Finite Math Examples

$3 x^{2} - 13 x + 19 = a (x - 2^{2} + b (- 2 c))$

Step 1

Rewrite the equation as $a (x - 2^{2} + b (- 2 c)) = 3 x^{2} - 13 x + 19$ .

$a (x - 2^{2} + b (- 2 c)) = 3 x^{2} - 13 x + 19$

Step 2

Simplify.

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Step 2.1

Raise $2$ to the power of $2$ .

$a (x - 1 \cdot 4 + b (- 2 c)) = 3 x^{2} - 13 x + 19$

Step 2.2

Multiply $- 1$ by $4$ .

$a (x - 4 + b (- 2 c)) = 3 x^{2} - 13 x + 19$

Step 3

Divide each term in $a (x - 4 + b (- 2 c)) = 3 x^{2} - 13 x + 19$ by $x - 4 + b (- 2 c)$ and simplify.

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Step 3.1

Divide each term in $a (x - 4 + b (- 2 c)) = 3 x^{2} - 13 x + 19$ by $x - 4 + b (- 2 c)$ .

$\frac{a (x - 4 + b (- 2 c))}{x - 4 + b (- 2 c)} = \frac{3 x^{2}}{x - 4 + b (- 2 c)} + \frac{- 13 x}{x - 4 + b (- 2 c)} + \frac{19}{x - 4 + b (- 2 c)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x - 4 + b (- 2 c)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{a (x - 4 + b (- 2 c))}{x - 4 + b (- 2 c)} = \frac{3 x^{2}}{x - 4 + b (- 2 c)} + \frac{- 13 x}{x - 4 + b (- 2 c)} + \frac{19}{x - 4 + b (- 2 c)}$

Step 3.2.1.2

Divide $a$ by $1$ .

$a = \frac{3 x^{2}}{x - 4 + b (- 2 c)} + \frac{- 13 x}{x - 4 + b (- 2 c)} + \frac{19}{x - 4 + b (- 2 c)}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Rewrite using the commutative property of multiplication.

$a = \frac{3 x^{2}}{x - 4 - 2 b c} + \frac{- 13 x}{x - 4 + b (- 2 c)} + \frac{19}{x - 4 + b (- 2 c)}$

Step 3.3.1.2

Rewrite using the commutative property of multiplication.

$a = \frac{3 x^{2}}{x - 4 - 2 b c} + \frac{- 13 x}{x - 4 - 2 b c} + \frac{19}{x - 4 + b (- 2 c)}$

Step 3.3.1.3

Move the negative in front of the fraction.

$a = \frac{3 x^{2}}{x - 4 - 2 b c} - \frac{13 x}{x - 4 - 2 b c} + \frac{19}{x - 4 + b (- 2 c)}$

Step 3.3.1.4

Rewrite using the commutative property of multiplication.

$a = \frac{3 x^{2}}{x - 4 - 2 b c} - \frac{13 x}{x - 4 - 2 b c} + \frac{19}{x - 4 - 2 b c}$

Step 3.3.2

Combine into one fraction.

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Step 3.3.2.1

Combine the numerators over the common denominator.

$a = \frac{3 x^{2} - 13 x}{x - 4 - 2 b c} + \frac{19}{x - 4 - 2 b c}$

Step 3.3.2.2

Combine the numerators over the common denominator.

$a = \frac{3 x^{2} - 13 x + 19}{x - 4 - 2 b c}$