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​

Answer 1

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).

Answer 2

Answer:

Remainder is -17/4

Step-by-step explanation:

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