Find the Degree x(x-4)(x+5)(x-1)=0

$x (x - 4) (x + 5) (x - 1) = 0$

Simplify and reorder the polynomial.

Simplify by multiplying through.

Apply the distributive property.

$(x \cdot x + x \cdot - 4) (x + 5) (x - 1)$

Simplify the expression.

Multiply $x$ by $x$ .

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

Move $- 4$ to the left of $x$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $5$ to the left of $x^{2}$ .

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $- 4$ .

$(x^{3} + 5 x^{2} - 4 x^{2} - 20 x) (x - 1)$

Subtract $4 x^{2}$ from $5 x^{2}$ .

$(x^{3} + x^{2} - 20 x) (x - 1)$

Expand $(x^{3} + x^{2} - 20 x) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$x^{3} x + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Simplify terms.

Simplify each term.

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

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

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

$x^{3} x^{1} + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

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

$x^{3 + 1} + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Add $3$ and $1$ .

$x^{4} + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Move $- 1$ to the left of $x^{3}$ .

$x^{4} - 1 \cdot x^{3} + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Rewrite $- 1 x^{3}$ as $- x^{3}$ .

$x^{4} - x^{3} + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

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

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

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

$x^{4} - x^{3} + x^{2} x^{1} + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

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

$x^{4} - x^{3} + x^{2 + 1} + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Add $2$ and $1$ .

$x^{4} - x^{3} + x^{3} + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Move $- 1$ to the left of $x^{2}$ .

$x^{4} - x^{3} + x^{3} - 1 \cdot x^{2} - 20 x \cdot x - 20 x \cdot - 1$

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 x \cdot x - 20 x \cdot - 1$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 (x \cdot x) - 20 x \cdot - 1$

Multiply $x$ by $x$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 x^{2} - 20 x \cdot - 1$

Multiply $- 1$ by $- 20$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 x^{2} + 20 x$

Simplify by adding terms.

Combine the opposite terms in $x^{4} - x^{3} + x^{3} - x^{2} - 20 x^{2} + 20 x$ .

Add $- x^{3}$ and $x^{3}$ .

$x^{4} + 0 - x^{2} - 20 x^{2} + 20 x$

Add $x^{4}$ and $0$ .

$x^{4} - x^{2} - 20 x^{2} + 20 x$

Subtract $20 x^{2}$ from $- x^{2}$ .

$x^{4} - 21 x^{2} + 20 x$

The largest exponent is the degree of the polynomial.

$4$

Find the Degree x(x-4)(x+5)(x-1)=0

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