1. Monday: Announcements
This is last week for 3rd grading period
Today’s assignments are the last grades
Unit 7 Reassessment sign-ups on the round table. Deadline is Friday morning to reassess.
Unit 8 is a 2 part unit (calculator and non-calculator)
Afternoon tutorials this week start at 4:10pm because of teacher duty

2. Add, Subtract, Multiply, and Divide Polynomials
Unit 8

3. Objectives I can add, subtract, and multiply polynomial expressions.
I can divide polynomial expressions using Long Division

4. Polynomials A polynomial is a monomial or sum of monomials.
The monomials that make up the polynomial are called terms of the polynomial.
A trinomial has 3 unlike terms
A binomial has 2 unlike terms

5. Standard Format

6. Standard Format

7. Addition and Subtraction
Polynomials and monomials may only be subtracted or added if they have like terms. Addition and subtraction cannot be done on unlike terms.
To add or subtract, you just COMBINE LIKE TERMS

8. Addition or Subtraction
Simplify the following:
(4x2 – 3x) – (x2 + 2x – 1)
4x2 – 3x – x2 - 2x + 1
3x2 – 5x + 1

9. Example #2 Simplify: (3x + y) – (x + y) – (x + 3y)

10. Example 3 Simplify (z2 – 6z – 10) + (2z2 + 4z – 11)

11. EXAMPLE 1
Add polynomials vertically and horizontally
a. Add 2x3 – 5x2 + 3x – 9 and x3 + 6x in a vertical format.
SOLUTION
a x3 – 5x2 + 3x – 9
+ x3 + 6x
3x3 + x2 + 3x + 2

12. GUIDED PRACTICE
for Examples 1 and 2
Find the sum or difference.
1. (t2 – 6t + 2) + (5t2 – t – 8)
SOLUTION
t2 – 6t + 2
+ 5t2 – t – 8
6t2 – 7t – 6

13. Multiply with Distributive Prop
Simplify: 3x(5x4 – x3 + 4x)
15x5 – 3x4 + 12x2

14. 2nd Example: (x + 3)(x2 + 3x + 9) x3 + 3x2 + 9x + 3x2 + 9x + 27

15. Example 3
Simplify: -3x2y(2x3y2 – 3x2y2 + 4x3y)
-6x5y3 + 9x4y3 –12x5y2

16. Dividing Numbers Quotient
When you divide a number by another number and there is no remainder:
Then the divisor is a factor!!
Also the quotient becomes another factor!!!
Divisor
Dividend

17. Dividing Polynomials
Long division of polynomials is similar to long division of whole numbers.
When you divide two polynomials you can check the answer using the following:
dividend = (quotient • divisor) + remainder
The result is written in the form:
quotient +
Dividing Polynomials

18. Dividing Polynomials
Example: Divide x2 + 3x – 2 by x + 1 and check the answer. 1. x
+ 2 2.
x x 3. 2x
– 2
2x + 2 4.
– 4 5.
remainder 6.
Answer: x + 2 +
– 4
Dividing Polynomials

19. Example: Divide & Check
Example: Divide 4x + 2x3 – 1 by 2x – 2 and check the answer. x2
+ x
+ 3
Write the terms of the dividend in descending order.
2x3 – 2x2
Since there is no x2 term in the dividend, add 0x2 as a placeholder.
2x2
+ 4x
2x2 – 2x 1. 2. 6x
– 1 4. 3.
6x – 6 5 5.
Answer: x2 + x + 3 5 6. 7. 8. 9.
Example: Divide & Check

20. Example: Division With Zero Remainder
Example: Divide x2 – 5x + 6 by x – 2. x
– 3
x2 – 2x
– 3x
+ 6
– 3x + 6
Answer: x – 3 with no remainder.
Example: Division With Zero Remainder

21. Homework
WS 8-1