Find All Integers k Such That the Trinomial Can Be Factored

Find the values of ${\displaystyle a}$ and ${\displaystyle c}$ in the trinomial ${\displaystyle 3x^2+kx-1}$ with the format ${\displaystyle a{x}^2+kx+c}$.

For the trinomial ${\displaystyle 3x^2+kx-1}$, find the value of ${\displaystyle a\cdot c}$.

To find all possible values of ${\displaystyle k}$, first find the factors of ${\displaystyle a\cdot c}$ ${\displaystyle -3}$. Once a factor is found, add it to its corresponding factor to get a possible value for ${\displaystyle k}$. The factors for ${\displaystyle -3}$ are all numbers between ${\displaystyle -3}$ and ${\displaystyle 3}$, which divide ${\displaystyle -3}$ evenly.