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Math Help - Remanider Theorem

  1. #1
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    Remanider Theorem

    Hello everyone, I am studying Engineering Mathematics and have a maths test Tuesday.. I have been given some example questions several of which include the remainder theorem..

    Please could someone show me the way with the following example.

    (I do have notes that refer to ap sqaured + bp + c but unfortunately my class notes are poor)

    Can anyone advise please? here is the problem...

    3xsquared + 11x -8 divided by x+5

    I'm off to try it somemore myself but ill keep checking back here, thanks all
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  2. #2
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    seems silly replying to my own thread,,, is this correct??

    (3)(-5)squared + (11)(-5) - 8 =12
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  3. #3
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    Quote Originally Posted by HNCMATHS View Post
    Hello everyone, I am studying Engineering Mathematics and have a maths test Tuesday.. I have been given some example questions several of which include the remainder theorem..

    Please could someone show me the way with the following example.

    (I do have notes that refer to ap sqaured + bp + c but unfortunately my class notes are poor)

    Can anyone advise please? here is the problem...

    3xsquared + 11x -8 divided by x+5

    I'm off to try it somemore myself but ill keep checking back here, thanks all
    Hi HNCMATHS,

    (3x^2+11x-8) \div (x+5)

    If you want to just divide, you might consider synthetic division. Are you familiar with this?

    If not, can you do polynomial long division?

    If you're just trying to find the remainder, do this:



    f(-5)=3(-5)^2+11(-5)-8

    f(-5)=12
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  4. #4
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    Hello there!

    Thanks very much for the reply, unfortunately i have to use the remainder theorem to prove i understand the 'remainder theorem'

    i think i have worked it out kinda, could you take a look at my own reply to this ?
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  5. #5
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    Quote Originally Posted by HNCMATHS View Post
    Hello there!

    Thanks very much for the reply, unfortunately i have to use the remainder theorem to prove i understand the 'remainder theorem'

    i think i have worked it out kinda, could you take a look at my own reply to this ?
    Your solution is the same as mine.
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  6. #6
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    \frac{p(x)}{x-a}=q(x)+Rem

    p(x)=(x-a)q(x)+Rem

    Therefore

    p(a)=Rem

    Hence

    [p(x)-Rem] is evenly divisible by x-a
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  7. #7
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    Another One

    Yes thank you Masters,

    If you dont mind could you help me with this next one its the divisor which is different and is making it hard for me...

    x^3 - x^2 +2x + 4 \div (2x + 1)
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  8. #8
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    The denominator is 2(x-[-0.5])

    Placing x=-0.5 into the numerator x^3-x^2+2x+4 gives the remainder
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  9. #9
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    Hello Archie,

    Unfortunately i dont follow

    I need to use the methods previous shown, i.e remainder theorem

    regards,

    chris
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  10. #10
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    Archie following your reply with 0.5 i have worked it out!!!!!

    excellent!

    Thanks so much
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  11. #11
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    Quote Originally Posted by HNCMATHS View Post
    Yes thank you Masters,

    If you dont mind could you help me with this next one its the divisor which is different and is making it hard for me...

    x^3 - x^2 +2x + 4 \div (2x + 1)
    Simply put, if you want to find the remainder, set the divisor = 0 and solve for x.

    2x+1=0

    x=-\frac{1}{2}

    Then, f\left(-\frac{1}{2}\right) will give you the remainder.
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  12. #12
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    Thank you both so much, what a fantastic site!
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  13. #13
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    Well done Chris!
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