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).

CB
Answered by Chris B. Further Mathematics tutor

3888 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

The equation 3x^2 – 5x + 4 = 0 has roots P and Q, find a quadratic equation with the roots (P + 1/2Q) and (Q + 1/2P)


The line y = 3x-4 intersects the curve y = x^2 - a, where a is an unknown constant number. Find all possible values of a.


l1 and l2 are tangents of a circle. l1 intersects the circle at (3-√3,5) with a gradient of √3, and l2 intersects the circle at (3+√2,4+√2) with a gradient of -1. Find the centre of the circle, and hence find the radius of the circle.


A circle has equation x^{2}-8x+y^{2}-6y=d. A line is tangent to this circle and passes through points A and B, (0,17) and (17,0) respectively. Find the radius of the circle.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences