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Math Help - Theorems

  1. #1
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    Exclamation Theorems

    1)Use the remainder theorem and the factor theorem to determine whether (b+4) is a factor of (b^3 +3b^2 - b+12)

    A. The remainder is 0 and, therefore, (b+4) is a factor of (b^3 +3b^2 - b+12)
    B. The remainder is 0 and, therefore, (b+4) isn't a factor of (b^3 +3b^2 - b+12)
    C. The remainder isn't 0 and, therefore, (b+4) is a factor of (b^3 +3b^2 - b+12)
    D. The remainder isn't 0 and, therefore, (b+4) isn't a factor of (b^3 +3b^2 - b+12)

    2) Use the remainder theorem to determine the remainder the remainder when 3t^2 +5t -7 is divided by t-5

    3)Use the remainder theorem and the factor theorem to determine whether (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)

    A. The remainder is 0 and, therefore, (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)
    B. The remainder is 0 and, therefore, (c+5) isn't a factor of (c^4 +7c^3 +6c^2 -18c+10)
    C. The remainder isn't 0 and, therefore, (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)
    D. The remainder isn't 0 and, therefore, (c+5) isn't a factor of (c^4 +7c^3 +6c^2 -18c+10)
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  2. #2
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    Hello, pyrogurl6989!

    I will assume you know the Remainder Theorem and the Factor Theorem.


    1) Use the remainder theorem and the factor theorem to determine
    whether b+4 is a factor of f(b) \:=\:b^3 +3b^2 - b+12

    Since f(\text{-}4)\;=\;(\text{-}4)^3 + 3(\text{-}4)^2 - (\text{-}4) + 12\;=\;-64 + 48 + 4 + 12  \;=\;0

    . . then: .(A) The remainder is 0, and therefore b+4 is a factor of f(b).



    2) Use the remainder theorem to determine the remainder
    when f(t)\:=\:3t^2 +5t -7 is divided by t-5

    Since f(5)\:=\:3(5^2) + 5(5) - 7 \:=\:93, then the remainder is 93.



    3)Use the remainder theorem and the factor theorem to determine
    whether c+5 is a factor of f(c) \:=\:c^4 +7c^3 +6c^2 -18c+10

    Since f(\text{-}5) \;=\;(\text{-}5)^4 + 7(\text{-}5)^3 + 6(\text{-}5)^2 - 18(\text{-}5) + 10 \;=\;625 - 875 + 150 + 90 + 10 \;=\;0

    . . then: .(A) The remainder is 0, and therefore c+5 is a factor of f(c)

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