7 of 87 of 8 Items Question Solve by factoring. n² + 2n – 24 = 0 (1 point) Responses –12, 2 –12, 2 –2, 12 –2, 12 –6, 4 –6, 4 –4, 6 –4, 6

Answer 1

To solve this equation by factoring, we look for two numbers that multiply to -24 and add up to 2. The numbers are 6 and -4.

So, we can rewrite the equation as:

n^2 + 6n - 4n - 24 = 0

Now, factor by grouping:

n(n + 6) - 4(n + 6) = 0
(n - 4)(n + 6) = 0

Setting each factor to zero:

n - 4 = 0
n = 4

n + 6 = 0
n = -6

Therefore, the solutions are n = 4 and n = -6. The pairs of solutions are:

-4, 6