# Algebra Examples

Step 1

Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.

Largest Degree:

Leading Coefficient:

Step 2

Step 2.1

Cancel the common factor of .

Step 2.1.1

Cancel the common factor.

Step 2.1.2

Divide by .

Step 2.2

Cancel the common factor of and .

Step 2.2.1

Factor out of .

Step 2.2.2

Cancel the common factors.

Step 2.2.2.1

Factor out of .

Step 2.2.2.2

Cancel the common factor.

Step 2.2.2.3

Rewrite the expression.

Step 2.3

Cancel the common factor of and .

Step 2.3.1

Factor out of .

Step 2.3.2

Cancel the common factors.

Step 2.3.2.1

Factor out of .

Step 2.3.2.2

Cancel the common factor.

Step 2.3.2.3

Rewrite the expression.

Step 2.4

Move the negative in front of the fraction.

Step 3

Create a list of the coefficients of the function except the leading coefficient of .

Step 4

Step 4.1

Arrange the terms in ascending order.

Step 4.2

The maximum value is the largest value in the arranged data set.

Step 4.3

is approximately which is negative so negate and remove the absolute value

Step 4.4

Write as a fraction with a common denominator.

Step 4.5

Combine the numerators over the common denominator.

Step 4.6

Add and .

Step 5

Step 5.1

Simplify each term.

Step 5.1.1

is approximately which is positive so remove the absolute value

Step 5.1.2

is approximately which is negative so negate and remove the absolute value

Step 5.2

Combine fractions.

Step 5.2.1

Combine the numerators over the common denominator.

Step 5.2.2

Add and .

Step 5.3

Arrange the terms in ascending order.

Step 5.4

The maximum value is the largest value in the arranged data set.

Step 6

Take the smaller bound option between and .

Smaller Bound:

Step 7

Every real root on lies between and .

and