence solve the equation $x ^ { 3 } - x ^ { 2 } - 4 x + 4 = 0$.

\hfill \mbox{\textit{OCR MEI C1  Q7 [5]}}