Question

Divide 3x*2+5x-1 by x+2 and verify divisor algorithm.​

Answer 1

First divide the given polynomial

3x-1

_________________

x+2) 3x^2+5x-13x

2

+5x−1

3x^2+6x3x

2

+6x

__(-)___(-)________

-x-1

-x-2

____(+)_(+)______

1

_________

Therefore the quotient is 3x-1 and remainder is 1

Now verify the division algorithm :

Dividend =quotient\times divisor + remainderDividend=quotient×divisor+remainder

3x^2+5x-1=(3x-1)\times (x+2)+13x

2

+5x−1=(3x−1)×(x+2)+1

By using Distributive property :

(x+y)(a+b)=x(a+b)+y(a+b)

3x^2+5x-1=(3x)(x+2)-1(x+2)+13x

2

+5x−1=(3x)(x+2)−1(x+2)+1

By using Distributive property :

a(x+y)=ax+ay

3x^2+5x-1=3x(x)+3x(2)-1(x)-1(2)+13x

2

+5x−1=3x(x)+3x(2)−1(x)−1(2)+1

3x^2+5x-1=3x^2+6x-x-2+13x

2

+5x−1=3x

2

+6x−x−2+1

Adding the like terms

3x^2+5x-1=3x^2+5x-13x

2

+5x−1=3x

2

+5x−1

Hence the Division Algorithm is verified