CAIE A-Level Mathematics A2 3.1.2 Polynomial Division Questions
Practise polynomial division, quotient and remainder calculations within the AS mathematics syllabus.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- divide polynomials by linear or quadratic factors
- identify quotient and remainder terms
- use polynomial division results in integration and algebraic problems
CAIE A-Level Mathematics A2 3.1.2 Polynomial Division Questions question 1
[Maximum number: 3]
Find the quotient and the remainder when 3x4−2x2 is divided by x+1.
Commence division and reach partial quotient of the form 3 x^3 +/- 3 x^2
or 3 x^4-2 x^2 (x+1)(A x^3+B x^2+C x+D)+E x+F, and reach A=3 and B= +/- 3
May be seen in synthetic division.
Obtain quotient 3 x^3-3 x^2+x-1 Do not ISW
Don't need to state which is the quotient and which
is remainder. However, if clearly muddled, then
M1A1A0 for both expressions correct.
Obtain remainder of 1
Do not ISW.
Marking guidance:
Allow e.g. 3 x^3-3 x^2+x-1+1/x+1 but NOT
remainder =1/x+1.
Alternative Method for Question 2
f(-1)=3-2=1= remainder
Do not ISW.
Use division or inspection or compare coefficients
3 x^4-2 x^2-1 (x+1)(3 x^3-3 x^2+x-1)
Obtain quotient 3 x^3-3 x^2+x-1
Do not ISW.
Allow e.g. 3 x^3-3 x^2+x-1+1/x+1 but NOT
remainder =1/x+1.
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