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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).

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