f(x)=-x3+3×2+6x-8

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

Multiply (-x3)⋅-1.

Multiply -1 by -1.

f(x)=1×3+3×2⋅-1+6x⋅-1+(-8)⋅-1

Multiply x3 by 1.

f(x)=x3+3×2⋅-1+6x⋅-1+(-8)⋅-1

f(x)=x3+3×2⋅-1+6x⋅-1+(-8)⋅-1

Multiply -1 by 3.

f(x)=x3-3×2+6x⋅-1+(-8)⋅-1

Multiply -1 by 6.

f(x)=x3-3×2-6x+(-8)⋅-1

Multiply -8 by -1.

f(x)=x3-3×2-6x+8

f(x)=x3-3×2-6x+8

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

-3,-6,8

Arrange the terms in ascending order.

b1=|-3|,|-6|,|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 0 and 8 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 -3 and 0 is 3.

b2=3+|-6|+|8|

The absolute value is the distance between a number and zero. The distance between -6 and 0 is 6.

b2=3+6+|8|

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

b2=3+6+8

b2=3+6+8

Simplify by adding numbers.

Add 3 and 6.

b2=9+8

Add 9 and 8.

b2=17

b2=17

Arrange the terms in ascending order.

b2=1,17

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

b2=17

b2=17

Take the smaller bound option between b1=9 and b2=17.

Smaller Bound: 9

Every real root on f(x)=-x3+3×2+6x-8 lies between -9 and 9.

-9 and 9

Find the Bounds of the Zeros f(x)=-x^3+3x^2+6x-8