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Factoring
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Factoring

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Transcript

  • 1.
    • Factoring is the process of finding polynomials, called factors , whose product equals a given polynomial.
    • A polynomial that cannot be written as a product of polynomials with integer coefficients is a prime or irreducible polynomial .
    • A polynomial is factored completely when it is written as a product of prime polynomials with integer coefficients.
  • 2.
    • Example Factor out the greatest common factor.
    • (a) (b)
    • Solution
    • (a)
    • (b)
  • 3.
    • Example Factor each polynomial by grouping.
    • (a) (b)
    • Solution
    • (a)
  • 4.
    • Solution
    • (b)
  • 5.
    • Example Factor each trinomial.
    • (a)
    • (b)
  • 6.
    • Solution (a) We must find integers a , b , c , d such that
    • By FOIL, we see that ac = 4 and bd = 6. Thus a and c
    • are 1 and 4 or 2 and 2.
    • Since the middle term is negative, consider only
    • negative values for b and d . The possibilities are –1
    • and –6 or –2 and –3.
  • 7.
    • Solution (a) Try these combinations of factors
    • The last trial gives the correct factorization.
  • 8.
    • Solution (b) Try the various combinations of factors
    • The last trial gives the correct factorization.
  • 9. Perfect Square Trinomials
  • 10.
    • Example Factor each polynomial.
    • (a) (b)
    • Solution
    • (a)
    • (b)
  • 11.
    • Solution
  • 12. Difference of Squares
  • 13.
    • Example Factor each polynomial.
    • (a) (b)
    • Solution
    • (a)
    • (b)
  • 14. Difference and Sum of Cubes Difference of cubes Sum of cubes
  • 15.
    • Example Factor each polynomial.
    • (a) (b)
    • Solution
    • (a)
  • 16.
    • Solution
    • (b)
  • 17.
    • Example Factor the polynomial
    • Solution Replacing 2 a – 1 with m and factoring gives
    • Now, replace m with 2 a – 1 in the factored form and
    • simplify.