Final answer:
The number that completes the factorization of the quadratic expression x² + 8x + 7 is 7, resulting in the factors (x + 1)(x + 7).
Step-by-step explanation:
The student is trying to find the missing number that completes the factorization of the quadratic expression x² + 8x + 7. To factorize the given quadratic expression into the form (x + a)(x + b), where a and b are numbers, we need to find two numbers that multiply to the constant term (here 7) and add up to the linear coefficient (here 8). By inspecting the factors of 7, we can conclude that the two numbers we are looking for are 7 and 1 since 7 * 1 = 7 and 7 + 1 = 8. Therefore, the complete factorization of the quadratic expression is (x + 1)(x + 7).