Skip to content

Course home

Sign up

Algebraic Methods

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157
Question 77

f(x)=9x3−6x2−32x+32f(x) = 9x^3 - 6x^2 - 32x + 32f(x)=9x3−6x2−32x+32

a.

Use the factor theorem to show that (x+2)(x + 2)(x+2) is a factor of f(x)f(x)f(x).

[2]
b.

Use algebraic division to show that f(x)=(x+2)(9x2−24x+16)f(x) = (x + 2)(9x^2 - 24x + 16)f(x)=(x+2)(9x2−24x+16).

[2]
c.

Hence, show that f(x)f(x)f(x) can be written in the form f(x)=(x+2)(ax+b)2f(x) = (x + 2)(ax + b)^2f(x)=(x+2)(ax+b)2, where a a\,a and b b\,b are integers to be found.

[2]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank