Factoring

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Review of GCF, Difference of Squares and Trinomial factoring

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Factoring

  1. 2. <ul><li>To Factor: Write a polynomial as a product. </li></ul><ul><li>Kinds of Factoring: </li></ul><ul><li>GCF </li></ul><ul><li>Difference of Squares </li></ul><ul><li>Trinomials </li></ul>
  2. 3. GCF: - can be done with any number of terms - find what is “common” to both Factor using GCF: 1. Look For… (GCF = 6) <ul><li>A Number that </li></ul><ul><li>goes into all terms </li></ul><ul><li>A variable that is </li></ul><ul><li>common to all terms </li></ul>When you have found the GCF, divide each term by the GCF. =6(x + 2) 2. (GCF = 10x) =10x(x – 3) 3. (GCF = 3) =3(9x 2 + 3x – 2)
  3. 4. Difference of Squares: 1. Binomial 2. Must be “-” 3. Both terms must be perfect squares 1. 2. 3. a 2 – b 2 = (a + b)(a – b) (2x + 3)(2x – 3) Use the square roots of the terms! (10x + 9)(10x – 9)
  4. 5. Factoring Trinomials Two Types: in the form x 2 + bx + c OR ax 2 + bx + c For the form x 2 + bx + c, … Review: Multiply (x + 4)(x + 2) Note: The two numbers in the quantities add up to 6 and multiply to 8. (x + ____)(x + ____) The two numbers must have a sum of “b” and a product of “c”.
  5. 6. Factor: 1. 2. 3. 4. (Think of 2 numbers that multiply to 10 and add to 7). (x + 5)(x + 2) Multiply to -16 and add to -6. (x – 8)(x + 2) (Multiply to -24 and add to 10). (x + 12)(x – 2) (Multiply to 34 and add to -35). (x – 34)( X - 1)
  6. 7. The first coefficient of 2 must be “split” as well as the last constant of 3 must be “split” so that the “inners” + “outers” = 7 Factoring ax 2 + bx + c: (____X + ____)(____X + ____) The blanks with the x must multiply to 2 The blanks after the “+” must multiply to 3. When you multiply the inners and outers they must add to 7 (2x + 1)(x + 3) Check with FOIL
  7. 8. Factor: 1. 2. 3. (4x + 1)(2x – 3) Find factors of 8 and factors of 3 (3x – 1)(2x + 7) (6x + 1 )(x – 10)

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