Algebra Examples

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

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Reorder.

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Step 1.1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.1.2.2

Rewrite using the commutative property of multiplication.

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

Step 1.2

Simplify each term.

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Step 1.2.1

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

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Step 1.2.1.1

Move $x^{2}$ .

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

Step 1.2.1.2

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

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

Step 1.2.1.3

Add $2$ and $2$ .

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

Step 1.2.2

Multiply $4$ by $- 2$ .

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

Step 1.2.3

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 1.2.3.1

Move $x^{3}$ .

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

Step 1.2.3.2

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

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

Step 1.2.3.3

Add $3$ and $2$ .

$- 8 x^{4} + 4 \cdot 5 x^{5}$

Step 1.2.4

Multiply $4$ by $5$ .

$- 8 x^{4} + 20 x^{5}$

Step 1.3

Reorder $- 8 x^{4}$ and $20 x^{5}$ .

$20 x^{5} - 8 x^{4}$

Step 2

The degree of a polynomial is the highest degree of its terms.

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Step 2.1

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

$20 x^{5} \to 5$

$- 8 x^{4} \to 4$

Step 2.2

The largest exponent is the degree of the polynomial.

$5$

Step 3

The leading term in a polynomial is the term with the highest degree.

$20 x^{5}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

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Step 4.1

The leading term in a polynomial is the term with the highest degree.

$20 x^{5}$

Step 4.2

The leading coefficient in a polynomial is the coefficient of the leading term.

$20$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $20 x^{5}$

Leading Coefficient: $20$