# Find the Bounds of the Zeros w(x)=x^3+216

w(x)=x3+216
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree: 3
Create a list of the coefficients of the function except the leading coefficient of 1.
216
There will be two bound options, b1 and b2, 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 1.
Arrange the terms in ascending order.
b1=|216|
The absolute value is the distance between a number and zero. The distance between 0 and 216 is 216.
b1=216+1
b1=217
b1=217
To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than 1, use that number. If not, use 1.
The absolute value is the distance between a number and zero. The distance between 0 and 216 is 216.
b2=216
Arrange the terms in ascending order.
b2=1,216
The maximum value is the largest value in the arranged data set.
b2=216
b2=216
Take the smaller bound option between b1=217 and b2=216.
Smaller Bound: 216
Every real root on w(x)=x3+216 lies between -216 and 216.
-216 and 216
Find the Bounds of the Zeros w(x)=x^3+216