Question

Divide 2x^4 - 3x^3 + 4x^2 - x +2 by 2x + 1 find the remainder and quotient

Answer 1

Answer:

On dividing f(x)=2x5+3x4+4x3+4x2+3x+2 by a polynomial g(x), where g(x)=x3+x2+x+1, the quotient obtained as 2x2+x+1. Find the remainder r(x).

Answer

By remainder theorem,

f(x)=q(x)g(x)+r(x)

∴2x5+3x4+4x3+4x2+3x+2=(2x2+x+1)(x3+x2+x+1)+r(x)

=2x2(x3+x2+x+1)+x(x3+x2+x+1)+1(x3+x2+x+1)+r(x)

=2x5+2x4+2x3+2x2+x4+x3+x2+x+x3+x2+x+1+r(x)

=2x5+3x4+4x3+4x2+2x+1+r(x)

r(x)=x+1

Step-by-step explanation:

December 30, 2019avatar

Pranjali Methai

Answer 2

amen amen amen amen amen