3x(x+7)

Write the polynomial as a function of x.

f(x)=3x(x+7)

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

Largest Degree: 2

Leading Coefficient: 3

Cancel the common factor of 3.

Cancel the common factor.

f(x)=3x(x+7)3

Divide x(x+7) by 1.

f(x)=x(x+7)

f(x)=x(x+7)

Apply the distributive property.

f(x)=x⋅x+x⋅7

Simplify the expression.

Multiply x by x.

f(x)=x2+x⋅7

Move 7 to the left of x.

f(x)=x2+7x

f(x)=x2+7x

f(x)=x2+7x

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

7

Arrange the terms in ascending order.

b1=|7|

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

b1=7+1

Add 7 and 1.

b1=8

b1=8

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

b2=7

Arrange the terms in ascending order.

b2=1,7

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

b2=7

b2=7

Take the smaller bound option between b1=8 and b2=7.

Smaller Bound: 7

Every real root on f(x)=3x(x+7) lies between -7 and 7.

-7 and 7

Find the Bounds of the Zeros 3x(x+7)