1. > 0 is always POSITIVE
< 0 is always NEGATIVE
The sign on the leading coefficient is the sign of the RHB.
Once the regions are labeled, shaded the desired regions by the inequality symbol.

2. + – + – + POSITIVE Factor by grouping. -6 -2 2
Use the sign of the leading term and place it at the RHB.
Signs alternate for every x.
Solve for x. x = -6, -2, 2
Shade the desired regions…Positive
Plot the solutions on the number line in numerical order.
Write the interval notation.

3. + – + – + POSITIVE Factor by grouping. -1 1 1
Use the sign of the leading term and place it at the RHB.
Signs alternate for every x.
Solve for x. x = 1, -1, 1
Shade the desired regions…Positive
Plot the solutions on the number line in numerical order.
Write the interval notation.
IT DOESN’T MATTER THAT THERE ARE TWO 1’S LISTED, PLOT BOTH!

4. + – + – + -3 -2 2 3 Divide everything by -1. POSITIVE
If we always make the leading term, then the RHB is positive and better for factoring. -3 -2 2 3
We also know that the degree of the leading term will tell us that there are at most 4 solutions, so make the tick marks, points, and alternate signs. -3 -2 2 3
We also know what regions to shade, it will be positive, so shade positive.
We should also write out the interval notation with blanks and fill them in when we find the solutions.
GO SOLVE FOR X!

5. – + – + Divide everything by -1. POSITIVE
If we always make the leading term, then the RHB is positive and better for factoring.
We also know that the degree of the leading term will tell us that there are at most 3 solutions, so make the tick marks, points, and alternate signs.
We also know what regions to shade, it will be positive, so shade positive.
We should also write out the interval notation with blanks and fill them in when we find the solutions.
GO SOLVE FOR X!

6. – + – + -2 1 3 Already factored. x = 3, -2, 1
Always graph open circles 1st.
NEGATIVE – + – +
When working with rational functions, fractions, make sure that there is just ONE fraction one the left side and ZERO on the right side. -2 1 3 -2 1 3
We count the number of factors for the tick marks. It is very important to understand that the factors from the bottom are graphed as open circles! Only the top factors will be closed circles if there is an equal to line.
To find the RHB, check every x term for negative signs. Odd negatives = negative, while even negatives = positive

7. + – + – + -1 1 POSITIVE x = 2, 2 Factor.
Always graph open circles 1st.
x = -1, 1 + – + – +
We count the number of factors for the tick marks. It is very important to understand that the factors from the bottom are graphed as open circles! Only the top factors will be closed circles if there is an equal to line. -1 1 2 2
We will need to adjust the graph because there is no space between the two positive 2’s. Squeeze the 2’s together.
To find the RHB, check every x term for negative signs. Odd negatives = negative, while even negatives = positive -1 1

8. + – + -8 -2 We need ZERO on the right side.
Always graph open circles 1st.
We need to turn the left side into one fraction. Get Common Denominators. + – + -8 -2 -8 -2
Multiply by -1 to both sides.
Flip symbol.
x = -8
x = -2
NEGATIVE

9. – + – + -7 -1 3 We need ZERO on the right side.
Always graph open circles 1st.
We need to turn the left side into one fraction. Get Common Denominators. – + – + -7 -1 3 -7 -1 3
x = -7
x = -1, 3
POSITIVE

10. + – + – + -1 1 2 Factor. Always graph open circles 1st.
Factor out -1 as GCF. + – + – + -1 1 2
Multiply both sides by -1 and flip inequality symbol. -1 1 2
x = 0, 2
x = -1, 1
POSITIVE
x2 + 1 can’t = 0, so there are no x-intercepts to graph for this factor.