Pre-Algebra Examples

$- 1 - 17$

Step 1

Write $- 1 - 17$ as a function.

$f (x) = - 1 - 17$

Step 2

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

Largest Degree: $0$

Leading Coefficient: $- 1$

Step 3

The leading coefficient needs to be $1$ . If it is not, divide the expression by it to make it $1$ .

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Step 3.1

Combine the numerators over the common denominator.

$f (x) = \frac{- 1 - 17}{- 1}$

Step 3.2

Subtract $17$ from $- 1$ .

$f (x) = \frac{- 18}{- 1}$

Step 3.3

Divide $- 18$ by $- 1$ .

$f (x) = 18$

Step 4

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

Largest Degree: $0$

Leading Coefficient: $- 17$

Step 5

Move the negative in front of the fraction.

$f (x) = - \frac{18}{17}$

Step 6

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

$0$

Step 7

There will be two bound options, $b_{1}$ and $b_{2}$ , 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 $1$ .

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Step 7.1

Arrange the terms in ascending order.

$b_{1} = 0$

Step 7.2

Add $0$ and $1$ .

$b_{1} = 1$

Step 8

To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than $1$ , use that number. If not, use $1$ .

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Step 8.1

Arrange the terms in ascending order.

$b_{2} = 0, 1$

Step 8.2

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

$b_{2} = 1$

Step 9

The bound options are the same.

Bound: $1$

Step 10

Every real root on $f (x) = - 1 - 17$ lies between $- 1$ and $1$ .

$- 1$ and $1$