x²+12x+35
(x+7)(x+5)
To factor the quadratic polynomial x²+12x+35, we need to find two numbers that multiply to 35 and add to 12. The factors of 35 are 1, 5, 7, and 35. To get the sum of 12, we can choose 5 and 7.
Therefore, we can write x²+12x+35 as (x+5)(x+7). This is the factored form of the quadratic polynomial.
We can check that this is correct by using the distributive property:
(x+5)(x+7) = x(x+7) + 5(x+7) = x² + 7x + 5x + 35 = x²+12x+35.
So, (x+5)(x+7) is the correct factorization of x²+12x+35.
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