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(2x+5)^2 - 1

= (4x^2 + 20x + 25) - 1

= 4x^2 + 20x + 24

Use 4 [from the first term] and 24 [last term] as the basis for your factors;

4 has 1, 2, 4 as it's factors

24 has 1, 2, 3, 4, 6, 12, 21 as it's factors

Find the most apporpriate one- you can use Synthetic Division or simply "Trial and Error"

You will soon get

(4x + 12) (x + 2) as the factors

But remember; (4x + 12) can still be factored.

Divide it by 4...

(4x + 12) / 4 = (x + 3)

So yor factors are now

4 (x + 3) (x + 2)