Question

Divide p(X)=4x^4+3x^3-2x^2+10x-8 by g(X)=2x^3-x^2+7x-5 and then verify division algorithm

please answer fast ​

Answer 1

Answer:

Answer

We know that the division algorithm states that:

Dividend=(Divisor×quotient)+Remainder

Here it is given that the dividend is p(x)=4x

3

+2x

2

−10x+2, the divisor is g(x), the quotient is 2x

2

+4x+1 and the remainder is 5, therefore,

4x

3

+2x

2

−10x+2=[g(x)(2x

2

+4x+1)]+5

⇒g(x)=

2x

2

+4x+1

4x

3

+2x

2

−10x+2

The division is shown above.

Hence, from the above division, we get that the divisor is g(x)=2x−3