Algebra Practice Test 2025 - Free Algebra Practice Questions and Study Guide.

To determine the correct factorization of the expression \(x^2 + 9x + 20\), we seek two numbers that both add up to 9 (the coefficient of \(x\)) and multiply to 20 (the constant term).

When looking for such pairs, the numbers 4 and 5 meet these criteria because:

- 4 + 5 = 9

- 4 × 5 = 20

Thus, we can express the quadratic \(x^2 + 9x + 20\) as the product of two binomials: \((x + 4)(x + 5)\). This factorization accurately reflects both the sum and product of the original expression's necessary coefficients.

Although there are other combinations presented in the choices, they do not meet the criteria required to yield the original expression when multiplied out. The correct option demonstrates how to derive the original quadratic from its factors by ensuring both addition and multiplication match the coefficients of the expression \(x^2 + 9x + 20\).