Using the factor theorem, factorise x^4 - 3x^3 - 3x^2 + 11x - 6

Well the question states that it wants you to use the factor theorem so it would be a good idea to write down the factor theorem to remind ourselves."A polynomial f(x) has a factor (x - a) if and only if f(a) = 0" There's no exact science behind this next part, we just start guessing at factors:f(-1) = (-1)^4 - 3(-1)^3 - 3(-1)^2 + 11(-1) - 6 = -16f(1) = 1^4 - 31^3 - 31^2 + 11 -6 = 0, thus (x - 1) is a factor(x - 1)( _ _ _ _ _ ) = (x^4 - 3x^3 - 3x^2 + 11x - 6)[Here I'll give an example of using the grid multiply two numbers and then I'll show how it can be used to find the missing polynomial in this equation but it is impossible to type the method in this box but I'll do it on the whiteboard during the interview :) ](x - 1)(x^3 - 2x^2 - 5x + 6)Once you're confident with the grid method you can try to do it without using the grid(x - 1)(x + 2)(x^2 - 4x +3)(x - 1)(x + 2)(x - 1)(x - 3)(x + 2)(x - 3)(x - 1)^2

KG
Answered by Kester G. Maths tutor

3780 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the integral of 3x-x^(3/2)


Given ∫4x^3+4e^2x+k intergrated between the bounds of 3 and 0 equals 2(46+e^6). Find k.


What is the chain rule?


Find the value of cot(π/3)


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