Precalculus Examples

$9 x^{2} - k x + 1$

Step 1

Find the values of $a$ and $c$ in the trinomial $9 x^{2} - k x + 1$ with the format $a x^{2} + k x + c$ .

$a = 9$

$c = 1$

Step 2

For the trinomial $9 x^{2} - k x + 1$ , find the value of $a \cdot c$ .

$a \cdot c = 9$

Step 3

To find all possible values of $k$ , first find the factors of $a \cdot c$ $9$ . Once a factor is found, add it to its corresponding factor to get a possible value for $k$ . The factors for $9$ are all numbers between $- 9$ and $9$ , which divide $9$ evenly.

Check numbers between $- 9$ and $9$

Step 4

Calculate the factors of $9$ . Add corresponding factors to get all possible $k$ values.

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Step 4.1

Since $9$ divided by $- 9$ is the whole number $- 1$ , $- 9$ and $- 1$ are factors of $9$ .

$- 9$ and $- 1$ are factors

Step 4.2

Add the factors $- 9$ and $- 1$ together. Add $- 10$ to the list of possible $k$ values.

$k = - 10$

Step 4.3

Since $9$ divided by $- 3$ is the whole number $- 3$ , $- 3$ and $- 3$ are factors of $9$ .

$- 3$ and $- 3$ are factors

Step 4.4

Add the factors $- 3$ and $- 3$ together. Add $- 6$ to the list of possible $k$ values.

$k = - 10, - 6$

Step 4.5

Since $9$ divided by $1$ is the whole number $9$ , $1$ and $9$ are factors of $9$ .

$1$ and $9$ are factors

Step 4.6

Add the factors $1$ and $9$ together. Add $10$ to the list of possible $k$ values.

$k = - 10, - 6, 10$

Step 4.7

Since $9$ divided by $3$ is the whole number $3$ , $3$ and $3$ are factors of $9$ .

$3$ and $3$ are factors

Step 4.8

Add the factors $3$ and $3$ together. Add $6$ to the list of possible $k$ values.

$k = - 10, - 6, 10, 6$

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