1. M3D14 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
1. Find the zeros of P(x) = x3 – 4x2 + 2x – 8 and sketch y = P(x).
2. Is (x + 2) a factor of x4 – 13x2 +36 ?
total:

2. 1. Find the zeros of P(x) = x3 – 4x2 + 2x – 8 and sketch y = P(x).+1
(4,0) +1 +1 +1 +1
(0, –8)
+1 graph +1 +1 +1
End behavior:
Be sure to put an inflection point somewhere. +2 +1

3. Yes it is! 2) Is (x + 2) a factor of x4 – 13x2 +36 ?
we need to factor to find out: 36
x4 – 13x2 +36 –9 –4
(x2 – 4)(x2 – 9) +1
–13
(x – 2)(x + 2)(x – 3)(x + 3) +4
Yes it is! +1
total:

4. Long Division of polynomials
Recall how to divide numbers
Example #1: 126 ÷ 5 =
divisor 5 =
__________
126
___
dividend 25
quotient –
remainder 1 –
remainder
Since there is a ___________, 5 is not a ______ of 126.
factor

5. Example #2:
Let P(x) = x2 + 3x + 2 and d(x) = x +1
x+ 2
Therefore, q(x) = _______
P(x) = ________ and the _________ = 0 because d(x) is a _______ of P(x).
remainder
factor

6. Example #3: Let P(x) = x3 – 4x2 – 7x + 10 and and d(x) = x – 1, find .
Use the distributive property.
Go over your signs in a different color! –
(_____)(__________)
x – 1
x2 – 3x – 10 +
(_____)(_____)(_____)
x – 1
x – 5
x + 2 + –
-10 -5 2 -3

7. + + Example #4: Let P(x) = 2x3 – 3x2 – 10x + 11 and d(x) = x + 2,
find
quotient q(x)
_____________ – –
dividend P(x)
_____________
divisor d(x)
_____________ + + – –
Since r(x) ≠ 0, then x + 2 is _____ a factor of P(x).
NOT
remainder r(x)
_____________

8. Or, the answer can be written as:
Division Algorithm
Example
Or, the answer can be written as:

9. Example #5: Let P(x) = 2x4 – 3x3 + 2x – 5 and d(x) = x + 1, find .
 We must include ___ coefficient placeholders for _______ terms.
missing – – + + – – + +

10. Are there any missing terms in P(x)?
Exercise #6: Let P(x) = x4 + 3x2 + x – 5 and d(x) = x2 – x + 2,
find
Are there any missing terms in P(x)? – – + – + _ – + –

11. Are there any missing terms in P(x)?
Exercise #7: Let P(x) = x4 + 5x3 + 3x – 2, and d(x) = x2 – 5,
find
Are there any missing terms in P(x)? _ – +
Work on the practice. _ – + _ – +

12. Complete the rest of the worksheets.
Check your answers:
Complete the rest of the worksheets.

13. Finish the worksheets