A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

baby456

  • one year ago

Please help me with factoring 10m^3n^2-15m^2n^1 medal + fan just don't just give me the answer. Explain IT.

  • This Question is Closed
  1. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mathstudent55

  2. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @dajakesta

  3. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large 10m^3n^2-15m^2n^1\) You are factoring a two-term polynomial. Start by factoring a common factor out of both terms. What is the GCF of both terms?

  4. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    5

  5. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Correct. For the number parts, 10 and -15, you can factor out 5. What about for the variable parts? What do m^3 and m^2 have in common?

  6. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    6

  7. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Not a number. It's a variable to a power.

  8. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435094377519:dw|

  9. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    m^3 and m^2 have m^2 in common.

  10. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Then we see what n^2 and n^1 have in common. |dw:1435094442799:dw| n^2 and n^1 have n in common.

  11. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That means the GCF of the two terms is 5m^2n

  12. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how did you get 2 from

  13. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The common factor is \(\large 5m^2n\) The 2 is the exponent of the m.

  14. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  15. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large 10m^3n^2-15m^2n^1\) Now we factor out the GCF: \(\large =5m^2n(~~~~~~~~~~~~~~)\)

  16. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how? i dont know i am so confused

  17. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what gcf

  18. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large =5m^2n(2mn - 3)\)

  19. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where are you getting the 2 and 3

  20. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The 2 and the 3 are the numbers you need so that when you multiply by the 5 outside you get back the 10 and 15 you started with.

  21. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Factoring is the opposite of the distributive property.

  22. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont get it

  23. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let me go back a few steps and show a simple example. Do you know the distributive property?

  24. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what?

  25. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Use the distributive property to simplify this expression: \(2(3 + 5)\)

  26. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    11 i think

  27. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No. I'll show you. The distributive property of multiplication over addition is this: \(2(3 + 5) = 2 \times 3 + 2 \times 5\)

  28. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435095136526:dw|

  29. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The distributive property shows you that you multiply the number outside parentheses by each of the numbers inside the parentheses. The you add the products.

  30. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is another example: |dw:1435095244847:dw|

  31. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  32. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but how does that help with factoring.

  33. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Factoring is doing the distributive property in reverse.

  34. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is an example of the distributive property using variables. |dw:1435095365764:dw|

  35. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  36. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We went from a product of a variable, m, and a binomial, 2m + n, to a result, \(2m^2 + mn\)

  37. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now let's do that problem in reverse. Let's say we are given the final answer above, and we are asked to factor.

  38. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    This is the problem we have now: |dw:1435095505073:dw|

  39. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    First, we find the greatest common factor of the two terms.

  40. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435095568553:dw|

  41. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now we take the problem, and we do the distributive property in reverse.

  42. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We need to find what to place inside the parentheses to get back to our original problem. |dw:1435095632204:dw|

  43. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435095685363:dw|

  44. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435095737610:dw|

  45. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435095761968:dw|

  46. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435095800516:dw|

  47. baby456
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont get it. it like my brain is stuck.

  48. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    This is the answer: |dw:1435095820650:dw|