1 / 28

Magicians

Magicians. Factoring Expressions Greatest Common Factor (GCF) Difference of 2 Squares. Objectives. I can factor expressions using the Greatest Common Factor Method (GCF) I can factor expressions using the Difference of 2 Squares Method. What is Factoring?.

nishi
Download Presentation

Magicians

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Magicians

  2. Factoring Expressions Greatest Common Factor (GCF) Difference of 2 Squares

  3. Objectives • I can factor expressions using the Greatest Common Factor Method (GCF) • I can factor expressions using the Difference of 2 Squares Method

  4. What is Factoring? • Quick Write: Write down everything you know about Factoring from Algebra-1 and Geometry? • You can use Bullets or give examples • 2 Minutes • Share with partner!

  5. Factoring? • Factoring is a method to find the basic numbers and variables that made up a product. • (Factor) x (Factor) = Product • Some numbers are Prime, meaning they are only divisible by themselves and 1

  6. Method 1 • Greatest Common Factor (GCF) – the greatest factor shared by two or more numbers, monomials, or polynomials • ALWAYS try this factoring method 1st before any other method • Divide Out the Biggest common number/variable from each of the terms

  7. Greatest Common Factorsaka GCF’s Find the GCF for each set of following numbers. Find means tell what the terms have in common. Hint: list the factors and find the greatest match. 2, 6 -25, -40 6, 18 16, 32 3, 8 2 -5 6 16 1 No common factors? GCF =1

  8. Find the GCF for each set of following numbers. Hint: list the factors and find the greatest match. x, x2 x2, x3 xy, x2y 2x3, 8x2 3x3, 6x2 4x2, 5y3 Greatest Common Factorsaka GCF’s x x2 xy 2x2 3x2 1 No common factors? GCF =1

  9. Factor out the GCF for each polynomial:Factor out means you need the GCF times the remaining parts. a) 2x + 4y 5a – 5b 18x – 6y 2m + 6mn 5x2y – 10xy Greatest Common Factorsaka GCF’s 2(x + 2y) How can you check? 5(a – b) 6(3x – y) 2m(1 + 3n) 5xy(x - 2)

  10. FACTORING by GCF 5xy( ) 3y – 2x2 + 5y2

  11. FACTORING (x3 – 4x2 + 2x – 3) 2x

  12. Ex 1 • 15x2 – 5x • GCF = 5x • 5x(3x - 1)

  13. Ex 2 • 8x2 – x • GCF = x • x(8x - 1)

  14. Ex 3 • 8x2y4+ 2x3y5 - 12x4y3 • GCX = 2x2y3 • 2x2y3(4y + xy2 – 6x2)

  15. Method #2 • Difference of Two Squares • a2 – b2 = (a + b)(a - b)

  16. What is a Perfect Square • Any term you can take the square root evenly (No decimal) • 25 • 36 • 1 • x2 • y4

  17. Difference of Perfect Squares x2 – 4 = the answer will look like this: ( )( ) take the square root of each part: ( x 2)(x 2) Make 1 a plus and 1 a minus: (x + 2)(x - 2 )

  18. FACTORING (x – 8)(x + 8)

  19. YOUR TURN!!

  20. Example 1 • (9x2 – 16) • (3x + 4)(3x – 4)

  21. Example 2 • x2 – 16 • (x + 4)(x –4)

  22. Ex 3 • 36x2 – 25 • (6x + 5)(6x– 5)

  23. More than ONE Method • It is very possible to use more than one factoring method in a problem • Remember: • ALWAYS use GCF first

  24. Example 1 • 2b2x – 50x • GCF = 2x • 2x(b2 – 25) • 2nd term is the diff of 2 squares • 2x(b + 5)(b - 5)

  25. Example 2 • 32x3 – 2x • GCF = 2x • 2x(16x2 – 1) • 2nd term is the diff of 2 squares • 2x(4x + 1)(4x - 1)

  26. Exit Slip • On the back of your Yellow Sheet write these 2 things: • 1. Define what factors are? • 2. What did you learn today that was not on the front of your yellow sheet? • Put them in Basket on way out!

  27. Homework • WS 5-1

More Related