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anonymous

  • one year ago

What is the remainder when (x3 − 3x2 − 13x + 78) is divided by (x + 4)?

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  1. anonymous
    • one year ago
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    If you know synthetic division, you can just use that to figure out the remainder. However, if you don't you can plug in x = -4 to find the remainder.

  2. anonymous
    • one year ago
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    So, either |dw:1436819332290:dw| or you can evaluate \((-4)^3-3(-4)^2-13(-4)+78.\)

  3. anonymous
    • one year ago
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    ok give me a sec

  4. anonymous
    • one year ago
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    o ok . o its 15

  5. anonymous
    • one year ago
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    so*

  6. anonymous
    • one year ago
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    Not quite. I think you made an arithmetic mistake.

  7. anonymous
    • one year ago
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    \[(-4)^3-3(-4)^2-13(-4)+78=-64-48+52+78=4+14=18\]

  8. anonymous
    • one year ago
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    oooooo

  9. anonymous
    • one year ago
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    Also, if you were to do the synthetic method (which I think is easier for these bigger numbers, you'd get:|dw:1436819716328:dw|

  10. anonymous
    • one year ago
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    Do you get it?

  11. anonymous
    • one year ago
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    yes thank you so much

  12. anonymous
    • one year ago
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    No problem.

  13. anonymous
    • one year ago
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    can you help me with one more

  14. anonymous
    • one year ago
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    Sure.

  15. anonymous
    • one year ago
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    Which of the following is a factor of f(x) = 4x3 + 11x2 − 75x + 18? my answer was (x+3)

  16. anonymous
    • one year ago
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    What were your other choices?

  17. anonymous
    • one year ago
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    (x − 3) (x + 3) (x − 1 over 3) (x + 1 over 3)

  18. anonymous
    • one year ago
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    Before I explain this, do you know how to do synthetic division? If not, it'd probably be better for me to explain how to do that first.

  19. anonymous
    • one year ago
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    ok explain plz

  20. anonymous
    • one year ago
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    Synthetic division basically lets you divide polynomials. So, you can see whether something is a factor of something else. Let's do it with this question. You said your answer was x + 3. Start off by setting the "factor" or what you're dividing equal to 0. So:\[x+3=0\]Now, solve for x.\[x=-3\]This is the number you're going to be using. Now, set up the question like this.|dw:1436820455972:dw| If you look, the numbers on the top are the coefficients next to the 'x'.

  21. anonymous
    • one year ago
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    Next, bring down the first number at the top.|dw:1436820595855:dw| Then, multiply this number by the number in the top left corner and place that number in the next column like so.|dw:1436820628993:dw|

  22. anonymous
    • one year ago
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    Add the two numbers in the column, and then bring down the sum and repeat.|dw:1436820714464:dw| If the remainder isn't 0, it isn't a factor.

  23. anonymous
    • one year ago
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    ooooooooo

  24. anonymous
    • one year ago
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    So, since 234 ≠ 0, x + 3 isn't a factor. So, now, try using x-3, and do what I did above and see how you do. I'll set it up for you.\[x-3=0\]\[x=3\]|dw:1436820965654:dw| Can you take it from there?

  25. anonymous
    • one year ago
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    so its A

  26. anonymous
    • one year ago
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    Yes, because the remainder becomes 0.|dw:1436821132952:dw|

  27. anonymous
    • one year ago
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    18 - 18 is 0, so yes, x - 3 is a factor.

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