Pre-Algebra Examples

Find the Bounds of the Zeros 3x(x+7)
Step 1
Write as a function.
Step 2
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree:
Leading Coefficient:
Step 3
The leading coefficient needs to be . If it is not, divide the expression by it to make it .
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Step 3.1
Cancel the common factor of .
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Step 3.1.1
Cancel the common factor.
Step 3.1.2
Divide by .
Step 3.2
Apply the distributive property.
Step 3.3
Multiply by .
Step 3.4
Move to the left of .
Step 4
Create a list of the coefficients of the function except the leading coefficient of .
Step 5
There will be two bound options, and , the smaller of which is the answer. To calculate the first bound option, find the absolute value of the largest coefficient from the list of coefficients. Then add .
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Step 5.1
Arrange the terms in ascending order.
Step 5.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 5.3
Add and .
Step 6
To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than , use that number. If not, use .
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Step 6.1
The absolute value is the distance between a number and zero. The distance between and is .
Step 6.2
Arrange the terms in ascending order.
Step 6.3
The maximum value is the largest value in the arranged data set.
Step 7
Take the smaller bound option between and .
Smaller Bound:
Step 8
Every real root on lies between and .
and