Finite Math Examples

$- 12.5 x + 0.1 x^{2} + 250$

Step 1

Factor $0.1$ out of $- 12.5 x + 0.1 x^{2} + 250$ .

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Step 1.1

Factor $0.1$ out of $- 12.5 x$ .

$0.1 (- 125 x) + 0.1 x^{2} + 250$

Step 1.2

Factor $0.1$ out of $0.1 x^{2}$ .

$0.1 (- 125 x) + 0.1 (x^{2}) + 250$

Step 1.3

Factor $0.1$ out of $250$ .

$0.1 (- 125 x) + 0.1 x^{2} + 0.1 \cdot 2500$

Step 1.4

Factor $0.1$ out of $0.1 (- 125 x) + 0.1 x^{2}$ .

$0.1 (- 125 x + x^{2}) + 0.1 \cdot 2500$

Step 1.5

Factor $0.1$ out of $0.1 (- 125 x + x^{2}) + 0.1 \cdot 2500$ .

$0.1 (- 125 x + x^{2} + 2500)$

Step 2

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$0.1 (- 125 u + u^{2} + 2500)$

Step 3

Factor $- 125 u + u^{2} + 2500$ using the AC method.

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Step 3.1

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 $2500$ and whose sum is $- 125$ .

$- 100, - 25$

Step 3.2

Write the factored form using these integers.

$0.1 ((u - 100) (u - 25))$

Step 4

Factor.

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Step 4.1

Replace all occurrences of $u$ with $x$ .

$0.1 ((x - 100) (x - 25))$

Step 4.2

Remove unnecessary parentheses.

$0.1 (x - 100) (x - 25)$