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

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Presentation on theme: "FACTORING REVIEW EXAMPLES 1. Factor x 2 + 3x – 4Solve x 2 + 3x – 4 = 0 Graph Y 1 = x 2 + 3x – 4 Find x-intercepts What _____× _____ = – 4 and _____+ _____."— Presentation transcript:

1 FACTORING REVIEW EXAMPLES 1

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

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

4 Graph Y 1 = x 2 + 3x + 2 Y 2 = 2x 2 + 6x + 4or Y 2 = 2(x 2 + 3x + 2) Y 3 = –3x 2 – 9x – 6 orY 3 = –3(x 2 + 3x + 2) 4 Find x-intercepts

5 Factor –x 2 – 6x – 8 by taking out common factor –1 Solve –x 2 – 6x – 8 = 0 Graph Y 1 = –x 2 – 6x – 8 5 – (x 2 + 6x + 8) – (x 2 + 6x + 8) = 0 Find x-intercepts

6 Can you factor x ? Can you solve x = 0 Graph Y 1 = x 2 – 4 6 NO Non-Real Answer Find x-intercepts There are NO x - intercepts

7 Graph Y 1 = x 2 – 4 7 Find x-intercepts Difference of Squares Using this method it VERY easy to forget BOTH answers!!!! OR

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

9 9 Common factor – 1 is negative. Graph opens down.

10 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 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 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 13 When subtracting rational exponents use a common denominator.

14 14 When subtracting rational exponents use a common denominator.

15 15 4(x – 5) 4 – 6(x – 5) 3 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 ] 2(x – 5) 3 [2(x – 5) – 3] 2(x – 5) 3 [2x – 10 – 3] 2(x – 5) 3 (2x – 13)

16 16

17 17

18 18 Factor by Decomposition Example 6x 2 – 11x + 3

19 19 Quadratic Formula ax 2 + bx + c = 0

20 20 Solve for x 3x 2 – 2x – 4 = 0

21 21 Non-real answer. Solve for x 5x 2 – 3x + 10 = 0

22 22 SYNTHETIC DIVISION Method I: SUBTRACTION – – 5 –12 – 3 –21 – Divide x 3 + 4x 2 – 5x – 12 by x – 3 Quotient is x 2 + 7x + 16 Remainder is 36 NOTE: x 3 + 4x 2 – 5x 12 (3) 3 + 4(3) 2 – 5(3) – 12 = 36

23 23 SYNTHETIC DIVISION Method II: ADDITION – 5 – Divide x 3 + 4x 2 – 5x – 12 by x – 3 Quotient is x 2 + 7x + 16 Remainder is 36 NOTE: x 3 + 4x 2 – 5x 12 (3) 3 + 4(3) 2 – 5(3) – 12 = 36

24 24 SYNTHETIC DIVISION Divide x 3 + 3x 2 – 5 by x + 2 Method I: SUBTRACTION –5 2 2 –4 1 1 –2 –1 Quotient is x 2 + x – 2 Remainder is –1 NOTE: x 3 + 3x 2 – 5 (–2) 3 + 3(–2) 2 – 5 = –1

25 25 SYNTHETIC DIVISION Divide x 3 + 3x 2 – 5 by x + 2 Method II: ADDITION –5 –2 – –2 –1 Quotient is x 2 + x – 2 Remainder is –1 NOTE: x 3 + 3x 2 – 5 (–2) 3 + 3(–2) 2 – 5 = –1

26 26 SYNTHETIC DIVISION Divide x 3 – 8 by x – 2 Method I: SUBTRACTION – –8 –2 –4 – Quotient is x 2 + 2x + 4 Remainder is 0 NOTE: x 3 – 8 (2) 3 – 8 = 0

27 27 Factor x 3 – 8 Difference of Cubes Formula a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) Factor 27x 3 – 64 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.

28 28 SYNTHETIC DIVISION Divide x by x + 3 Method I: SUBTRACTION – –3 9 0 Quotient is x 2 – 3x + 9 Remainder is 0 NOTE: x (–3) = 0

29 29 Factor x Sum of Cubes Formula a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) 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.


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