Algebra Examples

$(18 x^{3} + 12 x^{2} - 3 x) \div 6 x^{2}$

Step 1

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

Tap for more steps...

Step 1.1

Factor $3 x$ out of $18 x^{3} + 12 x^{2} - 3 x$ .

Tap for more steps...

Step 1.1.1

Factor $3 x$ out of $18 x^{3}$ .

$(3 x (6 x^{2}) + 12 x^{2} - 3 x) \div 6 x^{2}$

Step 1.1.2

Factor $3 x$ out of $12 x^{2}$ .

$(3 x (6 x^{2}) + 3 x (4 x) - 3 x) \div 6 x^{2}$

Step 1.1.3

Factor $3 x$ out of $- 3 x$ .

$(3 x (6 x^{2}) + 3 x (4 x) + 3 x (- 1)) \div 6 x^{2}$

Step 1.1.4

Factor $3 x$ out of $3 x (6 x^{2}) + 3 x (4 x)$ .

$(3 x (6 x^{2} + 4 x) + 3 x (- 1)) \div 6 x^{2}$

Step 1.1.5

Factor $3 x$ out of $3 x (6 x^{2} + 4 x) + 3 x (- 1)$ .

$3 x (6 x^{2} + 4 x - 1) \div 6 x^{2}$

Step 1.2

Rewrite the division as a fraction.

$\frac{3 x (6 x^{2} + 4 x - 1)}{6} x^{2}$

Step 1.3

Cancel the common factor of $3$ and $6$ .

Tap for more steps...

Step 1.3.1

Factor $3$ out of $3 x (6 x^{2} + 4 x - 1)$ .

$\frac{3 (x (6 x^{2} + 4 x - 1))}{6} x^{2}$

Step 1.3.2

Cancel the common factors.

Tap for more steps...

Step 1.3.2.1

Factor $3$ out of $6$ .

$\frac{3 (x (6 x^{2} + 4 x - 1))}{3 \cdot 2} x^{2}$

Step 1.3.2.2

Cancel the common factor.

$\frac{3 (x (6 x^{2} + 4 x - 1))}{3 \cdot 2} x^{2}$

Step 1.3.2.3

Rewrite the expression.

$\frac{x (6 x^{2} + 4 x - 1)}{2} x^{2}$

Step 1.4

Multiply $\frac{x (6 x^{2} + 4 x - 1)}{2} x^{2}$ .

Tap for more steps...

Step 1.4.1

Combine $\frac{x (6 x^{2} + 4 x - 1)}{2}$ and $x^{2}$ .

$\frac{x (6 x^{2} + 4 x - 1) x^{2}}{2}$

Step 1.4.2

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

Tap for more steps...

Step 1.4.2.1

Move $x^{2}$ .

$\frac{x^{2} x (6 x^{2} + 4 x - 1)}{2}$

Step 1.4.2.2

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

Tap for more steps...

Step 1.4.2.2.1

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

$\frac{x^{2} x^{1} (6 x^{2} + 4 x - 1)}{2}$

Step 1.4.2.2.2

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

$\frac{x^{2 + 1} (6 x^{2} + 4 x - 1)}{2}$

Step 1.4.2.3

Add $2$ and $1$ .

$\frac{x^{3} (6 x^{2} + 4 x - 1)}{2}$

Step 2

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$\frac{x^{3} (6 x^{2} + 4 x - 1)}{2}$

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{x^{3} (6 x^{2} + 4 x - 1)}{2}$

Step 4.2

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

$\frac{1}{2}$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $\frac{x^{3} (6 x^{2} + 4 x - 1)}{2}$

Leading Coefficient: $\frac{1}{2}$