Question

If ax3+bx2+cx+d is divided by (x-2) the coefficients of quotient are 2,-1,3 and the remainder is 4, then the polynomial is

Answer 1

$\textbf{Given:}$

$\text{When}\;\mathrm{ax^3+bx^2+cx+d}\;\text{is divided by (x-2)},}$

$\text{Quotient=}\mathrm{2x^2-x+3}$

$\text{Remainder=4}$

$\textbf{To find:}$

$\text{The polynomial}$

$\textbf{Solution:}$

$\textbf{Division algorithm:}$

$\textbf{Dividend=(Divisor \times Quotient)+Remainder}$

$\text{Using division algorithm}$

$\textbf{The required polynomial is}$

$\mathrm{=(x-2)(2x^2-x+3)+4}$

$\mathrm{=(2x^3-x^2+3x-4x^2+2x-6)+4}$

$\mathrm{=(2x^3-5x^2+5x-6)+4}$

$\mathrm{=2x^3-5x^2+5x+2}$

$\textbf{Answer:}$

$\textbf{The required polynomial is}$

$\mathrm{\bf\,2x^3-5x^2+5x+2}$

Answer 2

Answer:

you did mistake -6+4 is not +2 it is -2