To factor the quadratic expression \(x^2 + 12x + 35\), we need to find two numbers that multiply to 35 (the constant term) and add to 12 (the coefficient of the linear term).
The two numbers that satisfy these conditions are 5 and 7, since:
- \(5 \times 7 = 35\)
- \(5 + 7 = 12\)
Therefore, the factored form of the expression is:
\[ (x + 5)(x + 7) \]
So, \(x^2 + 12x + 35\) factors to \((x + 5)(x + 7)\).
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