Show that the cubic function f(x) = x^3 - 7x - 6 has a root x = -1 and hence factorise it fully.

f(-1) = (-1)^3 - (-1)*7 - 6 = -1 + 7 - 6 = 0

Hence f(x) = (x+1)(x^2 + ax - 6)

Expand this out

f(x) = x^3 + ax^2 - 6x + x^2 + ax - 6 

      = x^3 + (a+1)x^2 + (a-6)x -6

By comparing co-efficients

a + 1 = 0

a - 6 = -7

a = -1

Thus 

f(x) = (x + 1)(x^2 - x - 6)

      = (x + 1)(x - 3)(x + 2)

Answered by James B. Maths tutor

3752 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

z = 5 - 3i Find z^2 in a form of a + bi, where a and b are real constants


A curve has equation y = f(x) and passes through the point (4,22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7 use intergration to find f(x).


What is a good method to go about sketching a polynomial?


A function is defined parametrically as x = 4 sin(3t), y = 2 cos(3t). Find and simplify d^2 y/dx^2 in terms of t and y.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences