Precalculus Examples

$3 x^{2} + k x - 1$

Step 1

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

$a = 3$

$c = - 1$

Step 2

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

$a \cdot c = - 3$

Step 3

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

Check numbers between $- 3$ and $3$

Step 4

Calculate the factors of $- 3$ . Add corresponding factors to get all possible $k$ values.

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Step 4.1

Since $- 3$ divided by $- 3$ is the whole number $1$ , $- 3$ and $1$ are factors of $- 3$ .

$- 3$ and $1$ are factors

Step 4.2

Add the factors $- 3$ and $1$ together. Add $- 2$ to the list of possible $k$ values.

$k = - 2$

Step 4.3

Since $- 3$ divided by $- 1$ is the whole number $3$ , $- 1$ and $3$ are factors of $- 3$ .

$- 1$ and $3$ are factors

Step 4.4

Add the factors $- 1$ and $3$ together. Add $2$ to the list of possible $k$ values.

$k = - 2, 2$