Question

divide 3x^2+5x-1 by x+2 and verify the divison algorithum

Answer 1

( OR )

Step-by-step explanation:

Given that Divide 3x^2+5x-13x 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-13x 2 +5x−1

3x^2+6x3x 2 +6x

__(-)___(-)________

-x1-x-2

____(+)_(+)______

1

_________

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

Now verify the division algorithm :

Dividend =quotient\times divisor + remainder Dividend=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)+13x2+5x−1

=3x+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.

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