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Algebra

Algebra. 10.8 Factoring Completely. Steps to Factor Completely. Factor out the GCF ( Greatest Common Factor ) Look for Special Patterns DTS a²- b² PST a²+ 2ab + b² a² - 2ab + b² 3. Factor ax² + bx + c

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Algebra

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  1. Algebra 10.8 Factoring Completely

  2. Steps to Factor Completely • Factor out the GCF (Greatest Common Factor) • Look for Special Patterns • DTS a²- b² • PST a²+ 2ab + b² • a² - 2ab + b² • 3. Factor ax² + bx + c • 4. If 4 terms, try FACTOR BY GROUPING • 5. Check that each factor is prime • 6. FOIL to check • 7. If part of an equation, solve using the ZERO PRODUCT PROPERTY (a + b)(a – b) (a + b)² (a - b)²

  3. Greatest Common Factor (GCF) A term that combines the GCF of the coefficients with the lowest power of the variable. Polynomial GCF Factored 9x²- 15x 3x 3x(3x – 5) 14x³- 21x2 7x² 7x²(2x – 3) 2x²- 8 2 2(x²- 4) DTS! 2(x + 2)(x – 2) 3(x²+ 6x + 9) 3x²+ 18x + 27 3 PST! 3(x + 3)²

  4. Factor! 4x³- 36x 4x(x + 3)(x – 3) 4x(x²- 9) DTS! 5n²(3n + 2)(3n – 2) 45n4- 20n2 5n²(9n²- 4) DTS! 4a(a + 2)(a + 3) 4a³+ 20a² + 24a 4a(a²+ 5a + 6) 7x³- 7x²- 84x 7x(x + 3)(x – 4) 7x(x²- x - 12)

  5. Solve! 2x³- 10x²+ 8x = 0 2x(x – 4)(x– 1)= 0 2x(x²- 5x + 4) = 0 x= 0, 4, 1 16y³- 100y = 0 4y(2y + 5)(2y – 5) = 0 4y(4y²- 25) DTS! y= 0, -5/2, 5/2 3x²- 30x + 75 = 0 3(x – 5)² = 0 3(x²- 10x + 25) = 0 x= 5 PST!

  6. Factor by Grouping (4 terms) x³+ 2x²+ 3x + 6 Divide into 2 parts LEFT side, RIGHT side GCF is x² GCF is 3 Each side has a GCF same same x² (x + 2) (x + 2) + 3 FACTOR each side FOIL to check ( ) (x + 2) x³+ 2x²+ 3x + 6 Check!

  7. Factor! x³- 2x²- 9x + 18 x² (x – 2) - 9 (x – 2) (x²- 9) (x – 2) (x + 3)(x – 3)(x – 2) DTS! x³- 3x²+ x - 3 x² (x – 3) + 1 (x – 3) (x²+ 1) (x – 3) (x²+ 1)(x – 3)

  8. A Few from the HW • P 629 # 19 and # 34

  9. Homework pg. 629 #19-35 odd pg. 632 Quiz 3 #1-25

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