Find all positive and negative integers b such that the trinomial is factorable.
-$$11 x ^ { 2 } + b x + 1$$
A) 12
B) $$\pm 12$$
C) 10
D) $$\pm 10$$

Question

Quizplus · Accepted Answer

For a trinomial of the form $ax^2 + bx + c$ to be factorable over the integers, the middle term $b$ must be such that there exist integers $m$ and $n$ where $ac = m \cdot n$ and $b = m + n$. Here, $a = 11$ and $c = 1$, so $ac = 11$. The pairs of integers that multiply to $11$ are $(1, 11)$ and $(-1, -11)$. Thus, $b$ can be $12$ or $-12$, making the trinomial factorable for $b = \pm 12$.

Find All Positive and Negative Integers B Such That the Trinomial