Precalculus Examples

9 x^{2} - k x + 1

$9 x^{2} - k x + 1$

Step 1

Find the values of

a

$a$ and

c

$c$ in the trinomial

9 x^{2} - k x + 1

$9 x^{2} - k x + 1$ with the format

a x^{2} + k x + c

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

a = 9

$a = 9$

c = 1

$c = 1$

Step 2

For the trinomial

9 x^{2} - k x + 1

$9 x^{2} - k x + 1$ , find the value of

a \cdot c

$a \cdot c$ .

a \cdot c = 9

$a \cdot c = 9$

Step 3

To find all possible values of

k

$k$ , first find the factors of

a \cdot c

$a \cdot c$

9

$9$ . Once a factor is found, add it to its corresponding factor to get a possible value for

k

$k$ . The factors for

9

$9$ are all numbers between

- 9

$- 9$ and

9

$9$ , which divide

9

$9$ evenly.

Check numbers between

- 9

$- 9$ and

9

$9$

Step 4

Calculate the factors of

9

$9$ . Add corresponding factors to get all possible

k

$k$ values.

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Step 4.1

Since

9

$9$ divided by

- 9

$- 9$ is the whole number

- 1

$- 1$ ,

- 9

$- 9$ and

- 1

$- 1$ are factors of

9

$9$ .

- 9

$- 9$ and

- 1

$- 1$ are factors

Step 4.2

Add the factors

- 9

$- 9$ and

- 1

$- 1$ together. Add

- 10

$- 10$ to the list of possible

k

$k$ values.

k = - 10

$k = - 10$

Step 4.3

Since

9

$9$ divided by

- 3

$- 3$ is the whole number

- 3

$- 3$ ,

- 3

$- 3$ and

- 3

$- 3$ are factors of

9

$9$ .

- 3

$- 3$ and

- 3

$- 3$ are factors

Step 4.4

Add the factors

- 3

$- 3$ and

- 3

$- 3$ together. Add

- 6

$- 6$ to the list of possible

k

$k$ values.

k = - 10, - 6

$k = - 10, - 6$

Step 4.5

Since

9

$9$ divided by

1

$1$ is the whole number

9

$9$ ,

1

$1$ and

9

$9$ are factors of

9

$9$ .

1

$1$ and

9

$9$ are factors

Step 4.6

Add the factors

1

$1$ and

9

$9$ together. Add

10

$10$ to the list of possible

k

$k$ values.

k = - 10, - 6, 10

$k = - 10, - 6, 10$

Step 4.7

Since

9

$9$ divided by

3

$3$ is the whole number

3

$3$ ,

3

$3$ and

3

$3$ are factors of

9

$9$ .

3

$3$ and

3

$3$ are factors

Step 4.8

Add the factors

3

$3$ and

3

$3$ together. Add

6

$6$ to the list of possible

k

$k$ values.

k = - 10, - 6, 10, 6

$k = - 10, - 6, 10, 6$

k = - 10, - 6, 10, 6

$k = - 10, - 6, 10, 6$

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