Explanation:
3.
the fact the three factor of n² is simply 1 tells us that the factors look like
(n + a)(n + b)
the fact that the last term is -24 (negative) tells us that one of a, b is positive and the other negative.
so, the factors are looking like
(n + a)(n - b)
and a×-b = -24.
the fact that the midterm is 2n means that a - b = 2.
so, the factors of 24 with difference of 2 are 6 and 4.
and the factoring is
(n + 6)(n - 4) = 0
the solutions to that are all values for n that make this equation true.
when is a multiplication 0 ?
when at least one factor is 0.
n + 6 = 0
n = -6
n - 4 = 0
n = 4
-6, 4 are the solutions.
that is the third answer option.
4.
-5 + 2x² = -6x
let's bring this into the firm of a regular quadratic equation :
2x² + 6x - 5 = 0
the general solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 2
b = 6
c = -5
and we get
x = (-6 ± sqrt(6² - 4×2×-5))/(2×2) =
= (-6 ± sqrt(36 - 4×2×-5))/4
that is the third answer option.