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Factoring polynomials

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Factoring polynomials

  1. 1. Factoring Polynomials1. Factoring Using the Distributive Prop 2. Difference of Two Squares 3. Difference of Two Cubes 4. Sum of Two Cubes 5. Trinomials 6. Grouping
  2. 2. Factoring Polynomials D is trib u tiv e P ro p e rty C a n yo u divid e a ll term s b y the sa m e nu m be r or lette r? 2 term s 3 term s 4 term sD iffere nc e of 2 s q ua res P e rfe c t S q ua re? G rou ping D iffere n ce of 2 cu b es T rial a nd Error S u m o f 2 cu b es
  3. 3. Distributive Property5x2y3 – 15x3y + 25x2y 5x2y(y2 – 3x + 5)
  4. 4. 2 TermsDifference of Squares 4x2 – 9y6(2x – 3y3)(2x + 3y3)
  5. 5. 2 Terms Difference of Cubes – 8x 3 27y 6 (2x – 3y2)(4x2 + 6xy2 + 9y4)First Factor Second Factor - Use first factorcube root of each term 1. Square 1st termsame sign 2. Change sign 3. Multiply the 2 terms 4. Square 2nd term (always +)
  6. 6. 2 Terms Sum of Cubes + 8x 3 27y 6 (2x + 3y2)(4x2 - 6xy2 + 9y4)First Factor Second Factor - Use first factorcube root of each term 1. Square 1st termsame sign 2. Change sign 3. Multiply the 2 terms 4. Square 2nd term (always +)
  7. 7. 3 Terms Perfect Square 4x 2 – 20x + 25 (2x - 5)2* The first and last term must be perfect squares a. Exponents have to be even to be perfect squares1. Take the square root of the first term2. Take the first sign3. Take the square root of the last term.4. Check: the middle term should be 2 times the first term times second term
  8. 8. Factoring Trinomials When the leading coefficient is 1
  9. 9. Factoring Trinomials1. Make sure trinomial is in descending order of variable. Divide out any common factors. Example: x 2 + 5x + 6
  10. 10. Factoring Trinomials2. Start out with two sets of parentheses. These are the factors. Example: x 2 + 5x + 6 ( )( )
  11. 11. Factoring Trinomials3. Put the variable given at the beginning of each factor Example: x2 + 5x + 6 ( x )( x )
  12. 12. Factoring Trinomials4A. Determine signs in factors. a) Since the last sign is + the signs are the same b) Since the first sign is + they are both + x 2 + 5x + 6 ( x + )( x + )
  13. 13. Factoring Trinomials4A. Find two factors of the last number that add up to the middle number. Example: x 2 + 5x + 6 ( x + 3 )( x + 2 )
  14. 14. Factoring Trinomials4B. Determine signs in factors. a) Since the last sign is + the signs are the same b) Since the first sign is - they are both + x2 - 5x + 6 ( x - )( x - )
  15. 15. Factoring Trinomials4B. Find two factors of the last number that add up to the middle number. Example: x 2 - 5x + 6( x - 3 )( x - 2 )
  16. 16. Factoring Trinomials4C. Determine signs in factors. a) Since the last sign is - the signs are different b) Since the first sign is + the bigger number goes by the + x 2 + 5x - 6( x + )( x - )
  17. 17. Factoring Trinomials4C. Find two factors of the last number whose difference is the middle number. Example: x 2 + 5x - 6( x + 6 )( x - 1 )
  18. 18. Factoring Trinomials4D. Determine signs in factors. a) Since the last sign is - the signs are different b) Since the first sign is - the bigger number goes by the + x 2 - 5x - 6( x + )( x - )
  19. 19. Factoring Trinomials4D. Find two factors of the last number whose difference is the middle number. Example: x2 - 5x - 6( x + 1 )( x - 6 )
  20. 20. 3 Terms Trial and Error (FOIL) 6x – 11x + 4 2 (2x - 1)(3x - 4) Signs:1. If last sign is + then both factors have the same sign a. If the first sign is + both factors have + sign b. If the first sign is – both factors have - sign2. If last sign is – then both factors have different signs
  21. 21. 4 Terms Groupingx3 – 4x2 + 3x - 12x 2(x - 4) + 3(x - 4) (x – 4)(x2 + 3)

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