1. Warm Ups: 1) (4x3 + 2x2 + 1) – (x2 + x – 5)
Factor:
4) 13t + 39y 5) x2 - 25

2. Warm Up:
Divide by hand (NO CALCULATORS!!!!!!):
1) ) 16

3. 4.3 Notes: Polynomial Long Division

4. Dividing polynomials is a lot like dividing regular numbers, except we have variables mixed in. 
Remember: When dividing, the exponents subtract. When adding or subtracting, exponents don’t change. Make sure you are combining like terms!

5. Dividing whole numbers: Dividing Polynomials:

7. More practice:
(4x4 + 2x3 – 9x2 – 36) ÷ (x2 + x – 4)

8. (2x3 – 5x2 + 3) ÷ (x + 1)

10. Warm Up Factor: 1) 3k2 – 3k 2) n2 – 13n + 22 3) 3x2 + 30x + 63 Divide:
4) (x3 + x2 – 9x – 6) ÷ (x2 – 9) 5) (x3 – 2x + 6) ÷ (x + 3)

11. Warm Up: Perform the following operations: 1) (x2 – 6x + 4)÷ (x + 1)
2) (3x4 – 5x3 + 3x + 2x2 – 2) ÷ (x – 2) >>>Careful!!!<<<

12. Synthetic Division:
There is a shortcut to long division, but it only works sometimes. How do we know if we can use the shortcut?
The form must be “x – a” or “ x + a” for the divisor (the polynomial you are dividing by).
> Another way to say this is the divisor must be 1 x to the first power.

13. Steps:
1. Check that the divisor is in the proper form (one x to the first power)
2. Check that the dividend (polynomial we are dividing) is in STANDARD FORM, and ALL exponent values MUST be represented from the highest exponent to no variable! (We can always add 0, as many as we need).
3. Use only the coefficients and the constant (last value with no variable), then the opposite value of the divisor.
4. Separate the last digit from the group, this will represent the remainder.
5. Drop down the first value in the dividend, multiply it by the divisor, then add it to the second value. This continues until we reach the end (multiply below the line, add above).
6.Once finished, we re-introduce the variables to our final values. This is our answer!

14. Let’s Try It:
A. (x3 + 4x2 – 5x + 5) ÷ (x – 3) B. (5x3 + 6x + 8) ÷ (x + 2)

15. HW: p #11 – 18,

16. Warm Up: Perform the following operations:
1) (10x4 + 4x2 + 5x3 – 9) ÷ (x + 1)
2) (2x4 + 2x3 – 10x – 9) ÷ (x3 + x2 – 5)

17. Quiz Review Warm Up: (use Friday box too)
Perform the following operations:
1) (4x3 + 2x2 + 1) – (x2 + x – 5) ) (-x2 + x + 4)(2x2 – x + 1)
3) (4x3 + 2x2 + 1) + (x2 + x – 5) ) (8x2 + 34x – 1) ÷ (4x – 1)
5) (x4 + 4x3 + 16x – 35) ÷ (x + 5)
Factor:
6) 7) 8) 9)