Lesson 2.1

In chapter 2.1, we will be able to graph polynomials and solve polynomial inequalities

• Steps
• Determine all the zeroes of the polynomial and their multiplicity. Use the fact above to determine the xx-intercept that corresponds to each zero will cross the xx-axis or just touch it and if the xx-intercept will flatten out or not.
• Determine the yy-intercept, (0,P(0))(0,P(0)).
• Use the leading coefficient test to determine the behavior of the polynomial at the end of the graph.
• Plot a few more points. This is left intentionally vague. The more points that you plot the better the sketch. At the least you should plot at least one at either end of the graph and at least one point between each pair of zeroes.

Steps

1. If solving an equation, put it in standard form with 0 on one side and simplify.
2. Know how many roots to expect.
3. If you’re down to a linear or quadratic equation (degree 1 or 2), solve by inspection or the quadratic formula.
4. Then go to step 7.
5. Find one rational factor or root. This is the hard part, but there are lots of techniques to help you.
6. If you can find a factor or root, continue with step 5 below; if you can’t, go to step 6.
7. Divide by your factor. This leaves you with a new reduced polynomial whose degree is 1 less.
8. For the rest of the problem, you’ll work with the reduced polynomial and not the original. Continue at step 3.
9. If you can’t find a factor or root, turn to numerical methods.
10. Then go to step 7.
11. If this was an equation to solve, write down the roots. If it was a polynomial to factor, write it in factored form, including any constant factors you took out in step 1.

SAT Question