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Factoring Trinomials When a=1

Factoring Trinomials When a=1. ALWAYS check for GCF first! Factor trinomials in the standard form ax²+ bx + c Solve equations in the standard form ax²+ bx + c = 0. Factoring when b and c are positive. x²+ 6 x + 8 factors(M) sum(A) 1, 8 9

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Factoring Trinomials When a=1

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  1. Factoring Trinomials When a=1 • ALWAYS check for GCF first! • Factor trinomials in the standard form ax²+ bx + c • Solve equations in the standard form ax²+ bx + c = 0

  2. Factoring when b and c are positive x²+ 6x + 8 • factors(M) sum(A) 1, 8 9 2, 4 6 • 2 and 4 multiply to give you 8 and add together to give you 6. • Answer: (x+2)(x+4) • Check using FOIL

  3. Factoring when b is negative and c is positive • Both factors need to be negative to have a positive product and a negative sum. x²- 10x + 16 M A -1,-16 -17 -2,-8 -10 -4,-4 -8

  4. Factoring when b is negative and c is positive • Both factors need to be negative to have a positive product and a negative sum. x²- 10x + 16 M A . -1,-16 -17 -2,-8 -10 -4,-4 -8 Answer: (x-2)(x-8)

  5. Factoring when b is positive and c is negative • One factor has to be positive and one has to be negative to get a negative product.x²+ x – 12 M A 1,-12 -11 -1, 12 11 2, -6 -4 -2, 6 4 3,-4 -1 -3, 4 1

  6. Factoring when b is positive and c is negative • One factor has to be positive and one has to be negative to get a negative product.x²+ x – 12 M A 1,-12 -11 -1, 12 11 2, -6 -4 -2, 6 4 3,-4 -1 -3, 4 1 Answer: (x-3)(x+4)

  7. Factoring when b is negative and c is negative • One factor has to be positive and one has to be negative to get a negative product. x²-7x – 18 M A 1,-18 -17 -1, 18 17 2,-9 -7 -2, 9 7 3,-6 -3 -3, 6 3

  8. Factoring when b is negative and c is negative • One factor has to be positive and one has to be negative to get a negative product. x²-7x – 18 M A 1,-18 -17 -1, 18 17 2,-9 -7 -2, 9 7 3,-6 -3 -3, 6 3 Answer: (x+2)(X-9)

  9. Factoring Trinomials when a>1 • Multiply a and c. • Need to find two numbers where the product is equal to a∙c(30) and the sum is equal to b (17). 6x²+ 17x + 5

  10. Factoring Trinomials when a>1 • Multiply a and c. • Need to find two numbers where the product is equal to a∙c(30) and the sum is equal to b (17). 6x²+ 17x + 5 M A 1, 30 31 2, 15 17 3, 10 13 5, 6 11

  11. Factoring Trinomials when a>1 2, 15 product = 30, sum = 17 6x²+ 17x + 5 • Re write the first and last terms. 6x² + 5 • Fill in the middle with the two numbers you found, followed by the variable. 6x²+ 2x + 15x + 5 • Now factor by grouping.

  12. Factoring Trinomials when a>1 (6x²+ 2x) + (15x + 5) group 2x(3x + 1) + 5(3x + 1) GCF (3x + 1)(2x + 5) final answer ***check by using FOIL

  13. Now you try… 10x²- 43x + 28

  14. Now you try… 10x²- 43x + 28 280-43 MA -2,-140 -142 -4,-70 -74 -8,-35 -43 -10,-28 -38 -14,-20 -34

  15. Now you try… 10x²- 43x + 28 280-43 MA -2,-140 -142 -4,-70 -74 -8,-35 -43 -10,-28 -38 -14,-20 -34

  16. Now you try… 10x²- 43x + 28 (10x²-8x) + (-35x + 28)

  17. Now you try… 10x²- 43x + 28 (10x²-8x) + (-35x + 28) 2x(5x – 4) + 7(-5x + 4)

  18. Now you try… 10x²- 43x + 28 (10x²-8x) + (-35x + 28) 2x(5x – 4) + 7(-5x + 4) 2x(5x – 4) + (-1)(7(5x – 4))

  19. Now you try… 10x²- 43x + 28 (10x²-8x) + (-35x + 28) 2x(5x – 4) + 7(-5x + 4) 2x(5x – 4) + 7(-1)(5x – 4) 2x(5x – 4) + (-7)(5x – 4) (5x – 4)(2x – 7) final answer

  20. Prime Polynomials • Some polynomials cannot be factored in any way and they are considered prime. Ex) 2x²+ 5x – 2 • No GCF • No grouping • No factors equal the sum of 5 • Prime

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