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Answer
\( x^{2}+8x+12 = (x + 2)(x + 6) \)
Solution
To factor the quadratic x² + 8x + 12, we look for two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of x). The numbers 2 and 6 satisfy these conditions since 2 × 6 = 12 and 2 + 6 = 8.
Thus, we factor the expression as:
(x + 2)(x + 6)
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Simplify this solution Bonus Knowledge
To factor the quadratic expression \( x^{2}+8x+12 \), we first look for two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of \( x \)). Those numbers are 2 and 6! So, we can write: \( x^{2}+8x+12 = (x+2)(x+6) \). This shows that the expression factors neatly into the product of two binomials. Perfectly simple, isn't it? Now let’s verify by multiplying the factors back together: \((x+2)(x+6) = x^2 + 6x + 2x + 12 = x^2 + 8x + 12\). The original quadratic is indeed the result!
