Question

Divide 6x^3+13x^2-4 by 3x+2

Answer 1

Answer:

Quotient=q=3x

2

+5x−2

Remainder=r=0Remainder=r=0

Given the polynomial

P(x)=6x^3+13x^2+x-2P(x)=6x

3

+13x

2

+x−2

we have to find the quotient and remainder when above polynomial is divided by 2x+1

The division is shown in attachment

The quotient and remainder is

Quotient=q=3x^2+5x-2Quotient=q=3x

2

+5x−2

Remainder=r=0Remainder=r=0

By division algorithm

Dividend=Divisor\times Quotient + RemainderDividend=Divisor×Quotient+Remainder

P(x)=(2x+1)\times (3x^2+5x-2)+0P(x)=(2x+1)×(3x

2

+5x−2)+0

P(x)=2x(3x^2+5x-2)+1(3x^2+5x-2)P(x)=2x(3x

2

+5x−2)+1(3x

2

+5x−2)

P(x)=6x^3+10x^2-4x+(3x^2+5x-2)P(x)=6x

3

+10x

2

−4x+(3x

2

+5x−2)

P(x)=6x^3+13x^2+x-2P(x)=6x

3

+13x

2

+x−2

which is verified