If frac{x^4+x^3+2x^2-2x+1}{x^3+x^2} = P(x) + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Perform polynomial division on the expression: $\frac{x^4+x^3+2x^2-2x+1}{x^3+x^2} = x + \frac{2x^2-2x+1}{x^2(x+1)}$.Comparing this with $P(x) + \f

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Perform polynomial division on the expression: $\frac{x^4+x^3+2x^2-2x+1}{x^3+x^2} = x + \frac{2x^2-2x+1}{x^2(x+1)}$.Comparing this with $P(x) + \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+1}$,we have $P(x) = x$ and $\frac{2x^2-2x+1}{x^2(x+1)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+1}$.Multiplying by $x^2(x+1)$,we get $2x^2-2x+1 = Ax(x+1) + B(x+1) + Cx^2$.Setting $x = 0$,we get $1 = B(1) \Rightarrow B = 1$.Setting $x = -1$,we get $2(-1)^2 - 2(-1) + 1 = C(-1)^2$ $\Rightarrow 2+2+1 = C$ $\Rightarrow C = 5$.Comparing the coefficients of $x^2$: $2 = A + C$ $\Rightarrow 2 = A + 5$ $\Rightarrow A = -3$.Thus,$A+B+C = -3 + 1 + 5 = 3$.

If $\frac{x^4+x^3+2x^2-2x+1}{x^3+x^2} = P(x) + \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+1}$,then $A+B+C = $

Similar Questions

The coefficient of $x^4$ in the power series expansion of $\frac{x^2-1}{(x^2+1)(x^2+2)}$ is

If $\frac{1}{x^4+x^2+1}=\frac{Ax+B}{x^2+x+1}+\frac{Cx+D}{x^2-x+1}$,then $\cos^{-1}(A+B+C+D)=$

$\text{If } \frac{3x^2+1}{(x^2+1)(x^2+2)^2} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{x^2+2} + \frac{Ex+F}{(x^2+2)^2}, \text{ then } A+C+E = $

If $\frac{1}{(3-5 x)(2+3 x)}=\frac{A}{3-5 x}+\frac{B}{2+3 x}$,then $A+B$ is equal to

If $\frac{3x + a}{x^2 - 3x + 2} = \frac{A}{x - 2} - \frac{10}{x - 1}$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module