Edexcel IGCSE Math B 3.E Algebraic division Question Bank

Practise dividing cubics by known linear factors, comparing coefficients, and using the quotient to complete factorisation.

Exam points

divide a cubic by a given linear factor to obtain the correct quadratic quotient
compare coefficients in an identity to find constants in a quadratic factor
factorise the quadratic quotient to write the original cubic as linear factors

[Maximum number: 5]

Given that (x-3) is a factor of $5 x^{3}+2 x^{2}+k x+36$ where k is a constant,

Given that, for all values of x,
$5x^3+2x^2-63x+36=(x-3)(ax^2+bx+c),$
where a, b and c are constants,
find the value of a, the value of b and the value of c.

$(x-3)(ax^2+bx+c)=ax^3+(b-3a)x^2+(c-3b)x-3c$
Comparing with $5x^3+2x^2-63x+36$ :
$a=5, \quad -3c=36\Rightarrow c=-12, \quad b-3a=2\Rightarrow b=17.$

Answer: a=5, b=17, c=-12.
Marks: B1, M1, A1, M1 dep, A1.

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3.E Algebraic division question 1