1. Long & Synthetic Division

2. 1st write as a division problem.

3. Correct x2
What would you multiply x by to get x3 ?

4. Multiply x2 by (x-7) and write under dividend
Then subtract by adding the opposite

5. Correct 5x
What would you multiply x by to get 5x2 ?

6. Multiply 5x by (x-7) and write under the previous difference
Then subtract by adding the opposite

7. Correct 40
What would you multiply x by to get 40x?

8. Multiply 40 by (x-7) and write under the previous difference
Then subtract by adding the opposite

9. This is the remainder

12. Show x-3 is a factor of then rewrite with x-3 times the quotient
Because the remainder is zero x-3 is a factor

13. Show x-5 is a factor of then rewrite with x-5 times the quotient
Because the remainder is zero x-5 is a factor

14. P343
1 – 13 odd
Divide using long division. Write your answer as

15. Write the coefficients of the numerator adding any place holders
Use Synthetic Division to do the long division problem
Write the opposite of the constant term 1 7 35
280 5 40
284
Write the coefficients of the numerator adding any place holders
Multiply by 7
Add
Drop the Coefficient Down
Synthetic Division only works when the denominator is x-a where a is a constant

16. Synthetic Division 7 35
280 1 5 40
284
The quotient will always be degree 1 less than the degree of the numerator

17. Synthetic Division
Write the opposite of the constant term 7 35
280
284 1 5 40
These are the coefficients of the quotient
This is the remainder

18. Use Synthetic Division to divide3
-12 40
-120
-120
-10 30 30
-20
Multiply by -4
Add

19. Use synthetic division2 4 8 14 28 4 7 14 33

20. Remainder Theorem: Let f be a polynomial function
Remainder Theorem: Let f be a polynomial function. If f(x) is divided by x-c, then the remainder is f(c)
If you divide a polynomial function synthetically by a number the remainder is the value that would result if you plugged that number in the equation for x
These two numbers will always be the same

21. = -305
Use synthetic division to find

22. Factor Therorem:Let f be a polynomial function
Factor Therorem:Let f be a polynomial function. Then x-c is a factor of f(x) if and only if f(c)=0
Since f(5)=0 then synthetically dividing by 5 will give a remainder of 0 and x-5 has to be a factor of f(x)

23. Is x-3 is a factor of :
If (x-3) is a factor of g(x) when we divide it into g(x) it will have no remainder.
So we can write g(x) as
What does g(3)=

24. Show x+1 is a factor of g(x) then write g(x) as the product of x+1 and the quotient-1 4 -4
What does g(-1)=

25. Write answers in the form
P344
21,23,27,29,31,33,35,37