Question

Jamie was given the problem, "Find the result when the factors of \(x^2 + 15x + 44\) are multiplied together." Before she could answer, her sister, Lauren, said, "I know the answer without factoring or multiplying!" What was Lauren's answer and how did she know? (you may solve first and then work backward to explain).

a) Lauren's answer was 44, and she knew because she guessed.
b) Lauren's answer was (x + 11)(x + 4), and she knew because she factored the expression.
c) Lauren's answer was 15, and she knew because she added the coefficients of the terms.
d) Lauren's answer was 0, and she knew because she set the expression equal to zero and solved for (x).

Answer 1

Lauren's answer was (x + 11)(x + 4), and she knew because she factored the expression.

The answer is option ⇒b

Explanation:

To find Lauren's answer, let's first factor the quadratic expression \(x^2 + 15x + 44\). We need to find two binomial factors that, when multiplied together, will give us the original expression.

To factor the expression, we can look for two numbers that multiply to give 44 and add up to 15, which are 11 and 4. Therefore, we can write the factored form as (x + 11)(x + 4).

Lauren knew the answer because she factored the expression by identifying the numbers that satisfy the condition. By multiplying the factors (x + 11) and (x + 4) together, we can verify that they indeed give us the original expression \(x^2 + 15x + 44\).

Therefore, the correct answer is option b) Lauren's answer was (x + 11)(x + 4), and she knew because she factored the expression.