How do you factorise a quadratic equation where the coefficient of x^2 isn't 1?

For this, we need to use the formula ax2+bx+c. Multiply the coefficient of a from your equation with the value of c. This gives you a value from which you need to find 2 factors of this value which also add together to give you the value of coefficient b. Rewrite your equation, with these 2 numbers as the new coefficients of b, splitting that x term into 2. Now, we split this new equation in half (I call this the wiggle method). Factorise fully the first half of the equation, and then repeat this on the other half. You should find that what's left in each bracket matches on either side of the equation (e.g. x(2x-1)+5(2x-1)). So one of our brackets in the final answer must be (2x-1), and we gain our second bracket by bringing together the coefficient of each bracket: (x+5). Therefore, our final answer will be (2x-1)(x+5), and if you expanded this, you should achieve the original equation in the question!It's important to remember here that not every equation can be factorised in this way, meaning we would use the quadratic formula to solve.

RG
Answered by Rosie G. Maths tutor

5592 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

15 machines work at the same rate. Together, the 15 machines can complete an order in 8 hours. 3 of the machines break down after working for 6 hours. The other machines carry on working until the order is complete. In total, how many hours does EACH


Prove that the square of an odd number is always 1 more than a multiple of 4


Anne picks a 4-digit number. The first digit is not zero. The 4-digit number is a multiple of 5. How many different 4-digit numbers could she pick?


What are the two roots for the equation x^2 + 7x + 10 = 0


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning