Pre-Algebra Examples

$80 x + 4 x^{2} - 4 x^{3}$

Step 1

Factor $- 4 x$ out of $80 x + 4 x^{2} - 4 x^{3}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $80 x$ .

$4 x^{2} - 4 x^{3} + 80 x$

Step 1.1.2

Reorder $4 x^{2}$ and $- 4 x^{3}$ .

$- 4 x^{3} + 4 x^{2} + 80 x$

Step 1.2

Factor $- 4 x$ out of $- 4 x^{3}$ .

$- 4 x (x^{2}) + 4 x^{2} + 80 x$

Step 1.3

Factor $- 4 x$ out of $4 x^{2}$ .

$- 4 x (x^{2}) - 4 x (- x) + 80 x$

Step 1.4

Factor $- 4 x$ out of $80 x$ .

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

Step 1.5

Factor $- 4 x$ out of $- 4 x (x^{2}) - 4 x (- x)$ .

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

Step 1.6

Factor $- 4 x$ out of $- 4 x (x^{2} - x) - 4 x (- 20)$ .

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

Step 2

Factor.

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Step 2.1

Factor $x^{2} - x - 20$ using the AC method.

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Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 20$ and whose sum is $- 1$ .

$- 5, 4$

Step 2.1.2

Write the factored form using these integers.

$- 4 x ((x - 5) (x + 4))$

Step 2.2

Remove unnecessary parentheses.

$- 4 x (x - 5) (x + 4)$