1. Long Division of Polynomials A different way to factor (7.5)

2. SAT Prep Quick poll! 1.

3. SAT Prep Quick poll! 2.

4. SAT Prep Quick poll! 3.

5. POD Factor: x 2 – x – 12 Can you use that pattern to factor this one completely? x 4 – x 2 – 12

6. Pattern review Difference of squares: a 2 – b 2 = (a + b)(a - b) Difference of cubes: a 3 – b 3 = (a - b)(a 2 + ab + b 2 ) Sum of cubes: a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) Factoring by grouping (split the middle term) If the discriminant is a perfect square, then the quadratic trinomial can be factored.

7. Factoring and division If then So, what is ? What are the remainders with these? What does that mean?

8. Division with a remainder We can divide polynomials, even if we get a remainder that isn’t zero. In that case, we don’t factor, but do something called long division of polynomials. It’s a lot like long division of numbers.

9. Division with a remainder First, let’s review the following terms, and do a simple long division problem. dividend divisor remainder quotient

10. Division with a remainder Here’s how it works for polynomials. becomes The tricky part to keep straight is what is positive and negative. A remainder of 0 means we have factors.

11. Try another Use the same technique here.

12. Try another This time the divisor is not linear, but the process is the same.

13. Try another You may find this result familiar.

14. A shortcut When the divisor is linear, we can use something called synthetic division to find a quick answer. What was our answer before? How does it compare to these numbers?

15. Shortcut again Try it with this one. Watch for spacers!