p(x)=x3+7×2-8x-5

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.

7,-8,-5

Arrange the terms in ascending order.

b1=|-5|,|7|,|-8|

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

b1=|-8|

The absolute value is the distance between a number and zero. The distance between -8 and 0 is 8.

b1=8+1

Add 8 and 1.

b1=9

b1=9

Simplify each term.

The absolute value is the distance between a number and zero. The distance between 0 and 7 is 7.

b2=7+|-8|+|-5|

The absolute value is the distance between a number and zero. The distance between -8 and 0 is 8.

b2=7+8+|-5|

The absolute value is the distance between a number and zero. The distance between -5 and 0 is 5.

b2=7+8+5

b2=7+8+5

Simplify by adding numbers.

Add 7 and 8.

b2=15+5

Add 15 and 5.

b2=20

b2=20

Arrange the terms in ascending order.

b2=1,20

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

b2=20

b2=20

Take the smaller bound option between b1=9 and b2=20.

Smaller Bound: 9

Every real root on p(x)=x3+7×2-8x-5 lies between -9 and 9.

-9 and 9

Find the Bounds of the Zeros p(x)=x^3+7x^2-8x-5