CAIE IGCSE Additional Math 3.1 Use Remainder and Factor Theorems Questions

Practise Cambridge IGCSE Additional Mathematics by using factors and remainders to determine polynomial coefficients, quotients and constants.

Exam points

Apply the factor theorem and remainder theorem to polynomial expressions.
Use known factors, roots and remainders to form equations in unknown coefficients.
Determine polynomial coefficients, quotients or remainders and verify the resulting factor conditions.

[Maximum number: 5]

The polynomial p is such that $\mathrm{p}(x)=x^{3}+a x^{2}+b x-2, \quad$ where a and b are constants.
It is given that:
- x+2 is a factor of p(x)
- when p(x) is divided by x-3 the remainder is 40.

Find the values of a and b.

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CAIE IGCSE Additional Math 3.1 Use Remainder and Factor Theorems Questions question 1