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Edexcel IGCSE Math B 3.D Factor theorem Question Bank

Practise using the factor theorem to test linear factors, find constants, and support full factorisation of cubics.

Syllabus
First assessment 2018
Course
Math B 4MB1

Exam points

  • substitute the root from a linear factor into f(x) and show whether the value is zero
  • use f(a)=0 conditions to find unknown constants before continuing a factorisation
  • link a verified factor to a quadratic factor and factorise the cubic fully

3.D Factor theorem question 1

[Maximum number: 2]

A=(2k2k−9−3kk+1),B=(1−53k).\mathbf A=\begin{pmatrix}2k^2&k-9\\-3k&k+1\end{pmatrix}, \qquad \mathbf B=\begin{pmatrix}1&-5\\3&k\end{pmatrix}.
The determinant of matrix A\mathbf A is equal to the determinant of matrix B\mathbf B.

Given that f(k)=2k3+5k2−28k−15f(k)=2k^3+5k^2-28k-15, use the factor theorem to show that (k+5) is a factor of f(k).

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