Question

Divide 3x^2+5x-1 by (x+2) and verify the division algorithm

Answer 1

hope that this answer will help u

Answer 2

Given that Divide $3x^2+5x-1$ by (x+2)

TO VERIFY :

The division algorithm for the given polynomial.

SOLUTION :

First divide the given polynomial

          3x-1

      _________________

x+2) $3x^2+5x-1$

       $3x^2+6x$

__(-)___(-)________

               -x-1

               -x-2

    ____(+)_(+)______

                   1

            _________

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

Now verify the division algorithm :

$Dividend =quotient\times divisor + remainder$

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

By using Distributive property :

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

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

By using Distributive property :

a(x+y)=ax+ay

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

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

Adding the like terms

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

Hence the Division Algorithm is  verified