Algebra Examples

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

Step 1

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

$a = 1$

$c = 4$

Step 2

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

$a \cdot c = 4$

Step 3

To find all possible values of $k$ , first find the factors of $a \cdot c$ $4$ . Once a factor is found, add it to its corresponding factor to get a possible value for $k$ . The factors for $4$ are all numbers between $- 4$ and $4$ , which divide $4$ evenly.

Check numbers between $- 4$ and $4$

Step 4

Calculate the factors of $4$ . Add corresponding factors to get all possible $k$ values.

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Step 4.1

Since $4$ divided by $- 4$ is the whole number $- 1$ , $- 4$ and $- 1$ are factors of $4$ .

$- 4$ and $- 1$ are factors

Step 4.2

Add the factors $- 4$ and $- 1$ together. Add $- 5$ to the list of possible $k$ values.

$k = - 5$

Step 4.3

Since $4$ divided by $- 2$ is the whole number $- 2$ , $- 2$ and $- 2$ are factors of $4$ .

$- 2$ and $- 2$ are factors

Step 4.4

Add the factors $- 2$ and $- 2$ together. Add $- 4$ to the list of possible $k$ values.

$k = - 5, - 4$

Step 4.5

Since $4$ divided by $1$ is the whole number $4$ , $1$ and $4$ are factors of $4$ .

$1$ and $4$ are factors

Step 4.6

Add the factors $1$ and $4$ together. Add $5$ to the list of possible $k$ values.

$k = - 5, - 4, 5$

Step 4.7

Since $4$ divided by $2$ is the whole number $2$ , $2$ and $2$ are factors of $4$ .

$2$ and $2$ are factors

Step 4.8

Add the factors $2$ and $2$ together. Add $4$ to the list of possible $k$ values.

$k = - 5, - 4, 5, 4$

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