Question 3 - A-Level Maths

Exam Board	AQA
Module	C1 (Core Mathematics 1)
Year	2010
Session	June
Topic	Factor & Remainder Theorem
Type	Direct remainder then factorise

3 The polynomial $\mathrm { p } ( x )$ is given by $$\mathrm { p } ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 7 x - 15$$

1. Use the Factor Theorem to show that $x + 3$ is a factor of $\mathrm { p } ( x )$.
2. Express $\mathrm { p } ( x )$ as the product of three linear factors.
Use the Remainder Theorem to find the remainder when $\mathrm { p } ( x )$ is divided by $x - 2$.
1. Verify that $\mathrm { p } ( - 1 ) < \mathrm { p } ( 0 )$.
2. Sketch the curve with equation $y = x ^ { 3 } + 7 x ^ { 2 } + 7 x - 15$, indicating the values where the curve crosses the coordinate axes.