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Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

Learn how to factor quadratic trinomials when the coefficient of x squared is 1 and explore special cases. This guide provides step-by-step instructions for factoring trinomials and introduces special product patterns.

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Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

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  1. Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

  2. Factoring Trinomials: Factoring is the opposite of distributing To factor a trinomial, turn it back into its factored form (the 2 binomials it came from) Quadratic Standard Form ax2+bx+c ex. 2x2+2x-12 Quadratic Factored Form (x-r1)(x-r2) ex. (2x-4)(x+3)

  3. Steps to Follow: 1. Factor out a GCF if possible 2. Set up a t-chart 3. Multiply a*c and list factors of that number (today we will only do problems when a=1, so just list factors of c) 4. Add those factors together and select the pair that adds to “b” 5. Write answer in factored form (x± )(x ± ) a*c b list pairs of factors of c here Add up those factors and write the sum here

  4. Think to yourself: What two numbers multiply to “ac” AND Add to “b“ Use the t-chart to help organize your thinking

  5. Factor x2-x-12 ac -12 b -1 Check for GCF Set up t-chart + 1 (-12) = -11 List factors of ac (in this case one will need to be + and one – ) Add those factors and select the pair that adds to b = 11 -1 (12) + + -2 (6) = 4 2 (-6) + = -4 + 3 (-4) = -1 -3 (4) (x+3)(x-4)

  6. x2- 5x + 6 Factor ac 6 b -5 1 (6) 7 -7 -1 (-6) How can you predict the sign of the factors that will work? 2 (3) 5 -2 (-3) -5 (x - 2)(x - 3)

  7. x2 + 3x + 7 Factor ac 7 b 3 1 (7) 8 -8 -1 (-7) If there aren’t factors that work, it is prime (meaning it cannot be factored into integers) prime

  8. Factoring is the opposite of distributing So x2 + 5x + 6 factored is (x+3)(x+2) x2 + x - 6 factored is (x-2)(x+3)

  9. Factoring Special Products Remember the Special Cases? Use the same patterns in reverse: Perfect Square Trinomial: a2 ± 2ab ± b2 = (a ± b) 2 Difference of Perfect Squares: a2 - b2 = (a+b) (a-b)

  10. Perfect Square Trinomial Pattern Factor *Look to see if: -first and last terms are perfect squares -and middle term is 2ab *If follows pattern, it will factor into Square root first term and make that a Square root last term and make that b

  11. FACTOR: Square root first term and make that a Square root last term and make that b Check that middle term is 2ab Perfect square polynomial: (4y + 3)2

  12. Difference of perfect squares: (9-3x2)(9+3x2)

  13. Doesn’t factor, no common factor except 1! Prime

  14. Perfect square polynomial: (2c-9)2

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