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Ffrocks3

  • one year ago

Explain the connection between factors of a polynomial, zeros of a polynomial function, and solutions of a polynomial equation.

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  1. skullpatrol
    • one year ago
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    Any ideas?

  2. ffrocks3
    • one year ago
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    none :( sorry

  3. skullpatrol
    • one year ago
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    What does "factors of a polynomial" mean to you?

  4. ffrocks3
    • one year ago
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    any polynomial which divides evenly into p(x)

  5. skullpatrol
    • one year ago
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    Just like factors of an integer, right?

  6. ffrocks3
    • one year ago
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    yea

  7. skullpatrol
    • one year ago
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    What is the definition of a "factor?"

  8. ffrocks3
    • one year ago
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    a number or quantity that when multiplied with another produces a given number or expression.

  9. skullpatrol
    • one year ago
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    so in the product ab a and b are called what?

  10. ffrocks3
    • one year ago
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    variables?

  11. skullpatrol
    • one year ago
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    |dw:1433721293619:dw|

  12. skullpatrol
    • one year ago
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    yes, variables represent numbers, right?

  13. ffrocks3
    • one year ago
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    mhm

  14. skullpatrol
    • one year ago
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    |dw:1433721463044:dw|

  15. skullpatrol
    • one year ago
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    In this^ frame work we may replace a, b, and c with polynomials because a polynomial is simply a sum of monomials.

  16. skullpatrol
    • one year ago
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    Let's say our given polynomial can be written as a product. Then each of the factors can be called a number or quantity that when multiplied with another produces a given number or expression.

  17. skullpatrol
    • one year ago
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    Now the "zeros of a polynomial function" is when we replace c in ab =c with 0. We want ab = 0 to be a true statement This can only be true if and only if a = 0 or b = 0. This^ is called the "zero-product property" Now you know why I made such a big deal out of the definition of a "factor" :)

  18. skullpatrol
    • one year ago
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    And, finally the solutions of a polynomial equation are those values of the variable that make the above equation a true statement.

  19. skullpatrol
    • one year ago
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    To summarize:

  20. skullpatrol
    • one year ago
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    |dw:1433722590439:dw|

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