Algebra Examples

$f (x) = {(x - 2)}^{5}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Use the Binomial Theorem.

$x^{5} + 5 x^{4} \cdot - 2 + 10 x^{3} {(- 2)}^{2} + 10 x^{2} {(- 2)}^{3} + 5 x {(- 2)}^{4} + {(- 2)}^{5}$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $- 2$ by $5$ .

$x^{5} - 10 x^{4} + 10 x^{3} {(- 2)}^{2} + 10 x^{2} {(- 2)}^{3} + 5 x {(- 2)}^{4} + {(- 2)}^{5}$

Step 1.2.2

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

$x^{5} - 10 x^{4} + 10 x^{3} \cdot 4 + 10 x^{2} {(- 2)}^{3} + 5 x {(- 2)}^{4} + {(- 2)}^{5}$

Step 1.2.3

Multiply $4$ by $10$ .

$x^{5} - 10 x^{4} + 40 x^{3} + 10 x^{2} {(- 2)}^{3} + 5 x {(- 2)}^{4} + {(- 2)}^{5}$

Step 1.2.4

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

$x^{5} - 10 x^{4} + 40 x^{3} + 10 x^{2} \cdot - 8 + 5 x {(- 2)}^{4} + {(- 2)}^{5}$

Step 1.2.5

Multiply $- 8$ by $10$ .

$x^{5} - 10 x^{4} + 40 x^{3} - 80 x^{2} + 5 x {(- 2)}^{4} + {(- 2)}^{5}$

Step 1.2.6

Raise $- 2$ to the power of $4$ .

$x^{5} - 10 x^{4} + 40 x^{3} - 80 x^{2} + 5 x \cdot 16 + {(- 2)}^{5}$

Step 1.2.7

Multiply $16$ by $5$ .

$x^{5} - 10 x^{4} + 40 x^{3} - 80 x^{2} + 80 x + {(- 2)}^{5}$

Step 1.2.8

Raise $- 2$ to the power of $5$ .

$x^{5} - 10 x^{4} + 40 x^{3} - 80 x^{2} + 80 x - 32$

Step 2

The largest exponent is the degree of the polynomial.

$5$