Question

Find the quotient when divided $x^2+1$ by $x+1$ using linear division method .

• A. $x+1$
• B. $2x-1$
• C. $x-1$
• D. $x-2$

Answer 1

The correct option is C $x-1$

$x^2+1$ by $x+1$

To get the term $x^2$ multiply $x+1$ by $x$ and subtract $x$

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

So, dividend = $x^2+1$ =$x$ $(x+1)$ - $x$ + 1 ......(1)

To get the term - $x$ multiply $x+1$ by -1 and add 1.

-1 $(x+1)$+1 = - $x$

So, $x^2+1$ =$x$ $(x+1)$ -1 $(x+1)$+1 + 1 ......from (1)

Hence, $x^2+1$ = $(x+1)$ $(x-1)$ +2......(2)

Equation (2) is in the form of :

$dividend=divisor\times quotient+remainder$

So, quotient = $x-1$