Factor the quadratic x^2 - 9x + 20.

• A. (x - 3)(x - 6)
• B. (x + 4)(x - 5)
• C. x^2 - 9x + 20
• D. (x - 4)(x - 5)

Answer: (D)

To factor a quadratic with leading coefficient 1, find two integers that multiply to the constant term and add to the coefficient of x. Here the constant is 20 and the middle coefficient is -9, so you want two numbers that multiply to 20 and sum to -9. The numbers -4 and -5 work because (-4) × (-5) = 20 and (-4) + (-5) = -9. Rewriting the middle term with these numbers gives x^2 - 4x - 5x + 20, which factors by grouping: x(x - 4) - 5(x - 4) = (x - 4)(x - 5). So the factorization is (x - 4)(x - 5). Other common attempts don’t fit the constant and middle-term requirements: for example, products that give 18 or signs that give the wrong middle-term coefficient won’t match x^2 - 9x + 20.