x^2 + 15x + 36
(x + 12)(x + 3)
The expression x^2 + 15x + 36 can be factored as (x+3)(x+12).
To see why, you can use the factoring technique known as guess and check. Here’s how it works:
Look at the constant term, which is 36. This means that the factors must have a product of 36.
Look for two numbers whose product is 36 and whose sum is the coefficient of x, which is 15. These numbers are 3 and 12 (because 3*12=36 and 3+12=15).
Write the expression as x^2 + 3x + 12x + 36, grouping the first two terms and the last two terms: (x^2 + 3x) + (12x + 36).
Factor out the greatest common factor from each group: x(x+3) + 12(x+3).
Combine the terms with a common factor: (x+3)(x+12).
So we have the expression x^2 + 15x + 36 = (x+3)(x+12).
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