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Rajan@2021
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Find the remainder (without division) on dividing f(x) by (x−2) where f(x)=2x 3 −7x 2 +3

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This is one of the basic question from chapter 6 of factorisation from ML Aggarwal in which we have been asked to calculate the remainder (without division) on dividing f(x) by (x2) where
f(x)=2x37x2+3

ML Aggarwal Avichal Publication

Factorisation Question no.  1(ii)

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1 Answer

  1. We know that the remainder theorem states that if a polynomial f(x) is divided by (x−a), the remainder is f(a).

    (i) Here, we have the polynomial f(x)=5×2−7x+4 which is divided by (x−2), therefore, by remainder theorem, the remainder is:

    R=f(2)=5(2)2 −7(2)+4
    =(5×4)−14+4
    =20−14+4
    =24−14
    =10

    Hence, the remainder is 10.

    (ii) Here, we have the polynomial f(x)=2×3−7×2 +3 which is divided by (x−2), therefore, by remainder theorem, the remainder is:

    R=f(2)=2(2)3 −7(2)2 +3
    =(2×8)−(7×4)+3
    =16−28+3
    =19−28
    =−9

    Hence, the remainder is −9.

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