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Factoring pst
The document provides instructions on factoring polynomials using perfect square trinomials. It begins with examples of multiplying perfect square binomials and identifies the pattern. Students are shown how to determine if a trinomial is a perfect square and factor it using the formula. The document concludes with examples of factoring various polynomials using perfect square trinomials.
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Factoring pst
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- 2. Objective The student willbe able to: factor perfect square trinomials. Designed by Skip Tyler, Varina High School
- 3. Review: Part I Multiply. 1.(x + 7)2 = x2 + 14x + 49 2. (x – 2) 2= x2 – 4x + 4 3. (5x + 2y)2= 25x2 + 20xy + 4y2 4. (2x – 9y) 2= 4x2 – 36xy + 81y2 5. (4x + 5y)(4x – 5y)= 16x2 – 25y2 6. (m + 2n)(m – 2n)= 2 2 m4 – 4n2
- 4. Determine the pattern 1 = 12 These are perfect squares! 4 = 22 You should be able to list 9 = 32 the first 15 perfect squares in 30 seconds… 16 = 42 25 = 52 Perfect squares 36 = 62 1, 4, 9, 16, 25, 36, 49, 64, 81, … 100, 121, 144, 169, 196, 225
- 5. Find the factors • Factors x2 + 14x + 49 =(x + 7)2=(x + 7) (x + 7) x2 – 4x + 4 =(x – 2)2=(x – 2)(x – 2) 25x2 + 20xy + 4y2 =(5x + 2y)(5x + 2y) 4x2 – 36xy + 81y2=(2x – 9y) (2x – 9y) 16x2 – 25y2 =(4x + 5y)(4x – 5y) m4 – 4n2 =(m2 + 2n)(m2 – 2n)
- 6. Factoring Chart This chartwill help you to determine which method of factoring to use. Type Number of Terms 1. GCF 2 or more 2. Diff. Of Squares 2 3. Trinomials 3
- 7. Review: Multiply (y+ 2)2 Do you remember these? (y + 2)(y + 2) (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 – 2ab + b2 First terms: y2 Using the formula, Outer terms: +2y (y + 2)2 = (y)2 + 2(y)(2) + (2)2 Inner terms: +2y (y + 2)2 = y2 + 4y + 4 Last terms: +4 Which one is quicker? Combine like terms. y2 + 4y + 4
- 8. 1) Factor x2+ 6x + 9 Perfect Square Trinomials (a + b)2 = a2 + 2ab + b2 Does this fit the form of our (a - b)2 = a2 – 2ab + b2 perfect square trinomial? 2) Is the first term a perfect square? Yes, a = x 2) Is the last term a perfect Since all three are true, square? write your answer! Yes, b = 3 (x + 3)2 6) Is the middle term twice the product of the a and b? You can still Yes, 2ab = 2(x)(3) = 6x factor the other way but this is quicker!
- 9. 2) Factor y2– 16y + 64 Perfect Square Trinomials (a + b)2 = a2 + 2ab + b2 Does this fit the form of our (a - b)2 = a2 – 2ab + b2 perfect square trinomial? 2) Is the first term a perfect square? Yes, a = y 2) Is the last term a perfect Since all three are true, square? write your answer! Yes, b = 8 (y – 8)2 6) Is the middle term twice the product of the a and b? Yes, 2ab = 2(y)(8) = 16y
- 10. 3) Factor 4p2+ 4p + 1 =(2p + 1)2 Does this fit the form of our Perfect Square Trinomials perfect square trinomial? (a + b)2 = a2 + 2ab + b2 2) Is the first term a perfect (a - b)2 = a2 – 2ab + b2 square? Yes, a = 2p 2) Is the last term a perfectSince all three are true, square? write your answer! Yes, b = 1 (2p + 1)2 6) Is the middle term twice the product of the a and b? Yes, 2ab = 2(2p)(1) = 4p
- 11. 4) Factor 25x2– 110xy + 121y2 Does this fit the form of our perfect square trinomial? Perfect Square Trinomials (a + b)2 = a2 + 2ab + b2 2) Is the first term a perfect (a - b)2 = a2 – 2ab + b2 square? Yes, a = 5x 4) Is the last term a perfect Since all three are true, square? write your answer! Yes, b = 11y (5x – 11y)2 6) Is the middle term twice the product of the a and b? Yes, 2ab = 2(5x)(11y) = 110xy
- 12. FACTORING POLYNOMIALS Factor the following: Factor the following: •g2 – 24g + 144= =(g-12 ) (g-12 ) •m2 + 10m + 25 = (m+5)(m+5) •4a2 – 24a+ 36 = (2m-6)(2a-6)
- 13. Factor m –12m + 36 2 • (m – 6)(m + 6) • (m – 6)2 • (m + 6)2 • (m – 18)2
- 14. Factor 2r +12r + 18 2 • prime • 2(r2 + 6r + 9) • 2(r – 3)2 • 2(r + 3)2 • 2(r – 3)(r + 3) Don’t forget to factor the GCF first!
- 15. Review Factor 9k2 +12k + 4 • (3k + 2)2 = (3k + 2) (3k + 2) • (3k – 2)2 = (3k – 2) (3k – 2) • (3k + 2)(3k – 2) = (3k + 2)(3k – 2) • I’ve got no clue…I’m lost!
- 16. Find the factors: = (x + 3) (x + 3) • x² + 6x + 9 = (x + 3)² • 9m² - 6m + 1 = (3m - 1)² = (3m - 1) (3m - 1) • 25s² - 20s + 4 = (5s - 2)² = (5s - 2) (5s - 2) • x² + 2xy + y² = (x + y)² = (x + y) (x + y)
- 17. Find the completefactors: 1. 4x² + 4x + 1 = = (x + 3) (x + 3) 3. 25s² - 60s + 36 = = (3m - 1) (3m - 1) 5. 27m² - 18m +3 = = (5s - 2) (5s - 2) = 8. 8x² -72xy + 162y² = (x + y) (x + y)
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- #2 This template can be used as a starter file for presenting training materials in a group setting. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables.
- #13 This template can be used as a starter file for presenting training materials in a group setting. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables.