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CAIE IGCSE Additional Math 3.2 Find Polynomial Factors Questions

Practise Cambridge IGCSE Additional Mathematics by using known factors and roots to construct complete polynomial factorisations.

Syllabus
2028–2030
Course
Additional Mathematics 0606

Exam points

  • Factorise polynomial expressions into linear and quadratic factors.
  • Use known roots, factors and coefficient conditions to identify remaining factors.
  • Write the fully factorised form with correct numerical or integer coefficients.

CAIE IGCSE Additional Math 3.2 Find Polynomial Factors Questions question 1

[Maximum number: 3]

The polynomial p is such that p(x)=3x3−7x2+ax+b\quad \mathrm{p}(x)=3 x^{3}-7 x^{2}+a x+b, where a and b are integers.
It is given that p′(−1)=21\mathrm{p}^{\prime}(-1)=21 and that x-2 is a factor of p(x).

Hence write p(x) as a product of linear factors with integer coefficients.

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