Find the Degree f(x)=-2x^3(x-1)(x+5)

$f (x) = - 2 x^{3} (x - 1) (x + 5)$

Step 1

Simplify and reorder the polynomial.

Apply the distributive property.

$(- 2 x^{3} x - 2 x^{3} \cdot - 1) (x + 5)$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$(- 2 (x \cdot x^{3}) - 2 x^{3} \cdot - 1) (x + 5)$

Multiply $x$ by $x^{3}$ .

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

$(- 2 (x^{1} x^{3}) - 2 x^{3} \cdot - 1) (x + 5)$

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

$(- 2 x^{1 + 3} - 2 x^{3} \cdot - 1) (x + 5)$

Add $1$ and $3$ .

$(- 2 x^{4} - 2 x^{3} \cdot - 1) (x + 5)$

Multiply $- 1$ by $- 2$ .

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

Expand $(- 2 x^{4} + 2 x^{3}) (x + 5)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{4}$ .

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

$- 2 (x^{1} x^{4}) - 2 x^{4} \cdot 5 + 2 x^{3} x + 2 x^{3} \cdot 5$

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

$- 2 x^{1 + 4} - 2 x^{4} \cdot 5 + 2 x^{3} x + 2 x^{3} \cdot 5$

Add $1$ and $4$ .

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

Multiply $5$ by $- 2$ .

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

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{3}$ .

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

$- 2 x^{5} - 10 x^{4} + 2 (x^{1} x^{3}) + 2 x^{3} \cdot 5$

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

$- 2 x^{5} - 10 x^{4} + 2 x^{1 + 3} + 2 x^{3} \cdot 5$

Add $1$ and $3$ .

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

Multiply $5$ by $2$ .

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

Add $- 10 x^{4}$ and $2 x^{4}$ .

$- 2 x^{5} - 8 x^{4} + 10 x^{3}$

Step 2

The largest exponent is the degree of the polynomial.

$5$

Find the Degree f(x)=-2x^3(x-1)(x+5)

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