Moderate -0.5 This is a straightforward polynomial long division question requiring a standard algorithm with no conceptual complications. The divisor is simple (quadratic with no x term), making the arithmetic manageable. It's slightly easier than average because it's purely procedural with clear steps, though it requires careful execution to avoid arithmetic errors.
\(2x\) seen in quotient and \(4x^3 + 2x\) seen in division
B1
If B0M0, B2 for quotient is \(2x + 4\) or remainder is \(-7x + 8\); B3 for both
\(8x^2 + kx\) [+12] seen in division
M1
NB \(k = -7\)
\(2x + 4\) seen and \(-7x + 8\) seen
A1
ignore wrong labelling
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2x$ seen in quotient and $4x^3 + 2x$ seen in division | B1 | If B0M0, B2 for quotient is $2x + 4$ or remainder is $-7x + 8$; B3 for both |
| $8x^2 + kx$ [+12] seen in division | M1 | NB $k = -7$ |
| $2x + 4$ seen and $-7x + 8$ seen | A1 | ignore wrong labelling |
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1 Find the quotient and the remainder when $4 x ^ { 3 } + 8 x ^ { 2 } - 5 x + 12$ is divided by $2 x ^ { 2 } + 1$.
\hfill \mbox{\textit{OCR C4 2016 Q1 [3]}}