p(x)=-x3+6×2-4x+2

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.

p(x)=1×3+6×2⋅-1+(-4x)⋅-1+2⋅-1

Multiply x3 by 1.

p(x)=x3+6×2⋅-1+(-4x)⋅-1+2⋅-1

p(x)=x3+6×2⋅-1+(-4x)⋅-1+2⋅-1

Multiply -1 by 6.

p(x)=x3-6×2+(-4x)⋅-1+2⋅-1

Multiply -1 by -4.

p(x)=x3-6×2+4x+2⋅-1

Multiply 2 by -1.

p(x)=x3-6×2+4x-2

p(x)=x3-6×2+4x-2

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

-6,4,-2

Arrange the terms in ascending order.

b1=|-2|,|4|,|-6|

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

b1=|-6|

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

b1=6+1

Add 6 and 1.

b1=7

b1=7

Simplify each term.

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

b2=6+|4|+|-2|

The absolute value is the distance between a number and zero. The distance between 0 and 4 is 4.

b2=6+4+|-2|

The absolute value is the distance between a number and zero. The distance between -2 and 0 is 2.

b2=6+4+2

b2=6+4+2

Simplify by adding numbers.

Add 6 and 4.

b2=10+2

Add 10 and 2.

b2=12

b2=12

Arrange the terms in ascending order.

b2=1,12

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

b2=12

b2=12

Take the smaller bound option between b1=7 and b2=12.

Smaller Bound: 7

Every real root on p(x)=-x3+6×2-4x+2 lies between -7 and 7.

-7 and 7

Find the Bounds of the Zeros p(x)=-x^3+6x^2-4x+2