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. Solve for x. x = -6, -2, 2 Plot the solutions on the number line in numerical order. -6-22 +– + –+ Use the sign of the leading term and place it at the RHB. Signs alternate for every x. Shade the desired regions…Positive Write the interval notation.

3. POSITIVE Factor by grouping. Solve for x. x = 1, -1, 1 Plot the solutions on the number line in numerical order. 11 +– + –+ Use the sign of the leading term and place it at the RHB. Signs alternate for every x. Shade the desired regions…Positive Write the interval notation. IT DOESN’T MATTER THAT THERE ARE TWO 1’S LISTED, PLOT BOTH!

4. -323 If we always make the leading term, then the RHB is positive and better for factoring. POSITIVE +–+–+ Divide everything by -1. -2 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. 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! -323-2

5. If we always make the leading term, then the RHB is positive and better for factoring. POSITIVE +––+ Divide everything by -1. 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. 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 When working with rational functions, fractions, make sure that there is just ONE fraction one the left side and ZERO on the right side. NEGATIVE +––+ Already factored. -231 3 1 x = 3, -2, 1Always graph open circles 1 st.

7. 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 Factor. POSITIVE +––+ 21 1 Always graph open circles 1 st. x = 2, 2 x = -1, 1 + 2 We will need to adjust the graph because there is no space between the two positive 2’s. Squeeze the 2’s together.

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

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

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