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FACTORING REVIEW

FACTORING REVIEW. EXAMPLES. Factor x 2 + 3 x – 4. Solve x 2 + 3 x – 4 = 0. What _____× _____ = – 4 and _____+ _____ = 3. Graph Y 1 = x 2 + 3 x – 4 Find x -intercepts. Factor x 2 + 3 x + 2 What _____× _____ = 2 and _____+ _____ = 3. Solve. Solve.

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FACTORING REVIEW

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  1. FACTORING REVIEW EXAMPLES

  2. Factorx2 + 3x – 4 Solve x2 + 3x – 4 = 0 What _____× _____ = – 4 and _____+ _____ = 3 Graph Y1 = x2 + 3x – 4 Find x-intercepts

  3. Factorx2 + 3x + 2 • What _____× _____ = 2 • and _____+ _____ = 3 Solve Solve Factor 2x2 + 6x + 4 by taking out common factor 2 2(x2+ 3x+ 2) = 0 2(x2+ 3x+ 2) Solve Factor –3x2 – 9x – 6 by taking out common factor – 3 – 3(x2+ 3x+ 2) = 0 – 3(x2+ 3x+ 2)

  4. Graph Y1 = x2 + 3x+ 2 Y2= 2x2 + 6x+ 4or Y2 = 2(x2 + 3x+ 2) Y3= –3x2 – 9x – 6 orY3 = –3(x2 + 3x+ 2) • Find x-intercepts

  5. Factor –x2 – 6x – 8 by taking out common factor –1 – (x2+ 6x+ 8) Graph Y1 = –x2 – 6x – 8 Find x-intercepts Solve –x2 – 6x – 8 = 0 – (x2+ 6x+ 8) = 0

  6. Can you factor x2 + 4 ? Can you solve x2 + 4 = 0 NO Non-Real Answer Graph Y1 = x2 – 4 • Find x-intercepts There are NO x - intercepts

  7. Can you factor ? Can you solve Difference of Squares OR Graph Y1 = x2 – 4 • Find x-intercepts Using this method it VERY easy to forget BOTH answers!!!!

  8. Factor 8x2 – 18 by taking out common factor 2 • Solve 8x2 – 18 = 0 • Solve 8x2 – 18 = 0 Common factor 2 is positive. Graph opens up. 8

  9. Factor Factor by taking out common factor – 1 • Solve = 0 • Solve = 0 Common factor – 1 is negative. Graph opens down.

  10. MORE COMMON FACTORING EXAMPLES When dividing out common factors look for the greatest common numerical factor and the smallest exponent on the variables.

  11. MORE COMMON FACTORING EXAMPLES When dividing out common factors look for the greatest common numerical factor and the smallest exponent on the variables. This example will NOT factor further.

  12. MORE COMMON FACTORING EXAMPLES When dividing out common factors look for the greatest common numerical factor and the smallest exponent on the variables.

  13. When subtracting rational exponents use a common denominator.

  14. When subtracting rational exponents use a common denominator.

  15. 4(x – 5)4 – 6(x – 5)3 2(x – 5)3[2(x – 5)– 3] 4(x – 5)4– 6(x – 5)3 2(x – 5)3[2x – 10 – 3] 2(x – 5)3 (2x – 13) 2(x – 5)3[2(x – 5)4-3– 3(x– 5)3-3] 2(x – 5)3[2(x – 5)1– 3(x– 5)0]

  16. Factor by Decomposition Example 6x2 – 11x + 3

  17. Quadratic Formula ax2 + bx +c= 0

  18. Solve for x 3x2– 2x– 4 = 0 Answers in simplest and exact radical form Approximate decimal answers to nearest hundredth.

  19. Solve for x 5x2 – 3x + 10 = 0 Non-real answer.

  20. SYNTHETIC DIVISION • Divide x3 + 4x2 – 5x – 12 by x– 3 Method I: SUBTRACTION – 3 1 4 – 5 –12 – 3 –21–48 1 7 16 36 • Quotient is x2 + 7x + 16 • Remainder is 36 • NOTE: x3 + 4x2 – 5x 12 • (3)3 + 4(3)2 – 5(3) – 12 = 36

  21. SYNTHETIC DIVISION • Divide x3 + 4x2 – 5x – 12 by x– 3 Method II: ADDITION 3 1 4 – 5 –12 3 2148 1 7 16 36 • Quotient is x2 + 7x + 16 • Remainder is 36 • NOTE: x3 + 4x2 – 5x 12 • (3)3 + 4(3)2 – 5(3) – 12 = 36

  22. SYNTHETIC DIVISION Divide x3 + 3x2 – 5 by x + 2 Method I: SUBTRACTION + 2 1 3 0 –5 • 2 2–4 • 1 1 –2 –1 • Quotient is x2 + x – 2 • Remainder is –1 • NOTE: x3 + 3x2– 5 • (–2)3+ 3(–2)2– 5 = –1

  23. SYNTHETIC DIVISION Divide x3 + 3x2 – 5 by x + 2 Method II: ADDITION - 2 1 3 0 –5 • –2–24 • 1 1 –2 –1 • Quotient is x2 + x – 2 • Remainder is –1 • NOTE: x3 + 3x2– 5 • (–2)3+ 3(–2)2– 5 = –1

  24. SYNTHETIC DIVISION Divide x3– 8 by x– 2 Method I: SUBTRACTION • – 2 1 0 0 –8 • –2 –4–8 • 1 2 4 0 • Quotient is x2 + 2x + 4 • Remainder is 0 • NOTE: x3– 8 • (2)3 – 8 = 0

  25. Difference of Cubes Formula a3– b3 = (a – b)(a2 + ab +b2) Factor x3– 8 If we compare this answer to the previous slide we see it is the same. This is a shortcut that will help with more difficult questions. Factor 27x3– 64

  26. SYNTHETIC DIVISION Divide x3 + 27 by x+ 3 Method I: SUBTRACTION • +3 1 0 0 27 • 3–927 • 1 –3 9 0 • Quotient is x2 – 3x + 9 • Remainder is 0 • NOTE: x3+ 27 • (–3)3 + 27 = 0

  27. Sum of Cubes Formula a3 + b3 = (a+ b)(a2 – ab+b2) Factor x3 + 27 If we compare this answer to the previous slide we see it is the same. This is a shortcut that will help with more difficult questions. Factor Factor

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