Examples

$4 x^{2} + k x + 4$

Step 1

Find the values of $a$ and $c$ in the trinomial $4 x^{2} + k x + 4$ with the format $a x^{2} + k x + c$ .

$a = 4$

$c = 4$

Step 2

For the trinomial $4 x^{2} + k x + 4$ , find the value of $a \cdot c$ .

$a \cdot c = 16$

Step 3

To find all possible values of $k$ , first find the factors of $a \cdot c$ $16$ . Once a factor is found, add it to its corresponding factor to get a possible value for $k$ . The factors for $16$ are all numbers between $- 16$ and $16$ , which divide $16$ evenly.

Check numbers between $- 16$ and $16$

Step 4

Calculate the factors of $16$ . Add corresponding factors to get all possible $k$ values.

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Step 4.1

Since $16$ divided by $- 16$ is the whole number $- 1$ , $- 16$ and $- 1$ are factors of $16$ .

$- 16$ and $- 1$ are factors

Step 4.2

Add the factors $- 16$ and $- 1$ together. Add $- 17$ to the list of possible $k$ values.

$k = - 17$

Step 4.3

Since $16$ divided by $- 8$ is the whole number $- 2$ , $- 8$ and $- 2$ are factors of $16$ .

$- 8$ and $- 2$ are factors

Step 4.4

Add the factors $- 8$ and $- 2$ together. Add $- 10$ to the list of possible $k$ values.

$k = - 17, - 10$

Step 4.5

Since $16$ divided by $- 4$ is the whole number $- 4$ , $- 4$ and $- 4$ are factors of $16$ .

$- 4$ and $- 4$ are factors

Step 4.6

Add the factors $- 4$ and $- 4$ together. Add $- 8$ to the list of possible $k$ values.

$k = - 17, - 10, - 8$

Step 4.7

Since $16$ divided by $1$ is the whole number $16$ , $1$ and $16$ are factors of $16$ .

$1$ and $16$ are factors

Step 4.8

Add the factors $1$ and $16$ together. Add $17$ to the list of possible $k$ values.

$k = - 17, - 10, - 8, 17$

Step 4.9

Since $16$ divided by $2$ is the whole number $8$ , $2$ and $8$ are factors of $16$ .

$2$ and $8$ are factors

Step 4.10

Add the factors $2$ and $8$ together. Add $10$ to the list of possible $k$ values.

$k = - 17, - 10, - 8, 17, 10$

Step 4.11

Since $16$ divided by $4$ is the whole number $4$ , $4$ and $4$ are factors of $16$ .

$4$ and $4$ are factors

Step 4.12

Add the factors $4$ and $4$ together. Add $8$ to the list of possible $k$ values.

$k = - 17, - 10, - 8, 17, 10, 8$

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