Question

divide 2x^4-9x^3+5x^2+3x-8 by x^2-4x+1 and verify the division algorithms.

Answer 1

hope this helps you.......

Answer 2

Step-by-step explanation:

On dividing the given factors,

Hence, Quotient $= 2 x^{2}-x-1$

Remainder = -7    

In division algorithm the quotient and divisor is multiplied and added with the remainder which results in the dividend. This method is usually used to verify if the quotient and remainder we obtained are right.

Verification of the division algorithms,

Quotient Divisor + Remainder

$\begin{array}{l}{\left(2 x^{2}-x-1\right)\left(x^{2}-4 x+1\right)+(-7)} \\ {\left(2 x^{4}-8 x^{3}+2 x^{2}-x^{3}+4 x^{2}-x-x^{2}+4 x-1\right)+(-7)} \\ {2 x^{4}-9 x^{3}+6 x^{2}+3 x-8}\end{array}$

Thus verified.