To solve x² - 8x + 15 = 0 we could try to use the Product, Sum, Numbers method (PSN).

The PSN method tells us that our numbers must multply to make the product of the first and last term, in this case 15. It also tells us that they must sum to the middle term, which is -8.

By thinking through all the factors of 15 (including negatives), we can work out which pair works:

15= 1 x 15, 3 x 5, -1 x -15 and -3 x -5

Of all these pairs, only the final pair add together to make -8, therefore these must be our two values of x.

We can then subsitute them in to say that:

x²- 3x + (-5x +15) = 0

Then we take the biggest factor out of both the first half and the second half:

x(x-3) -5(x-3) = 0

Which shows us that x² - 8x + 15 = (x-3) (x-5)

So it can only be equal to zero when x = 3 or when x = 5

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