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Precalculus Examples

4 x^{2} + k x + 4

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

Step 1

Find the values of

a

$a$ and

c

$c$ in the trinomial

4 x^{2} + k x + 4

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

a x^{2} + k x + c

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

a = 4

$a = 4$

c = 4

$c = 4$

Step 2

For the trinomial

4 x^{2} + k x + 4

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

a \cdot c

$a \cdot c$ .

a \cdot c = 16

$a \cdot c = 16$

Step 3

To find all possible values of

k

$k$ , first find the factors of

a \cdot c

$a \cdot c$

16

$16$ . Once a factor is found, add it to its corresponding factor to get a possible value for

k

$k$ . The factors for

16

$16$ are all numbers between

- 16

$- 16$ and

16

$16$ , which divide

16

$16$ evenly.

Check numbers between

- 16

$- 16$ and

16

$16$

Step 4

Calculate the factors of

16

$16$ . Add corresponding factors to get all possible

k

$k$ values.

Tap for more steps...

Step 4.1

Since

16

$16$ divided by

- 16

$- 16$ is the whole number

- 1

$- 1$ ,

- 16

$- 16$ and

- 1

$- 1$ are factors of

16

$16$ .

- 16

$- 16$ and

- 1

$- 1$ are factors

Step 4.2

Add the factors

- 16

$- 16$ and

- 1

$- 1$ together. Add

- 17

$- 17$ to the list of possible

k

$k$ values.

k = - 17

$k = - 17$

Step 4.3

Since

16

$16$ divided by

- 8

$- 8$ is the whole number

- 2

$- 2$ ,

- 8

$- 8$ and

- 2

$- 2$ are factors of

16

$16$ .

- 8

$- 8$ and

- 2

$- 2$ are factors

Step 4.4

Add the factors

- 8

$- 8$ and

- 2

$- 2$ together. Add

- 10

$- 10$ to the list of possible

k

$k$ values.

k = - 17, - 10

$k = - 17, - 10$

Step 4.5

Since

16

$16$ divided by

- 4

$- 4$ is the whole number

- 4

$- 4$ ,

- 4

$- 4$ and

- 4

$- 4$ are factors of

16

$16$ .

- 4

$- 4$ and

- 4

$- 4$ are factors

Step 4.6

Add the factors

- 4

$- 4$ and

- 4

$- 4$ together. Add

- 8

$- 8$ to the list of possible

k

$k$ values.

k = - 17, - 10, - 8

$k = - 17, - 10, - 8$

Step 4.7

Since

16

$16$ divided by

1

$1$ is the whole number

16

$16$ ,

1

$1$ and

16

$16$ are factors of

16

$16$ .

1

$1$ and

16

$16$ are factors

Step 4.8

Add the factors

1

$1$ and

16

$16$ together. Add

17

$17$ to the list of possible

k

$k$ values.

k = - 17, - 10, - 8, 17

$k = - 17, - 10, - 8, 17$

Step 4.9

Since

16

$16$ divided by

2

$2$ is the whole number

8

$8$ ,

2

$2$ and

8

$8$ are factors of

16

$16$ .

2

$2$ and

8

$8$ are factors

Step 4.10

Add the factors

2

$2$ and

8

$8$ together. Add

10

$10$ to the list of possible

k

$k$ values.

k = - 17, - 10, - 8, 17, 10

$k = - 17, - 10, - 8, 17, 10$

Step 4.11

Since

16

$16$ divided by

4

$4$ is the whole number

4

$4$ ,

4

$4$ and

4

$4$ are factors of

16

$16$ .

4

$4$ and

4

$4$ are factors

Step 4.12

Add the factors

4

$4$ and

4

$4$ together. Add

8

$8$ to the list of possible

k

$k$ values.

k = - 17, - 10, - 8, 17, 10, 8

$k = - 17, - 10, - 8, 17, 10, 8$

k = - 17, - 10, - 8, 17, 10, 8

$k = - 17, - 10, - 8, 17, 10, 8$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$