1. Activity Set 3.4 CLASS PPTX Visual Algebra for Teachers

2. Chapter 3 REAL NUMBERS AND QUADRATIC FUNCTIONS Visual Algebra for Teachers

3. Activity Set 3.4 Multiplying and Factoring Polynomials Visual Algebra for Teachers

4. PURPOSE To learn:  How to find the product of binomials and/or trinomials  How to factor some special trinomials We have already learned how to multiply binomials and factor trinomials of the form using algebra pieces. In this section, we’ll learn how to do this without the use of manipulatives for some special trinomials

5. INTRODUCTION

6. POLYNOMIAL MULTIPLICATION The distributive property (of multiplication over addition) states or Multiplication of polynomials is based on the distributive property.

7. Example (polynomial  ) Distribute the (3x + 7) Distribute the x and then the 5 Multiply through Simplify

8. Classwork (as assigned) #1 a, b, c, d and e (sharing and extra credit) #1 f (class discussion)

9. FACTORING BY GROUPING One technique for factoring quadratics is called factoring by grouping. There is a visual technique, the “box” method, associated with factoring by grouping. You can see it is a lot like what we have already done with algebra pieces. To use this method, factor out any common terms.

10. FACTORING BY GROUPING Step 1 Sketch a blank 2  2 array and add the leading term, ax 2, to the top left corner and the constant term, c, to the bottom right corner

11. FACTORING BY GROUPING Step 2 Find two terms that when multiplied together give you ax 2  c and when added together, give you the remaining term bx, in your quadratic.

12. GROUPING EXAMPLE Factor 6x 2 + 7x + 2 by grouping

13. GROUPING EXAMPLE Factor 6x 2 + 7x + 2 by grouping Wee see we need two numbers that add to 7 and multiply to 12. These must be m = 3 and n = 4 (or visa versa).

14. FACTORING BY GROUPING Step 3 (with our example: 6x 2 + 7x + 2) Factor the common terms out of each row and each column.

15. FACTORING BY GROUPING Step 4 (with our example: 6x 2 + 7x + 2) The sum of the factors for the columns (the top edge value) and the sum of the factors for the rows (the left edge values) are the factors for the quadratic

16. Classwork (as assigned) #2 a, b, c, d, e, f, and g (sharing and extra credit)

17. SPECIAL FACTORIZATIONS Two important special factorizations are and the difference of perfect squares

18. Classwork (as assigned) #4 a, b, and c (sharing and extra credit)

19. Homework Coursepack: Homework 3.4 (skip #10) Use the box / grouping method Study for extra credit question on final exam