f(x)=x3+x2-72

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

Largest Degree: 3

Leading Coefficient: 1

Create a list of the coefficients of the function except the leading coefficient of 1.

1,-72

Arrange the terms in ascending order.

b1=|1|,|-72|

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

b1=|-72|

The absolute value is the distance between a number and zero. The distance between -72 and 0 is 72.

b1=72+1

Add 72 and 1.

b1=73

b1=73

Simplify each term.

The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1.

b2=1+|-72|

The absolute value is the distance between a number and zero. The distance between -72 and 0 is 72.

b2=1+72

b2=1+72

Add 1 and 72.

b2=73

Arrange the terms in ascending order.

b2=1,73

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

b2=73

b2=73

The bound options are the same.

Bound: 73

Every real root on f(x)=x3+x2-72 lies between -73 and 73.

-73 and 73

Find the Bounds of the Zeros f(x)=x^3+x^2-72