Topic: Multiplying and Factoring Polynomials

Algebra I – Chapter 8 Day #2 Topic: Multiplying and Factoring Polynomials Standards/Goals:  A.APR.1.: I can multiply a monomial and a trinomial together.  C.1.e.: I can factor a monomial from a polynomial. Before we begin learning how to multiplying monomials with trinomials, let’s briefly review how to add/subtract polynomials. REVIEW: Find each sum. #1. (4a – 5) + (3a + 6) #2. (6x + 9) + (

#3. #6.

REVIEW: Find each difference. #1. (3a – 5) – (5a + 1) #2. (9x + 2) – ( – 5)

#3. (8p – 5q) – ( #4.

Now, we will quickly review the distributive property: EXAMPLES: Find the product of the following. #1. 2x(3x + 1) #2. #3.

Now, try these TWO Multiple Choice Questions to test your ability to distribute properly. #1. What is a simpler form of: ? a. b. c. d.

#2. What is the simplified form of: ? a. b. c. 2

d. Now, try these: EXAMPLES: Simplify each product. 1. 4x(2x – 7) 2. 3y(3y + 4) 3. 2z2(2z – 3)

4. 3a(–4a – 6) 5. 6b(3b2 + 2b – 4) 6. 3c2(2c2 – 4c + 3)

Let’s now review something known as the GCF, that you have learned in previous math classes. ‘GCF’ stands for ‘Greatest Common Factor’. EXAMPLES: Find the GCF for the following expressions. #1. #2. #3.

Now, let’s take thing a step forward, by writing not only the GCF, but also writing the expression in what we call ‘factored form.’ EXAMPLES: What is the factored form of each expression? #1. #2. #3.

Now, try these: EXAMPLES: Find the GCF of the terms of each polynomial. #1. 12x2 – 6x #2. 4y2 + 12y + 8 #3. 6z3 + 15z2 – 9z

EXAMPLES: Factor each polynomial. #1. 8a + 10 #2. 12b2 – 18b #3. 9c3 + 12c2

#4. 5d3 – 10d2 + 20d #5. 6e2 + 10e – 8 #6. 8g3 – 24g2 + 16g

EXAMPLE: A circle with radius ‘r’ is cut from a square that has side length 3r. Write an expression in factored form for the shaded area. 3

HOMEWORK – Chapter 8 Day #2 Name ______Date ______Simplify each product. 1. 3w(w + 2) 2. (z + 5)2z 3. 3m2(4 + m)

4. 2p(p2  6p + 1) 5. y(5y3  3y2 + 2y) 6. 3a(3a2 + 2a  7)

7. 6x3(3x2  x + 10) 8. 4h(h3  8h2 + 2h) 9. 4n(n2 + 5n + 6)

Find the GCF of the terms of each polynomial. 10. 16q + 32 11. 4t3  24t 12. 32y  24

13. x3 + 3x2 + 5x 14. 5d3 + 20d – 35 15. 2m3 + 10m2 + 12m

16. 7g4 + 21g3  14g2 17. 15z3 + 3z2  27z 18. 33w7 + 55w5  22w3

Factor each polynomial. 19. 9t  3 20. 12j3 + 28 21. 72x2  63x 4

22. 12k3  9k2 + 6 23. 30n3 + 18n2 + 54n 24. 32z4  80z3 + 112z2

25. 12n4 + 16n3 + 20n2 26. 24y6 + 36y4 + 42y2 27. 7q5 + 21q3  49q

28. You are painting a rectangular wall with length 5x2 ft and width 12x ft. There is a rectangular door that measures x ft by 2x ft that will not be painted. What is the area of the wall that is to be painted? Write your answer in factored form.

Simplify. Write in standard form. 29. 3m(2m2  5m + 10) 30. 5t2(6t3 + 12t) 31. 10x(4x2 + x  3)

32. 2v(3v3  6v2 + 2v) 33. 5y(y + 2)  y(y  3) 34. 2b2(4b2 + 3b)

Factor each polynomial. 35. 13cd3 + 39c2d2 36. 5x3y4  25xy2 37. 42m5n + 28m4

38. 36fg2 + 54f2g4 39. 8s8t4 + 20s4t3 40. 12a2b5 + 156a2b3