CAIE A-Level Mathematics A2 3.1.3 Factor and Remainder Theorems Questions

Practise applying factor and remainder theorems to factorise polynomials and solve equations.

Exam points

apply the factor theorem to identify polynomial factors
use the remainder theorem to determine unknown constants
factorise polynomials completely and solve resulting equations

[Maximum number: 2]

The polynomial $x^{3}+5 x^{2}+31 x+75$ is denoted by p(x).

Show that (x+3) is a factor of p(x).

Substitute x=-3 to obtain value of p(-3)
Obtain p(-3)=0 and hence given result
Alternative method for Question 10(a)

Divide p(x) by ( x+3 ) to obtain quotient $x^{2} \pm 2 x+\ldots$
Obtain quotient $x^{2}+2 x+25$ , with zero remainder and hence given result

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CAIE A-Level Mathematics A2 3.1.3 Factor and Remainder Theorems Questions question 1