Question 1 - A-Level Maths

Exam Board	SPS
Module	SPS SM Pure (SPS SM Pure)
Year	2023
Session	February
Topic	Factor & Remainder Theorem
Type	Standard verify, factorise, solve

1. $$f ( x ) = x ^ { 3 } + x ^ { 2 } - 12 x - 18$$

Use the factor theorem to show that $( x + 3 )$ is a factor of $f ( x )$.
(2)
Factorise $f ( x )$ to a linear and quadratic factor.
(2)
Hence find exact values for all the solutions of the equation $\mathrm { f } ( x ) = 0$
(3)