Question

On dividing x^3-8x^2+20x-10 by a polynomial g(x) the quotient and the remainder were x-4 and 6 respectively. Find g(x).

Answer 1

It is given that the quotient and remainder when $x^3-8x^2+20x-10$ is divided by $g(x)$ are $x-4$ and 6. That is

$x^3-8x^2+20x-10 =(x-4)g(x)+6\\ (x-4)g(x)=x^3-8x^2+20x-16\\ (x-4)g(x)=x^3-4x^2-4(x^2-5x+4)\\ (x-4)g(x)=x^2(x-4)-4(x-4)(x-1)\\ (x-4)g(x)=(x^2-4x+1)(x-4)\\ g(x)=x^2-4x+1$

Answer 2

Answer:

Step-by-step explanation:

the answer is $x^{2} -4x+4$