Finite Math Examples

$5 z^{7} + 5 z^{6} - \frac{10 (z^{5})}{2} \cdot z^{8} + 8 z^{7} + 8 z^{6}$

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

Cancel the common factor of $10$ and $2$ .

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Step 1.1.1.1

Factor $2$ out of $10 z^{5}$ .

$5 z^{7} + 5 z^{6} - \frac{2 (5 z^{5})}{2} \cdot z^{8} + 8 z^{7} + 8 z^{6}$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $2$ out of $2$ .

$5 z^{7} + 5 z^{6} - \frac{2 (5 z^{5})}{2 (1)} \cdot z^{8} + 8 z^{7} + 8 z^{6}$

Step 1.1.1.2.2

Cancel the common factor.

$5 z^{7} + 5 z^{6} - \frac{2 (5 z^{5})}{2 \cdot 1} \cdot z^{8} + 8 z^{7} + 8 z^{6}$

Step 1.1.1.2.3

Rewrite the expression.

$5 z^{7} + 5 z^{6} - \frac{5 z^{5}}{1} \cdot z^{8} + 8 z^{7} + 8 z^{6}$

Step 1.1.1.2.4

Divide $5 z^{5}$ by $1$ .

$5 z^{7} + 5 z^{6} - (5 z^{5}) \cdot z^{8} + 8 z^{7} + 8 z^{6}$

Step 1.1.2

Multiply $z^{5}$ by $z^{8}$ by adding the exponents.

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Step 1.1.2.1

Move $z^{8}$ .

$5 z^{7} + 5 z^{6} - (5 (z^{8} z^{5})) + 8 z^{7} + 8 z^{6}$

Step 1.1.2.2

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

$5 z^{7} + 5 z^{6} - (5 z^{8 + 5}) + 8 z^{7} + 8 z^{6}$

Step 1.1.2.3

Add $8$ and $5$ .

$5 z^{7} + 5 z^{6} - (5 z^{13}) + 8 z^{7} + 8 z^{6}$

Step 1.1.3

Multiply $5$ by $- 1$ .

$5 z^{7} + 5 z^{6} - 5 z^{13} + 8 z^{7} + 8 z^{6}$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $5 z^{7}$ and $8 z^{7}$ .

$13 z^{7} + 5 z^{6} - 5 z^{13} + 8 z^{6}$

Step 1.2.2

Add $5 z^{6}$ and $8 z^{6}$ .

$13 z^{7} - 5 z^{13} + 13 z^{6}$

Step 2

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

$13 z^{7} \to 7$

$- 5 z^{13} \to 13$

$13 z^{6} \to 6$

Step 3

The largest exponent is the degree of the polynomial.

$13$