How do i find the value of A and B ?

Question

Given that 3x⁴-x²+7x-3=(x²-1)Q(X)+Ax+B , find the value of A and B . 

Answer 1

3x⁴-x²+7x-3=(x²-1)Q(X)+Ax+B

Since from LHS is a polynomial of the forth degree, therefore Q(X) should be a polinomial of the second degree: Q(x)=Cx²+Dx+E. Plug in into  equation and equate like terms in both sides.

 

3x⁴-x²+7x-3=(x²-1)(Cx²+Dx+E)+Ax+B

3x⁴-x²+7x-3=Cx⁴+Dx³+(E-C)x²-Dx-E+Ax+B

Equating like  terms, we have

x⁴ | 3=C

x³ | 0=D

x² | -1=E-C

x¹ | 7=A-D

x⁰ | -3=B-E

 

C=3, D=0, E=2

A=7,  B=-5