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anonymous

  • one year ago

Can someone help me with an algerba 1 question?

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  1. diamondboy
    • one year ago
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    Sure

  2. anonymous
    • one year ago
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    The question is Factor completely 2x3y4 − 8x2y3 + 6xy2.

  3. diamondboy
    • one year ago
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    What's d question?

  4. anonymous
    • one year ago
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    so bassicaly find the GCF

  5. diamondboy
    • one year ago
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    ok

  6. mathstudent55
    • one year ago
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    \(2x^3y^4 − 8x^2y^3 + 6xy^2\)

  7. anonymous
    • one year ago
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    yes

  8. anonymous
    • one year ago
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    The notes that i took in class says that first i need to find a number that goes into all three coeffiecent evenly which is 2

  9. mathstudent55
    • one year ago
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    Step 1 of factoring: Try to factor a common factor. What is the largest common factor of all three terms?

  10. diamondboy
    • one year ago
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    |dw:1442526155297:dw|

  11. diamondboy
    • one year ago
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    can you go on from this?

  12. mathstudent55
    • one year ago
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    Correct. The number part of the GCF is 2. Now you need the variable part of the GCF.

  13. anonymous
    • one year ago
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    Okay it said start with a varible with the lowest degree i dont know what that means is the the exponent?

  14. diamondboy
    • one year ago
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    yes

  15. mathstudent55
    • one year ago
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    |dw:1442526095341:dw|

  16. mathstudent55
    • one year ago
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    Degree of a variable is the exponent. You are correct.

  17. anonymous
    • one year ago
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    okay but both x and y have an exponet that is the same

  18. anonymous
    • one year ago
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    3 and 2

  19. mathstudent55
    • one year ago
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    Below, I broke up the numbers into their factors. You can see clearly (the red helps) that the only number factor all three terms have is 2. \(\color{red}2\cdot x^3 \cdot y^4 − \color{red}2\cdot 2 \cdot 2 \cdot x^2y^3 + \color{red}2 \cdot 3 \cdot xy^2\)

  20. anonymous
    • one year ago
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    yes i understand that :)

  21. mathstudent55
    • one year ago
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    Now let's look at the variables to see what variables appear in all factors. \(\color{red}2\cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y − \color{red}2\cdot 2 \cdot 2 \cdot x \cdot x\cdot y \cdot y \cdot y + \color{red}2 \cdot 3 \cdot x \cdot y \cdot y\) Normally, you don;t have to do what I did above, but I just want you to see what the exponents really mean. Now we see how many x's and y's are in common to all terms.

  22. anonymous
    • one year ago
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    okay I got that

  23. anonymous
    • one year ago
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    so which ever one has the less is the one you need?

  24. mathstudent55
    • one year ago
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    \(\color{red}2\cdot \color{green}x \cdot x \cdot x \cdot \color{purple}{y \cdot y} \cdot y \cdot y − \color{red}2\cdot 2 \cdot 2 \cdot \color{green}x \cdot x\cdot \color{purple}{y \cdot y} \cdot y + \color{red}2 \cdot 3 \cdot \color{green}x \cdot \color{purple}{y \cdot y}\)

  25. mathstudent55
    • one year ago
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    Yes. Since the 3rd term only has one x, and the other terms have more than one x, the three terms have only 1 x in common. Since the third term has only 2 y's, and the other terms have more than 2 y's, all three terms have only 2 y's in common.

  26. anonymous
    • one year ago
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    so 2x? is what your dividing everything by?

  27. anonymous
    • one year ago
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    or 2xy?

  28. anonymous
    • one year ago
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    2xy^2

  29. mathstudent55
    • one year ago
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    Every term has a factor of 2. Every term has a factor of x Every term has a factor of y^2 The GCF is 2xy^2 We divide all three terms by 2xy^2 Now we pull out the common factor, 2xy^2.

  30. mathstudent55
    • one year ago
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    Correct. Use 2xy^2.

  31. anonymous
    • one year ago
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    okay imma try to see if i can fiqure i out and tell me if im right?

  32. mathstudent55
    • one year ago
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    ok

  33. anonymous
    • one year ago
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    ok heres what i got

  34. anonymous
    • one year ago
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    2xy2(x2y2 − 4xy + 3)

  35. mathstudent55
    • one year ago
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    \(2xy^2(x^2y^2 - 4 xy + 3)\) Excellent. You got the same I did.

  36. mathstudent55
    • one year ago
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    We are not done, though.

  37. anonymous
    • one year ago
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    AHhhh lol i thought we were

  38. mathstudent55
    • one year ago
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    Now think of the product xy as a variable. Let's say xy = z. That means x^2y^2 = z^2

  39. anonymous
    • one year ago
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    yes

  40. mathstudent55
    • one year ago
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    If you think of the variables that way, we can make a substitution. Wherever we see xy, we will replace it with z. Then wherever we see x^2y^2 we will replace it with z^2.

  41. anonymous
    • one year ago
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    ok

  42. mathstudent55
    • one year ago
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    Now we have this: \(=2xy^2(x^2y^2 - 4 xy + 3)\) After the substitution we have this: \(=2xy^2(z^2 - 4 z + 3)\)

  43. mathstudent55
    • one year ago
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    The trinomial in the parentheses is a quadratic trinomial in z. We need to try to factor it.

  44. anonymous
    • one year ago
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    ok

  45. mathstudent55
    • one year ago
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    To factor a trinomial of the form \(x^2 + ax + c\), you need to find two number that multiply to b and add to a. Our trinomial is of that form, so wee need to try to find two numbers that multiply to 3 and add to -4.

  46. anonymous
    • one year ago
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    Also i forgot to post the answers. 2(x3y4 − 4x2y3 + 3xy2) 2x(x2y4 − 4xy3 + 3y2) 2xy2(x2y2 − 4xy + 3) Prime

  47. mathstudent55
    • one year ago
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    According to your choices, we are done, and the answer is C.

  48. anonymous
    • one year ago
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    Thank you so much! :D

  49. mathstudent55
    • one year ago
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    Just for completeness, let's just finish factoring because the trinomial is also factorable.

  50. anonymous
    • one year ago
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    Ok

  51. mathstudent55
    • one year ago
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    From now on, it's just extra info. In fact, from the point I began with the substitution it's extra info. Since the two numbers have to multiply to 3, a positive number, the two numbers must be both positive or both negative. Since they need to add to -4, a negative number, the two numbers must contain at least one negative number. The two numbers are -3 and -1 \(=2xy^2(z -3)(z - 1)\) Now we substitute xy back for z to get the final complete factorization: \(=2xy^2(xy -3)(xy - 1)\)

  52. mathstudent55
    • one year ago
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    You're welcome.

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