To factor the quadratic expression \( x^2 - 8x - 48 \), we need to find two numbers that multiply to the constant term (-48) and add up to the linear coefficient (-8).
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The numbers that satisfy these conditions are -12 and 4, since:
- \( -12 \times 4 = -48 \)
- \( -12 + 4 = -8 \)
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Now, we can rewrite the quadratic expression using these two numbers: \[ x^2 - 8x - 48 = (x - 12)(x + 4) \]
Thus, the factored form of \( x^2 - 8x - 48 \) is \((x - 12)(x + 4)\).