f(x)= 2x^3 -7x^2 + 2x +3. Given that (x-3) is a factor of f(x), express f(x) in a fully factorised form.

We will mainly be using a whiteboard but here are some notes:Is (x-3) is a factor of f(x), then if x=3, f(x) =0. I.e. x=3 is a solution too. If we know x =3 is a solution we can solve the other 2 roots by dividing f(x) by 3.
f(x) dividing by x-3 we get 2x^2 -1x-1 So we have to make that equal to 0. And use trial and error.So for e.g. if x=1 then we get 2x^2 -1x-1 =0. So x=1 is a solution.
Now to find the last solution, divide 2x^2-1x-1 by x-1. We get 2x+1. Making 2x+1 =0 we get x=-0.5
Therefore, x=3,x=1,x=-0.5Hence solution is (x-3), (2x+1), (x-1)

Answered by Rumana R. Maths tutor

3871 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you solve trigonometric equations?


Find the integral between 1 and -2 for (4-x^2-3x^3)


If a particle of mass m is launched vertically upwards from the ground with velocity u m/s, how long will it take to return to the ground in terms of m, u and g?


How can the y=sin(x) graph be manipulated?


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