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Factor x^2 - 4x - 21

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Answer
(x−7)(x+3)\boxed{(x - 7)(x + 3)}

Checking the result by multiplying the factors back out gives x2+3x−7x−21=x2−4x−21x^2 + 3x - 7x - 21 = x^2 - 4x - 21, which matches the original expression.

Problem: Factor the quadratic expression x2−4x−21x^2 - 4x - 21.

Steps

  1. Find two numbers that multiply to −21-21 and add to −4-4
    The numbers are −7 and 3\text{The numbers are } -7 \text{ and } 3
  2. Rewrite the middle term using these two numbers
    x2−7x+3x−21x^2 - 7x + 3x - 21
  3. Factor by grouping
    x(x−7)+3(x−7)x(x - 7) + 3(x - 7)
  4. Factor out the common binomial (x−7)(x - 7)
    (x−7)(x+3)(x - 7)(x + 3)

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