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anonymous

  • one year ago

which of the following is a facftor of both x^2 -x-6 and x^2= 5x+6

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  1. mathstudent55
    • one year ago
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    \(x^2 -x-6\) First equation \(x^2= 5x+6\) \(x^2- 5x-6 = 0\) Second equation

  2. mathstudent55
    • one year ago
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    The first equation can be factored in the form it's given. To factor the second equation, we need it in the form shown in the second line above.

  3. mathstudent55
    • one year ago
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    Do you know how to factor those trinomials?

  4. anonymous
    • one year ago
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    substracting one line?

  5. anonymous
    • one year ago
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    by -1

  6. mathstudent55
    • one year ago
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    No. I'll show you.

  7. mathstudent55
    • one year ago
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    Here is an example.

  8. anonymous
    • one year ago
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    Ok thanks

  9. mathstudent55
    • one year ago
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    |dw:1444524163180:dw|

  10. mathstudent55
    • one year ago
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    This is a trinomial in which the x^2 term is just x^2. We don't have a number multiplying the x^2.

  11. mathstudent55
    • one year ago
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    |dw:1444524269218:dw|

  12. mathstudent55
    • one year ago
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    You need to find 2 numbers that multiply to -2 and add to -1.

  13. anonymous
    • one year ago
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    \[\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\] Ax^2+Bx + C

  14. mathstudent55
    • one year ago
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    What are two numbers that multiply to -2? There are two possibilities: -2 and 1 -1 and 2 Notice that both -2 * 1 = -2 and -1 * 2 = -2

  15. mathstudent55
    • one year ago
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    We also need that the two numbers add to -1. -2 + 1 = -1 -1 + 2 = 1 The first line above, -2 and 1 does add to -1. The second line above does not. That means the two numbers we need are -2 and 1

  16. mathstudent55
    • one year ago
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    We set up the factors like this below: |dw:1444524436826:dw|

  17. mathstudent55
    • one year ago
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    Now all we do is place the two numbers we found like this below: |dw:1444524489908:dw|

  18. mathstudent55
    • one year ago
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    That is how a trinomial of the type \(x^2 + ax + b\) is factored

  19. anonymous
    • one year ago
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    what I wrote is the quadratic formula using your 2 equations x^2 -x-6 and x^2= 5x+6 you can see that for x^2 -x-6 = A = 1 B=-1 C =-6 and for x^2-5x-6 A = 1 B = -5 and C = -6

  20. anonymous
    • one year ago
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    thanks I get it :)

  21. mathstudent55
    • one year ago
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    Now let's look at the two trinomials you have. \(x^2 -x-6\) First trinomial \(x^2- 5x-6\) Second trinomial

  22. anonymous
    • one year ago
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    Ok thanks @mathstudent55 youre cool :)

  23. mathstudent55
    • one year ago
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    Since both of these trinomials have a plain x^2 term (with a coefficient of 1), we can factor them easily. We set them up like this: |dw:1444524646962:dw|

  24. mathstudent55
    • one year ago
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    |dw:1444524732670:dw|

  25. mathstudent55
    • one year ago
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    |dw:1444524792102:dw|

  26. anonymous
    • one year ago
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    -3 x 2 for the first one and -3 x -2 for second

  27. mathstudent55
    • one year ago
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    You are correct for the first one. The second has a mistake. When you wrote the original post, I think you wrote an = when you meant to write a +. Is that correct?

  28. mathstudent55
    • one year ago
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    Should the second trinomial be x^2 + 5x + 6 ? Your equal sign instead of the first plus sign is a typo?

  29. anonymous
    • one year ago
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    @mathstudent55 is right, if you didn't make a typo something is off.

  30. mathstudent55
    • one year ago
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    |dw:1444525027158:dw|

  31. mathstudent55
    • one year ago
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    |dw:1444525062059:dw|

  32. mathstudent55
    • one year ago
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    Which factor is in common? |dw:1444525083439:dw|