Finite Math Examples

$- 5 {(2 (x + 4))}^{3} + 4$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 5 {(2 x + 2 \cdot 4)}^{3} + 4$

Step 1.1.2

Multiply $2$ by $4$ .

$- 5 {(2 x + 8)}^{3} + 4$

Step 1.1.3

Use the Binomial Theorem.

$- 5 ({(2 x)}^{3} + 3 {(2 x)}^{2} \cdot 8 + 3 (2 x) \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Apply the product rule to $2 x$ .

$- 5 (2^{3} x^{3} + 3 {(2 x)}^{2} \cdot 8 + 3 (2 x) \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4.2

Raise $2$ to the power of $3$ .

$- 5 (8 x^{3} + 3 {(2 x)}^{2} \cdot 8 + 3 (2 x) \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4.3

Apply the product rule to $2 x$ .

$- 5 (8 x^{3} + 3 (2^{2} x^{2}) \cdot 8 + 3 (2 x) \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4.4

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

$- 5 (8 x^{3} + 3 (4 x^{2}) \cdot 8 + 3 (2 x) \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4.5

Multiply $4$ by $3$ .

$- 5 (8 x^{3} + 12 x^{2} \cdot 8 + 3 (2 x) \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4.6

Multiply $8$ by $12$ .

$- 5 (8 x^{3} + 96 x^{2} + 3 (2 x) \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4.7

Multiply $2$ by $3$ .

$- 5 (8 x^{3} + 96 x^{2} + 6 x \cdot 8^{2} + 8^{3}) + 4$

Step 1.1.4.8

Raise $8$ to the power of $2$ .

$- 5 (8 x^{3} + 96 x^{2} + 6 x \cdot 64 + 8^{3}) + 4$

Step 1.1.4.9

Multiply $64$ by $6$ .

$- 5 (8 x^{3} + 96 x^{2} + 384 x + 8^{3}) + 4$

Step 1.1.4.10

Raise $8$ to the power of $3$ .

$- 5 (8 x^{3} + 96 x^{2} + 384 x + 512) + 4$

Step 1.1.5

Apply the distributive property.

$- 5 (8 x^{3}) - 5 (96 x^{2}) - 5 (384 x) - 5 \cdot 512 + 4$

Step 1.1.6

Simplify.

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Step 1.1.6.1

Multiply $8$ by $- 5$ .

$- 40 x^{3} - 5 (96 x^{2}) - 5 (384 x) - 5 \cdot 512 + 4$

Step 1.1.6.2

Multiply $96$ by $- 5$ .

$- 40 x^{3} - 480 x^{2} - 5 (384 x) - 5 \cdot 512 + 4$

Step 1.1.6.3

Multiply $384$ by $- 5$ .

$- 40 x^{3} - 480 x^{2} - 1920 x - 5 \cdot 512 + 4$

Step 1.1.6.4

Multiply $- 5$ by $512$ .

$- 40 x^{3} - 480 x^{2} - 1920 x - 2560 + 4$

Step 1.2

Add $- 2560$ and $4$ .

$- 40 x^{3} - 480 x^{2} - 1920 x - 2556$

Step 2

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- 40 x^{3} \to 3$

$- 480 x^{2} \to 2$

$- 1920 x \to 1$

$- 2556 \to 0$

Step 3

The largest exponent is the degree of the polynomial.

$3$