p(x)=6×4+19×3+24×2+24x+8

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

Largest Degree: 4

Leading Coefficient: 6

Cancel the common factor of 6.

Cancel the common factor.

p(x)=6×46+19×36+24×26+24×6+86

Divide x4 by 1.

p(x)=x4+19×36+24×26+24×6+86

p(x)=x4+19×36+24×26+24×6+86

Cancel the common factor of 24 and 6.

Factor 6 out of 24×2.

p(x)=x4+19×36+6(4×2)6+24×6+86

Cancel the common factors.

Factor 6 out of 6.

p(x)=x4+19×36+6(4×2)6(1)+24×6+86

Cancel the common factor.

p(x)=x4+19×36+6(4×2)6⋅1+24×6+86

Rewrite the expression.

p(x)=x4+19×36+4×21+24×6+86

Divide 4×2 by 1.

p(x)=x4+19×36+4×2+24×6+86

p(x)=x4+19×36+4×2+24×6+86

p(x)=x4+19×36+4×2+24×6+86

Cancel the common factor of 24 and 6.

Factor 6 out of 24x.

p(x)=x4+19×36+4×2+6(4x)6+86

Cancel the common factors.

Factor 6 out of 6.

p(x)=x4+19×36+4×2+6(4x)6(1)+86

Cancel the common factor.

p(x)=x4+19×36+4×2+6(4x)6⋅1+86

Rewrite the expression.

p(x)=x4+19×36+4×2+4×1+86

Divide 4x by 1.

p(x)=x4+19×36+4×2+4x+86

p(x)=x4+19×36+4×2+4x+86

p(x)=x4+19×36+4×2+4x+86

Cancel the common factor of 8 and 6.

Factor 2 out of 8.

p(x)=x4+19×36+4×2+4x+2(4)6

Cancel the common factors.

Factor 2 out of 6.

p(x)=x4+19×36+4×2+4x+2⋅42⋅3

Cancel the common factor.

p(x)=x4+19×36+4×2+4x+2⋅42⋅3

Rewrite the expression.

p(x)=x4+19×36+4×2+4x+43

p(x)=x4+19×36+4×2+4x+43

p(x)=x4+19×36+4×2+4x+43

p(x)=x4+19×36+4×2+4x+43

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

196,4,4,43

Arrange the terms in ascending order.

b1=|43|,|196|,|4|,|4|

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

b1=|4|

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

b1=4+1

Add 4 and 1.

b1=5

b1=5

Simplify each term.

196 is approximately 3.16‾ which is positive so remove the absolute value

b2=196+|4|+|4|+|43|

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

b2=196+4+|4|+|43|

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

b2=196+4+4+|43|

43 is approximately 1.3‾ which is positive so remove the absolute value

b2=196+4+4+43

b2=196+4+4+43

Find the common denominator.

Write 4 as a fraction with denominator 1.

b2=196+41+4+43

Multiply 41 by 66.

b2=196+41⋅66+4+43

Multiply 41 and 66.

b2=196+4⋅66+4+43

Write 4 as a fraction with denominator 1.

b2=196+4⋅66+41+43

Multiply 41 by 66.

b2=196+4⋅66+41⋅66+43

Multiply 41 and 66.

b2=196+4⋅66+4⋅66+43

Multiply 43 by 22.

b2=196+4⋅66+4⋅66+43⋅22

Combine.

b2=196+4⋅66+4⋅66+4⋅23⋅2

Reorder the factors of 3⋅2.

b2=196+4⋅66+4⋅66+4⋅22⋅3

Multiply 2 by 3.

b2=196+4⋅66+4⋅66+4⋅26

b2=196+4⋅66+4⋅66+4⋅26

Combine fractions.

Combine fractions with similar denominators.

b2=19+4⋅6+4⋅6+4⋅26

Multiply.

Multiply 4 by 6.

b2=19+24+4⋅6+4⋅26

Multiply 4 by 6.

b2=19+24+24+4⋅26

Multiply 4 by 2.

b2=19+24+24+86

b2=19+24+24+86

b2=19+24+24+86

Simplify the numerator.

Add 19 and 24.

b2=43+24+86

Add 43 and 24.

b2=67+86

Add 67 and 8.

b2=756

b2=756

Cancel the common factor of 75 and 6.

Factor 3 out of 75.

b2=3(25)6

Cancel the common factors.

Factor 3 out of 6.

b2=3⋅253⋅2

Cancel the common factor.

b2=3⋅253⋅2

Rewrite the expression.

b2=252

b2=252

b2=252

Arrange the terms in ascending order.

b2=1,252

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

b2=252

b2=252

Take the smaller bound option between b1=5 and b2=252.

Smaller Bound: 5

Every real root on p(x)=6×4+19×3+24×2+24x+8 lies between -5 and 5.

-5 and 5

Find the Bounds of the Zeros p(x)=6x^4+19x^3+24x^2+24x+8