Algebra Examples

4 x^{3} - 20 x^{2} + 24 x

$4 x^{3} - 20 x^{2} + 24 x$

Step 1

Factor

4 x

$4 x$ out of

4 x^{3} - 20 x^{2} + 24 x

$4 x^{3} - 20 x^{2} + 24 x$ .

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Step 1.1

Factor

4 x

$4 x$ out of

4 x^{3}

$4 x^{3}$ .

4 x (x^{2}) - 20 x^{2} + 24 x

$4 x (x^{2}) - 20 x^{2} + 24 x$

Step 1.2

Factor

4 x

$4 x$ out of

- 20 x^{2}

$- 20 x^{2}$ .

4 x (x^{2}) + 4 x (- 5 x) + 24 x

$4 x (x^{2}) + 4 x (- 5 x) + 24 x$

Step 1.3

Factor

4 x

$4 x$ out of

24 x

$24 x$ .

4 x (x^{2}) + 4 x (- 5 x) + 4 x (6)

$4 x (x^{2}) + 4 x (- 5 x) + 4 x (6)$

Step 1.4

Factor

4 x

$4 x$ out of

4 x (x^{2}) + 4 x (- 5 x)

$4 x (x^{2}) + 4 x (- 5 x)$ .

4 x (x^{2} - 5 x) + 4 x (6)

$4 x (x^{2} - 5 x) + 4 x (6)$

Step 1.5

Factor

4 x

$4 x$ out of

4 x (x^{2} - 5 x) + 4 x (6)

$4 x (x^{2} - 5 x) + 4 x (6)$ .

4 x (x^{2} - 5 x + 6)

$4 x (x^{2} - 5 x + 6)$

4 x (x^{2} - 5 x + 6)

$4 x (x^{2} - 5 x + 6)$

Step 2

Factor.

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Step 2.1

Factor

x^{2} - 5 x + 6

$x^{2} - 5 x + 6$ using the AC method.

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Step 2.1.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

6

$6$ and whose sum is

- 5

$- 5$ .

- 3, - 2

$- 3, - 2$

Step 2.1.2

Write the factored form using these integers.

4 x ((x - 3) (x - 2))

$4 x ((x - 3) (x - 2))$

4 x ((x - 3) (x - 2))

$4 x ((x - 3) (x - 2))$

Step 2.2

Remove unnecessary parentheses.

4 x (x - 3) (x - 2)

$4 x (x - 3) (x - 2)$

4 x (x - 3) (x - 2)

$4 x (x - 3) (x - 2)$

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

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