Factor x^2 + 4x - 21.

• A. (x + 7)(x - 3)
• B. (x - 7)(x + 3)
• C. (x + 21)(x - 1)
• D. (x + 4)(x - 5)

Answer: (A)

The idea is to factor a quadratic by finding two numbers that multiply to the constant term and add to the coefficient of x. For x^2 + 4x - 21, the constant term is -21 and the x-term coefficient is 4. We look for two numbers that multiply to -21 and add to 4. The pair 7 and -3 fits: 7 × (-3) = -21 and 7 + (-3) = 4.

Rewrite the middle term using these numbers: x^2 + 7x - 3x - 21. Factor by grouping: x(x + 7) - 3(x + 7) = (x + 7)(x - 3). Since order doesn’t matter, this is the same as (x - 3)(x + 7).