How do I factorise x^2 + 8x + 15?

Factorising is the process of putting brackets into an equation. Ideally the end equation should be as simple as possible, with the smallest numbers possible.

The first step is to find the factor pairs of the final number (15) which add or subract together to make the number before the single x in the middle. So in this case we need to find factors of 15 which add up to 8. The two factor pairs of 15 are 1 and 15, and 3 and 5. 3 and 5 add up to make 8, so we'll take those to the next step.

The next thing we do is rewrite the equation to include our 3 and our 5. Keep the x^2 and the number on the end the same, but 8x can be written as 3x + 5x. This gives us a new equation - x^2 +3x +5x + 15. This new equation can now be factorised.

Factorise the first two terms, by taking out the common factor. In this case, the common factor is x, so the first two terms are factorised to x(x+3). Do the same for the second two terms. With these, x is not a common factor but 5 is, so take this out, so you get 5(x+3).

Now combine the two halves of the equation to get: x(x+3) + 5(x+3)

(x+3) is a common factor, so that will form one of our final brackets. The other bracket is made of the two terms outside the bracket, so it will be (x+5). This gives us a final answer of (x+3)(x+5).

Chloe B. GCSE Maths tutor, GCSE Biology tutor, GCSE Chemistry tutor, ...

2 years ago

Answered by Chloe, who has applied to tutor GCSE Maths with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£22 /hr

Haider M.

Degree: Medicine (Bachelors) - Exeter University

Subjects offered:Maths, Physics+ 7 more

Extended Project Qualification
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“A bit about me I am currently in my 2nd year of medical school at the University of Exeter. I really enjoy learning about science, especially the science of health disease, and would love nothing more than to pass down this knowledge ...”

£20 /hr

Sam F.

Degree: Economics with Placement (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Extended Project Qualification

“Studying for BSc Hons Economics, A level economics, maths and physics. Able to tutor GCSE/AS/A2 Economics, Maths and GCSE physics! ”

£24 /hr

Sohini C.

Degree: Medicine,MBBCh (Bachelors) - Cardiff University

Subjects offered:Maths, Science+ 3 more

-Personal Statements-
-Medical School Preparation-

“Hi, I'm Sohini. I'm a fourth year medical student at Cardiff uni and keen to help students with Science and Maths GCSE subjects. I can also help with medical school applications, especially personal statements and interviews. ”

About the author

£18 /hr

Chloe B.

Degree: Veterinary Science (Bachelors) - Bristol University

Subjects offered:Maths, Chemistry+ 1 more


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

The Curve C has the equation 2x^2-11+13. The point Q lies on C such that the gradient of the normal to C at Q is -1/9. Find the x-co-ordinate of Q

Where does the quadratic equation come from?

Solve the equation x^2-9x+20=0

Simplify and solve the following equation: x^2 -8x +15=0

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss