CAIE A-Level Mathematics A2 3.1.2 Polynomial Division Questions

Practise polynomial division, quotient and remainder calculations within the AS mathematics syllabus.

Exam points

divide polynomials by linear or quadratic factors
identify quotient and remainder terms
use polynomial division results in integration and algebraic problems

[Maximum number: 3]

Find the quotient and remainder when $8 x^{3}+4 x^{2}+2 x+7$ is divided by $4 x^{2}+1$ .

Commence division and reach quotient of the form $2 x \pm 1$
Or by inspection $8 x^{3}+4 x^{2}+2 x+7=\left(4 x^{2}+1\right)(2 x \pm 1) +\mathrm{r}$
Or by inspection $8 x^{3}+4 x^{2}+2 x+7=\left(4 x^{2}+1\right)(2 x \pm 1)$
+r

Obtain (quotient) 2 x+1
Obtain (remainder) 6
3

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CAIE A-Level Mathematics A2 3.1.2 Polynomial Division Questions question 1