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What is the remainder when 3x^4 - 8x^2 + 3x - 2 is divided by (x - 2)

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xataexa | Student, Kindergarten | Salutatorian

Posted September 23, 2013 at 12:57 PM via web

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What is the remainder when 3x^4 - 8x^2 + 3x - 2 is divided by (x - 2)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 23, 2013 at 1:00 PM (Answer #1)

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For any polynomial P(x), the remainder when it is divided by (x - a) is equal to P(a).

When the polynomial P(x) = 3x^4 - 8x^2 + 3x - 2 is divided by (x - 2), the remainder is P(2) = 3*2^4 - 8*2^2 + 3*2 - 2 = 20

The remainder when 3x^4 - 8x^2 + 3x - 2 is divided by (x - 2) is 20

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steveschoen | College Teacher | (Level 3) Assistant Educator

Posted September 23, 2013 at 2:13 PM (Answer #2)

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Hi, xata,

I would like to add that, with 20 being the remainder, if you remember the long division, there were 3 different ways you could express the remainder: 1) as a decimal, 2) as a fraction, or 3) with R then the number after it.  For polynomials, #1 isn't used.  For the other two, though, it could depend upon how your teacher would want the remainder expressed.  For, if as a fraction, the remainder would be shown as:

20/(x-2)

Good luck, xata.  I hope this helps.

Till Then,

Steve

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