Find the quotient when divided $3 x^{2} + 3$ by $x + 1$ using linear division method .

3 x - 3

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3 x - 4

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2 x - 3

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3 x - 7

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Solution

The correct option is A $3 x - 3$
$3 x^{2} + 3$ by $x + 1$

To get the term $3 x^{2}$ multiply $x + 1$ by $3 x$ and subtract $3 x$

$3 x$ $(x + 1)$ - $3 x$ = $3 x^{2}$

So, dividend = $3 x^{2} + 3$ = $3 x$ $(x + 1)$ - $3 x$ + 3 ......(1)

To get the term - $3 x$ multiply $x + 1$ by -3 and add 3.

-3 $(x + 1)$ +3 = - $3 x$

So, $3 x^{2} + 3$ = $3 x$ $(x + 1)$ -3 $(x + 1)$ +3 + 3 ......from (1)

Hence, $3 x^{2} + 3$ = $(x + 1)$ $(3 x - 3)$ +6......(2)

Equation (2) is in the form of :

$d i v i d e n d = d i v i s o r \times q u o t i e n t + r e m a i n d e r$

So, quotient = $3 x - 3$

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