Finite Math Examples

Find the Bounds of the Zeros
Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.
Largest Degree:
Leading Coefficient:
Simplify each term.
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Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Create a list of the coefficients of the function except the leading coefficient of .
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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Arrange the terms in ascending order.
The maximum value is the largest value in the arranged data set.
is approximately which is negative so negate and remove the absolute value
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Add and .
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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Simplify each term.
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is approximately which is positive so remove the absolute value
is approximately which is negative so negate and remove the absolute value
Combine the numerators over the common denominator.
Add and .
Arrange the terms in ascending order.
The maximum value is the largest value in the arranged data set.
Take the smaller bound option between and .
Smaller Bound:
Every real root on lies between and .
and
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