Finite Math Examples

$7 x^{4} - 28 x^{2} + 28 x - 56$

Step 1

Factor $7$ out of $7 x^{4} - 28 x^{2} + 28 x - 56$ .

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Step 1.1

Factor $7$ out of $7 x^{4}$ .

$7 (x^{4}) - 28 x^{2} + 28 x - 56$

Step 1.2

Factor $7$ out of $- 28 x^{2}$ .

$7 (x^{4}) + 7 (- 4 x^{2}) + 28 x - 56$

Step 1.3

Factor $7$ out of $28 x$ .

$7 (x^{4}) + 7 (- 4 x^{2}) + 7 (4 x) - 56$

Step 1.4

Factor $7$ out of $- 56$ .

$7 x^{4} + 7 (- 4 x^{2}) + 7 (4 x) + 7 \cdot - 8$

Step 1.5

Factor $7$ out of $7 x^{4} + 7 (- 4 x^{2})$ .

$7 (x^{4} - 4 x^{2}) + 7 (4 x) + 7 \cdot - 8$

Step 1.6

Factor $7$ out of $7 (x^{4} - 4 x^{2}) + 7 (4 x)$ .

$7 (x^{4} - 4 x^{2} + 4 x) + 7 \cdot - 8$

Step 1.7

Factor $7$ out of $7 (x^{4} - 4 x^{2} + 4 x) + 7 \cdot - 8$ .

$7 (x^{4} - 4 x^{2} + 4 x - 8)$

Step 2

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

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Step 2.1

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

$7 (x^{2} x^{2} - 4 x^{2} + 4 x - 8)$

Step 2.2

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

$7 (x^{2} x^{2} + x^{2} \cdot - 4 + 4 x - 8)$

Step 2.3

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

$7 (x^{2} (x^{2} - 4) + 4 x - 8)$

Step 3

Rewrite $4$ as $2^{2}$ .

$7 (x^{2} (x^{2} - 2^{2}) + 4 x - 8)$

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$7 (x^{2} ((x + 2) (x - 2)) + 4 x - 8)$

Step 4.2

Remove unnecessary parentheses.

$7 (x^{2} (x + 2) (x - 2) + 4 x - 8)$

Step 5

Factor $4$ out of $4 x - 8$ .

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Step 5.1

Factor $4$ out of $4 x$ .

$7 (x^{2} (x + 2) (x - 2) + 4 (x) - 8)$

Step 5.2

Factor $4$ out of $- 8$ .

$7 (x^{2} (x + 2) (x - 2) + 4 x + 4 \cdot - 2)$

Step 5.3

Factor $4$ out of $4 x + 4 \cdot - 2$ .

$7 (x^{2} (x + 2) (x - 2) + 4 (x - 2))$

Step 6

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

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Step 6.1

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

$7 ((x - 2) (x^{2} (x + 2)) + 4 (x - 2))$

Step 6.2

Factor $x - 2$ out of $4 (x - 2)$ .

$7 ((x - 2) (x^{2} (x + 2)) + (x - 2) \cdot 4)$

Step 6.3

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

$7 ((x - 2) (x^{2} (x + 2) + 4))$

Step 7

Apply the distributive property.

$7 ((x - 2) (x^{2} x + x^{2} \cdot 2 + 4))$

Step 8

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 8.1

Multiply $x^{2}$ by $x$ .

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Step 8.1.1

Raise $x$ to the power of $1$ .

$7 ((x - 2) (x^{2} x^{1} + x^{2} \cdot 2 + 4))$

Step 8.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 ((x - 2) (x^{2 + 1} + x^{2} \cdot 2 + 4))$

Step 8.2

Add $2$ and $1$ .

$7 ((x - 2) (x^{3} + x^{2} \cdot 2 + 4))$

Step 9

Move $2$ to the left of $x^{2}$ .

$7 ((x - 2) (x^{3} + 2 x^{2} + 4))$

Step 10

Remove unnecessary parentheses.

$7 (x - 2) (x^{3} + 2 x^{2} + 4)$