1. Warm-up over Lesson 5-1

2. Simplify b2 ● b5 ● b3.
A. b5
B. b8
C. b10
D. b30
5-Minute Check 1

3. A. B. C. D.
5-Minute Check 2

4. Simplify (10a2 – 6ab + b2) – (5a2 – 2b2).
A. 15a2 + 8ab + 3b2
B. 10a2 – 6ab – b2
C. 5a2 + 6ab – 3b2
D. 5a2 – 6ab + 3b2
5-Minute Check 3

5. Simplify 7w(2w2 + 8w – 5). A. 14w3 + 56w2 – 35w B. 14w2 + 15w – 35
C. 9w2 + 15w – 12
D. 2w2 + 15w – 5
5-Minute Check 4

6. Find the product of 3y(2y2 – 1)(y + 4).
A. 18y5 + 72y4 – 9y3 – 36y2
B. 6y4 + 24y3 – 3y2 – 12y
C. –18y3 – 3y2 + 12y
D. 6y3 – 2y + 4
5-Minute Check 6

7. Chapter 5 Lesson 2 (Part A)
Dividing Polynomials
Long Division

8. Mathematical Practices 6 Attend to precision.
Content Standards
A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Mathematical Practices
6 Attend to precision.
CCSS

9. Divide polynomials using long division.
You divided monomials.
Divide polynomials using long division.
Then/Now

10. Example # 1 = a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1
Divide a Polynomial by a Monomial
Sum of quotients
Divide.
= a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1
Answer: a – 3b2 + 2a2b3
Example 1

11. Example #2
Simplify

12. Example #3
Simplify

13. A. 2x3y – 3x5y2 B. 1 + 2x3y – 3x5y2 C. 6x4y2 + 9x7y3 – 6x9y4
D x7y3 – 3x9y4
Example 1

14. Remembering Long Division……

15. Example # 4 Use long division to find (x2 – 2x – 15) ÷ (x – 5).
Division Algorithm
Use long division to find (x2 – 2x – 15) ÷ (x – 5).
x(x – 5) = x2 – 5x
3(x – 5) = 3x – 15
–2x – (–5x) = 3x
Answer: The quotient is x + 3. The remainder is 0.
Example 2

16. Example # 5
Use long division to find the quotient.

17. Example # 6
Use long division to find the quotient.

18. Example # 7
Use long division to find the quotient.

19. Use long division to find (x2 + 5x + 6) ÷ (x + 3).
A. x + 2
B. x + 3
C. x + 2x
D. x + 8
Example 2

20. Example # 8 Which expression is equal to (a2 – 5a + 3)(2 – a)–1?
Divide Polynomials
Which expression is equal to (a2 – 5a + 3)(2 – a)–1?
A a + 3 B C D
Example 3

21. Divide Polynomials
Read the Test Item
Since the second factor has an exponent of –1, this is a division problem.
Solve the Test Item
3(–a + 2) = –3a + 6
–a(–a + 2) = a2 – 2a
Rewrite 2 – a as –a + 2.
–5a – (–2a) = –3a
Subtract. 3 – 6 = –3
Example 3

22. The quotient is –a + 3 and the remainder is –3.
Divide Polynomials
The quotient is –a + 3 and the remainder is –3.
Therefore, .
Answer: The answer is D.
Example 3

23. Which expression is equal to (x2 – x – 7)(x – 3)–1?B. C. D.
Example 3

24. Pg . 315: 1-7 and all

25. Reflection……
If a polynomial is divided by a binomial and the remainder is 0, what does this tell you about the relationship between the binomial and the polynomial?
End of the Lesson