Which of the following is a correct factorization of 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)

When factoring a quadratic with leading coefficient 1, look for two numbers that multiply to the constant term and add to the coefficient of x. Here that constant term is -21 and the coefficient of x is 4, so we need two numbers whose product is -21 and whose sum is 4. The pair -3 and 7 fits: (-3) × 7 = -21 and (-3) + 7 = 4. So the quadratic factors as (x - 3)(x + 7). Since multiplication is commutative, (x + 7)(x - 3) is the same factorization.

The other options don’t match because they would expand to different linear sums or different constant terms: for example, (x - 7)(x + 3) has a sum of -4 and expands to x^2 - 4x - 21; (x + 21)(x - 1) expands to x^2 + 20x - 21; (x + 4)(x - 5) expands to x^2 - x - 20.