Pre-Algebra Examples

$x^{2} + k x + 25$

Step 1

Find the values of $a$ and $c$ in the trinomial $x^{2} + k x + 25$ with the format $a x^{2} + k x + c$ .

$a = 1$

$c = 25$

Step 2

For the trinomial $x^{2} + k x + 25$ , find the value of $a \cdot c$ .

$a \cdot c = 25$

Step 3

To find all possible values of $k$ , first find the factors of $a \cdot c$ $25$ . Once a factor is found, add it to its corresponding factor to get a possible value for $k$ . The factors for $25$ are all numbers between $- 25$ and $25$ , which divide $25$ evenly.

Check numbers between $- 25$ and $25$

Step 4

Calculate the factors of $25$ . Add corresponding factors to get all possible $k$ values.

Tap for more steps...

Step 4.1

Since $25$ divided by $- 25$ is the whole number $- 1$ , $- 25$ and $- 1$ are factors of $25$ .

$- 25$ and $- 1$ are factors

Step 4.2

Add the factors $- 25$ and $- 1$ together. Add $- 26$ to the list of possible $k$ values.

$k = - 26$

Step 4.3

Since $25$ divided by $- 5$ is the whole number $- 5$ , $- 5$ and $- 5$ are factors of $25$ .

$- 5$ and $- 5$ are factors

Step 4.4

Add the factors $- 5$ and $- 5$ together. Add $- 10$ to the list of possible $k$ values.

$k = - 26, - 10$

Step 4.5

Since $25$ divided by $1$ is the whole number $25$ , $1$ and $25$ are factors of $25$ .

$1$ and $25$ are factors

Step 4.6

Add the factors $1$ and $25$ together. Add $26$ to the list of possible $k$ values.

$k = - 26, - 10, 26$

Step 4.7

Since $25$ divided by $5$ is the whole number $5$ , $5$ and $5$ are factors of $25$ .

$5$ and $5$ are factors

Step 4.8

Add the factors $5$ and $5$ together. Add $10$ to the list of possible $k$ values.

$k = - 26, - 10, 26, 10$