Algebra Examples

25 x^{2} - k x + 4

$25 x^{2} - k x + 4$

Step 1

Find the values of

a

$a$ and

c

$c$ in the trinomial

25 x^{2} - k x + 4

$25 x^{2} - k x + 4$ with the format

a x^{2} + k x + c

$a x^{2} + k x + c$ .

a = 25

$a = 25$

c = 4

$c = 4$

Step 2

For the trinomial

25 x^{2} - k x + 4

$25 x^{2} - k x + 4$ , find the value of

a \cdot c

$a \cdot c$ .

a \cdot c = 100

$a \cdot c = 100$

Step 3

To find all possible values of

k

$k$ , first find the factors of

a \cdot c

$a \cdot c$

100

$100$ . Once a factor is found, add it to its corresponding factor to get a possible value for

k

$k$ . The factors for

100

$100$ are all numbers between

- 100

$- 100$ and

100

$100$ , which divide

100

$100$ evenly.

Check numbers between

- 100

$- 100$ and

100

$100$

Step 4

Calculate the factors of

100

$100$ . Add corresponding factors to get all possible

k

$k$ values.

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Step 4.1

Since

100

$100$ divided by

- 100

$- 100$ is the whole number

- 1

$- 1$ ,

- 100

$- 100$ and

- 1

$- 1$ are factors of

100

$100$ .

- 100

$- 100$ and

- 1

$- 1$ are factors

Step 4.2

Add the factors

- 100

$- 100$ and

- 1

$- 1$ together. Add

- 101

$- 101$ to the list of possible

k

$k$ values.

k = - 101

$k = - 101$

Step 4.3

Since

100

$100$ divided by

- 50

$- 50$ is the whole number

- 2

$- 2$ ,

- 50

$- 50$ and

- 2

$- 2$ are factors of

100

$100$ .

- 50

$- 50$ and

- 2

$- 2$ are factors

Step 4.4

Add the factors

- 50

$- 50$ and

- 2

$- 2$ together. Add

- 52

$- 52$ to the list of possible

k

$k$ values.

k = - 101, - 52

$k = - 101, - 52$

Step 4.5

Since

100

$100$ divided by

- 25

$- 25$ is the whole number

- 4

$- 4$ ,

- 25

$- 25$ and

- 4

$- 4$ are factors of

100

$100$ .

- 25

$- 25$ and

- 4

$- 4$ are factors

Step 4.6

Add the factors

- 25

$- 25$ and

- 4

$- 4$ together. Add

- 29

$- 29$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29

$k = - 101, - 52, - 29$

Step 4.7

Since

100

$100$ divided by

- 20

$- 20$ is the whole number

- 5

$- 5$ ,

- 20

$- 20$ and

- 5

$- 5$ are factors of

100

$100$ .

- 20

$- 20$ and

- 5

$- 5$ are factors

Step 4.8

Add the factors

- 20

$- 20$ and

- 5

$- 5$ together. Add

- 25

$- 25$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29, - 25

$k = - 101, - 52, - 29, - 25$

Step 4.9

Since

100

$100$ divided by

- 10

$- 10$ is the whole number

- 10

$- 10$ ,

- 10

$- 10$ and

- 10

$- 10$ are factors of

100

$100$ .

- 10

$- 10$ and

- 10

$- 10$ are factors

Step 4.10

Add the factors

- 10

$- 10$ and

- 10

$- 10$ together. Add

- 20

$- 20$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29, - 25, - 20

$k = - 101, - 52, - 29, - 25, - 20$

Step 4.11

Since

100

$100$ divided by

1

$1$ is the whole number

100

$100$ ,

1

$1$ and

100

$100$ are factors of

100

$100$ .

1

$1$ and

100

$100$ are factors

Step 4.12

Add the factors

1

$1$ and

100

$100$ together. Add

101

$101$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29, - 25, - 20, 101

$k = - 101, - 52, - 29, - 25, - 20, 101$

Step 4.13

Since

100

$100$ divided by

2

$2$ is the whole number

50

$50$ ,

2

$2$ and

50

$50$ are factors of

100

$100$ .

2

$2$ and

50

$50$ are factors

Step 4.14

Add the factors

2

$2$ and

50

$50$ together. Add

52

$52$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29, - 25, - 20, 101, 52

$k = - 101, - 52, - 29, - 25, - 20, 101, 52$

Step 4.15

Since

100

$100$ divided by

4

$4$ is the whole number

25

$25$ ,

4

$4$ and

25

$25$ are factors of

100

$100$ .

4

$4$ and

25

$25$ are factors

Step 4.16

Add the factors

4

$4$ and

25

$25$ together. Add

29

$29$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29

$k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29$

Step 4.17

Since

100

$100$ divided by

5

$5$ is the whole number

20

$20$ ,

5

$5$ and

20

$20$ are factors of

100

$100$ .

5

$5$ and

20

$20$ are factors

Step 4.18

Add the factors

5

$5$ and

20

$20$ together. Add

25

$25$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29, 25

$k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29, 25$

Step 4.19

Since

100

$100$ divided by

10

$10$ is the whole number

10

$10$ ,

10

$10$ and

10

$10$ are factors of

100

$100$ .

10

$10$ and

10

$10$ are factors

Step 4.20

Add the factors

10

$10$ and

10

$10$ together. Add

20

$20$ to the list of possible

k

$k$ values.

k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29, 25, 20

$k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29, 25, 20$

k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29, 25, 20

$k = - 101, - 52, - 29, - 25, - 20, 101, 52, 29, 25, 20$

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