# Finite Math Examples

Find the Bounds of the Zeros
Step 1
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree:
Step 2
Simplify each term.
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
Divide by .
Step 3
Create a list of the coefficients of the function except the leading coefficient of .
Step 4
There will be two bound options, and , the smaller of which is the answer. To calculate the first bound option, find the absolute value of the largest coefficient from the list of coefficients. Then add .
Step 4.1
Arrange the terms in ascending order.
Step 4.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.3
Step 5
To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than , use that number. If not, use .
Step 5.1
The absolute value is the distance between a number and zero. The distance between and is .
Step 5.2
Arrange the terms in ascending order.
Step 5.3
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