Find which of the following trinomials is not factorable using integers.
A) $t ^ { 2 } + 12 t + 24$
B) $x ^ { 2 } - 11 x + 30$

Question

Quizplus · Accepted Answer

To factor a trinomial, we need to find two integers whose product is the constant term and whose sum is the coefficient of the linear term. For option A, the constant term is 24 and the coefficient of the linear term is 12. We can try to factor it as (t+a)(t+b), where a and b are integers. The possible factor pairs for 24 are (1,24), (2,12), (3,8), and (4,6). None of these pairs add up to 12, so the trinomial cannot be factored using integers. Therefore, option A is the best choice. Option B can be factored as (x-5)(x-6), so it is factorable using integers.

Find Which of the Following Trinomials Is Not Factorable Using t2+12t+24t ^ { 2 } + 12 t + 24t2+12t+24

Find Which of the Following Trinomials Is Not Factorable Using $t ^ { 2 } + 12 t + 24$