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​

2 thoughts on “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​”

1. Answer:

   Remainder is -17/4

   Step-by-step explanation:

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

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2. 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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