Question

Consider the trinomial x^2 + 2x - 24. As a first step to factoring it, find the factors of -24 such that the sum of those factors is:

A) 6
B) -6
C) 8
D) -8

Answer 1

The factors of -24 that add up to 2 are -4 and 6, so the correct answer is B) -6.

Step-by-step explanation:

To factor the trinomial x^2 + 2x - 24, we are looking for two numbers that multiply to -24 and add up to the coefficient of the middle term, which is 2. Here are some factor pairs of -24:

• 1 and -24
• -1 and 24
• 2 and -12
• -2 and 12
• 3 and -8
• -3 and 8
• 4 and -6
• -4 and 6

When adding these factor pairs, the pair that sums to 2 is 6 and -4. Therefore, the factor that satisfies the condition of multiplying to -24 and adding up to 2 is -4 and 6. Consequently, the correct option is B) -6.