Examples

10 x^{2} + k x + 8

$10 x^{2} + k x + 8$

Step 1

Find the values of

a

$a$ and

c

$c$ in the trinomial

10 x^{2} + k x + 8

$10 x^{2} + k x + 8$ with the format

a x^{2} + k x + c

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

a = 10

$a = 10$

c = 8

$c = 8$

Step 2

For the trinomial

10 x^{2} + k x + 8

$10 x^{2} + k x + 8$ , find the value of

a \cdot c

$a \cdot c$ .

a \cdot c = 80

$a \cdot c = 80$

Step 3

To find all possible values of

k

$k$ , first find the factors of

a \cdot c

$a \cdot c$

80

$80$ . Once a factor is found, add it to its corresponding factor to get a possible value for

k

$k$ . The factors for

80

$80$ are all numbers between

- 80

$- 80$ and

80

$80$ , which divide

80

$80$ evenly.

Check numbers between

- 80

$- 80$ and

80

$80$

Step 4

Calculate the factors of

80

$80$ . Add corresponding factors to get all possible

k

$k$ values.

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Step 4.1

Since

80

$80$ divided by

- 80

$- 80$ is the whole number

- 1

$- 1$ ,

- 80

$- 80$ and

- 1

$- 1$ are factors of

80

$80$ .

- 80

$- 80$ and

- 1

$- 1$ are factors

Step 4.2

Add the factors

- 80

$- 80$ and

- 1

$- 1$ together. Add

- 81

$- 81$ to the list of possible

k

$k$ values.

k = - 81

$k = - 81$

Step 4.3

Since

80

$80$ divided by

- 40

$- 40$ is the whole number

- 2

$- 2$ ,

- 40

$- 40$ and

- 2

$- 2$ are factors of

80

$80$ .

- 40

$- 40$ and

- 2

$- 2$ are factors

Step 4.4

Add the factors

- 40

$- 40$ and

- 2

$- 2$ together. Add

- 42

$- 42$ to the list of possible

k

$k$ values.

k = - 81, - 42

$k = - 81, - 42$

Step 4.5

Since

80

$80$ divided by

- 20

$- 20$ is the whole number

- 4

$- 4$ ,

- 20

$- 20$ and

- 4

$- 4$ are factors of

80

$80$ .

- 20

$- 20$ and

- 4

$- 4$ are factors

Step 4.6

Add the factors

- 20

$- 20$ and

- 4

$- 4$ together. Add

- 24

$- 24$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24

$k = - 81, - 42, - 24$

Step 4.7

Since

80

$80$ divided by

- 16

$- 16$ is the whole number

- 5

$- 5$ ,

- 16

$- 16$ and

- 5

$- 5$ are factors of

80

$80$ .

- 16

$- 16$ and

- 5

$- 5$ are factors

Step 4.8

Add the factors

- 16

$- 16$ and

- 5

$- 5$ together. Add

- 21

$- 21$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24, - 21

$k = - 81, - 42, - 24, - 21$

Step 4.9

Since

80

$80$ divided by

- 10

$- 10$ is the whole number

- 8

$- 8$ ,

- 10

$- 10$ and

- 8

$- 8$ are factors of

80

$80$ .

- 10

$- 10$ and

- 8

$- 8$ are factors

Step 4.10

Add the factors

- 10

$- 10$ and

- 8

$- 8$ together. Add

- 18

$- 18$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24, - 21, - 18

$k = - 81, - 42, - 24, - 21, - 18$

Step 4.11

Since

80

$80$ divided by

1

$1$ is the whole number

80

$80$ ,

1

$1$ and

80

$80$ are factors of

80

$80$ .

1

$1$ and

80

$80$ are factors

Step 4.12

Add the factors

1

$1$ and

80

$80$ together. Add

81

$81$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24, - 21, - 18, 81

$k = - 81, - 42, - 24, - 21, - 18, 81$

Step 4.13

Since

80

$80$ divided by

2

$2$ is the whole number

40

$40$ ,

2

$2$ and

40

$40$ are factors of

80

$80$ .

2

$2$ and

40

$40$ are factors

Step 4.14

Add the factors

2

$2$ and

40

$40$ together. Add

42

$42$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24, - 21, - 18, 81, 42

$k = - 81, - 42, - 24, - 21, - 18, 81, 42$

Step 4.15

Since

80

$80$ divided by

4

$4$ is the whole number

20

$20$ ,

4

$4$ and

20

$20$ are factors of

80

$80$ .

4

$4$ and

20

$20$ are factors

Step 4.16

Add the factors

4

$4$ and

20

$20$ together. Add

24

$24$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24

$k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24$

Step 4.17

Since

80

$80$ divided by

5

$5$ is the whole number

16

$16$ ,

5

$5$ and

16

$16$ are factors of

80

$80$ .

5

$5$ and

16

$16$ are factors

Step 4.18

Add the factors

5

$5$ and

16

$16$ together. Add

21

$21$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24, 21

$k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24, 21$

Step 4.19

Since

80

$80$ divided by

8

$8$ is the whole number

10

$10$ ,

8

$8$ and

10

$10$ are factors of

80

$80$ .

8

$8$ and

10

$10$ are factors

Step 4.20

Add the factors

8

$8$ and

10

$10$ together. Add

18

$18$ to the list of possible

k

$k$ values.

k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24, 21, 18

$k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24, 21, 18$

k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24, 21, 18

$k = - 81, - 42, - 24, - 21, - 18, 81, 42, 24, 21, 18$

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