Question

on dividing 3x^4-10x^3+5x^2+11x-12 by g(x) q(x) = x^2-1 and r(x) =x-4 find g(x)​

Answer 1

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