Question

factorise the following 25 x2 -9a2 k2​

Answer 1

Answer:

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Question from Geri, a student:

what does x squared plus twenty five factor out to?

Hi Geri,

Let's try x2 - 25 first.

x2 - 25 = x2 - 52 = (x - 5)(x + 5)

I know this because if you multiply (x - 5) by (x + 5) and simplify you get x2 - 25. This means that for any number x, x2 - 25 = (x - 5)(x + 5). For example if x = 12 then

122 - 52 = 144 - 25 = 119 = (12 - 5)(12 + 5) = 7 × 17.

Now what about x2 + 25? If x = 2 for example then x2 + 25 = 4 + 25 = 29 which is a prime number. Thus the only factors of 29 are 29 and 1 and hence the only factorization of 29 is 29 × 1. Similarly if x = 4 then x2 + 25 = 41 which is again prime. Hence the only factorization of x2 + 25 which is valid for every number x is

x2 + 25 = (x2 + 25) × 1

This is certainly not what you are looking for and thus we say x2 + 25 doesn't factor.