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Factoring Trinomials

Factoring Trinomials. Steps: Check for GCF (Greatest Common Factor) Multiply the leading coefficient by the constant (last number) Find the multiples of the new last number. Factoring Trinomials. Determine which set of multiples adds to give you the

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Factoring Trinomials

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  1. Factoring Trinomials Steps: • Check for GCF (Greatest Common Factor) • Multiply the leading coefficient by the constant (last number) • Find the multiples of the new last number

  2. Factoring Trinomials • Determine which set of multiples adds to give you the center coefficient but multiplies to give you the new constant • Find the sign of the numbers: • If the second sign is positive then both numbers will be the first sign • If the second sign is negative then the largest multiple found will be the first sign

  3. Factoring Trinomials 6. Divide the multiples by the first coefficient from the original problem The finished factorization should look similar to this: (x#)(x#) Make sure there are as many x’s in the factorization as in the original problem

  4. Examples: 6x2 + 7x – 3 8x2 + 2x - 6 6x2 – 17x - 45

  5. Examples: 6x2 + 7x + 2 5x2 -22x + 8 2x2 + 12x + 18

  6. Factoring Polynomials by Grouping Steps: • Check for GCF (Greatest Common Factor) • Group first two terms and last two terms together and put a plus sign between them • Factor out the GCF from each group

  7. Factoring Polynomials by Grouping Steps: • If the set of parentheses are the same continue; if they are not, regroup from step 2 • Write the two new GCF’s together in a set of parenthesis times the remaining group

  8. Examples: 3x2 – 2v – 6x + xv 4x2 + v + 2xv + 2x x3 – x2 + x - 1

  9. Examples: 4x2 + 20x – 3xy – 15y x3 + 2x2 + 9x - 18 3x3 – 6x2 + 15x - 30

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