How to factorise a quadratic with a coefficient of x^2 greater than one, for example 4x2+4x-15?

Firstly, label each coefficient: coefficient in front of x2 “a”, is equal to 4. “b” is the coefficient in front of x is equal to +4 “c” is equal to -15

The procedure for factorising starts with working out the grouping values: We want two numbers that multiply to get, “a” * ”c”= 4*-15 = -60 And adds to equal “b” = 4

Try combinations of numbers that multiply to get -60 and add to get 4. Try -15 and 4: -154 equals -60, however adds to get -11, so not the combination Try 10 and -6: 10-6 equals -60 and adds to get a difference of 4, so is the combination.

Now we split the middle of term of the quadratic, using the combination: 4x can be rewritten as 10x-6x, therefore 4x2+10x -6x-15

Now group the terms and factorise The first group is the first part of the quadratic: 4x2+10x, this can be factorised into 2x(2x+5) The second group is -6x-15, this can be factorised into -3(2x+5) So 4x2+10x -6x-15 can written as: 2x(2x+5)-3(2x+5). You can see 2x+5 is common, so you can factorise that out, hence you are left with the answer: (2x+5)(2x-3)

Answered by Bhavin S. Maths tutor

7365 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The value of a new car is £18,000. The value of the car decreases by 25% in the first year and 12% in each of the next 4 years. Work out the value of the car after 5 years?


How do you find the mean of a grouped frequency table?


Naoby invests £6000 for 5 years. The investment gets compound interest of x% per annum. At the end of 5 years the investment is worth £8029.35 Work out the value of x.


Prove that (2n+3)^2-(2n-3)^2 is a multiple of 8 for positive integer values of n


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