-4×3+9×2+3x-6

Write the polynomial as a function of x.

f(x)=-4×3+9×2+3x-6

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

Largest Degree: 3

Leading Coefficient: -4

Cancel the common factor of -4.

Cancel the common factor.

f(x)=-4×3-4+9×2-4+3x-4+-6-4

Divide x3 by 1.

f(x)=x3+9×2-4+3x-4+-6-4

f(x)=x3+9×2-4+3x-4+-6-4

Move the negative in front of the fraction.

f(x)=x3-9×24+3x-4+-6-4

Move the negative in front of the fraction.

f(x)=x3-9×24-3×4+-6-4

Cancel the common factor of -6 and -4.

Factor -2 out of -6.

f(x)=x3-9×24-3×4+-2⋅3-4

Cancel the common factors.

Factor -2 out of -4.

f(x)=x3-9×24-3×4+-2⋅3-2⋅2

Cancel the common factor.

f(x)=x3-9×24-3×4+-2⋅3-2⋅2

Rewrite the expression.

f(x)=x3-9×24-3×4+32

f(x)=x3-9×24-3×4+32

f(x)=x3-9×24-3×4+32

f(x)=x3-9×24-3×4+32

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

-94,-34,32

Arrange the terms in ascending order.

b1=|-34|,|32|,|-94|

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

b1=|-94|

-94 is approximately -2.25 which is negative so negate -94 and remove the absolute value

b1=94+1

Write 1 as a fraction with a common denominator.

b1=94+44

Combine the numerators over the common denominator.

b1=9+44

Add 9 and 4.

b1=134

b1=134

Simplify each term.

-94 is approximately -2.25 which is negative so negate -94 and remove the absolute value

b2=94+|-34|+|32|

-34 is approximately -0.75 which is negative so negate -34 and remove the absolute value

b2=94+34+|32|

32 is approximately 1.5 which is positive so remove the absolute value

b2=94+34+32

b2=94+34+32

Combine fractions.

Combine fractions with similar denominators.

b2=9+34+32

Simplify the expression.

Add 9 and 3.

b2=124+32

Divide 12 by 4.

b2=3+32

b2=3+32

b2=3+32

To write 3 as a fraction with a common denominator, multiply by 22.

b2=3⋅22+32

Combine 3 and 22.

b2=3⋅22+32

Combine the numerators over the common denominator.

b2=3⋅2+32

Simplify the numerator.

Multiply 3 by 2.

b2=6+32

Add 6 and 3.

b2=92

b2=92

Arrange the terms in ascending order.

b2=1,92

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

b2=92

b2=92

Take the smaller bound option between b1=134 and b2=92.

Smaller Bound: 134

Every real root on f(x)=-4×3+9×2+3x-6 lies between -134 and 134.

-134 and 134

Find the Bounds of the Zeros -4x^3+9x^2+3x-6