Question

Find all integers b so that the trinomial x^2 + bx + 12 can be factored.

a) b = -13
b) b = -10
c) b = 10
d) b = 13

Answer 1

The trinomial x^2 + bx + 12 can be factored if b = 4√3 or b = -4√3.

Step-by-step explanation:

The trinomial x^2 + bx + 12 can be factored if the quadratic equation has two real solutions. To find the values of b that satisfy this condition, we can use the discriminant, b^2 - 4ac, where a = 1, b = b, and c = 12. If the discriminant is greater than or equal to zero, the trinomial can be factored.

Therefore, we need to find all values of b that make b^2 - 4ac ≥ 0. With c = 12, we have:

b^2 - 4(1)(12) ≥ 0.
b^2 - 48 ≥ 0.
b^2 ≥ 48.
b ≥ ±√48.
b ≥ ±4√3.

Hence, the values of b that make x^2 + bx + 12 factorable are b = 4√3 and b = -4√3.