x^3 + 2x^2 - 9x - 18 = (x^2 - a^2)(x + b) where a,b are integers. Work out the three linear factors of x^3 + 2x^2 - 9x - 18. (Note: x^3 indicates x cubed and x^2 indicates x squared).

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x+ 2x- 9x - 18. However it is very difficult to approach the problem like this. fortunately the question has given us that the cubic expression factorises to(x2-a2)(x+b). If we expand this back out we get x+ bx- a2x - a2b. We can then compare this cubic to our original and see that a2 = 9 and b = 2.

So we now have x3+2x2-9x-18 = (x2-9)(x+2). We know that we can factorise x2-9 to (x+3)(x-3) so our linear factorisation of the original cubic is (x+3)(x-3)(x+2).

Related Further Mathematics GCSE answers

All answers ▸

A curve has equation y = x^2 - 7x. P is a point on the curve, and the tangent to the curve at P has gradient 1. Work out the coordinates of P.


Why does the discriminant b^2-4ac determine the number of roots of the quadratic equation ax^2+bx+c=0?


find the stationary point of the curve for the equation y=x^2 + 3x + 4


How do I determine if a stationary point on a curve is the maximum or minimum?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences