find the remainder in the following case when f(x) is divided by g(x). f (x)=2x^3-3x^2-4x-5,g(x)=2x+1​

Question

find the remainder in the following case when f(x) is divided by g(x). f (x)=2x^3-3x^2-4x-5,g(x)=2x+1​

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Bella 5 months 2021-07-18T22:55:53+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-18T22:57:13+00:00

    Answer:

    Remainder is -17/4

    Step-by-step explanation:

    consider , f(x)/g(x) = ( 2x^3 -3x^2-4x-5)/(2x+1)

    0
    2021-07-18T22:57:23+00:00

    Step-by-step explanation:

    Given :

    f(x)=2x^3-3x^2-4x-5,

    g(x)=2x+1

    To find:

    Find the remainder when f(x) is divided by g(x) ?

    Solution:

    Given Polynomial f(x) = 2x^3-3x^2-4x-5

    Given divisor g(x)=2x+1

    We know that

    Remainder Theorem

    Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if P(x) is divided by x-a then the remainder is P(a).

    Now ,

    On applying this theorem to f(x)

    If f(x) is divided by g(x) = 2x+1 then the remainder is f(-1/2).

    Since 2x+1 = 0

    => 2x = -1

    => x = -1/2

    f(-1/2)

    => 2(-1/2)^3-3(-1/2)^2-4(-1/2)-5

    => 2(-1/8)-3(1/4)-(-4/2)-5

    => (-2/8)-(3/4)-(-2)-5

    => (-1/4)-(3/4)+2-5

    => (-1-3)/4 +(2-5)

    => (-4/4)+(-3)

    => (-1)+(-3)

    =>-1-3

    => -4

    Therefore, f(-1/2)=-4

    Answer:

    The remainder if f(x) is divided by g(x) is 4

    Used formulae:

    Remainder Theorem:

    • Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if P(x) is divided by x-a then the remainder is P(a).

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