Algebra Examples

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

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 each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.1.3

Multiply $- 5$ by $2$ .

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

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

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

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Step 1.1.4.1.1

Move $x$ .

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

Step 1.1.4.1.2

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

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Step 1.1.4.1.2.1

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

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

Step 1.1.4.1.2.2

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

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

Step 1.1.4.1.3

Add $1$ and $2$ .

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

Step 1.1.4.2

Multiply $2$ by $3$ .

$4 x + 6 x^{3} - 10 x^{2}$

Step 1.2

Move $4 x$ .

$6 x^{3} - 10 x^{2} + 4 x$

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.

$6 x^{3} \to 3$

$- 10 x^{2} \to 2$

$4 x \to 1$

Step 2.2

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$6 x^{3}$

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.

$6 x^{3}$

Step 4.2

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

$6$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $6 x^{3}$

Leading Coefficient: $6$