Question

$(12 {x}^{2}+11x+2) \div (4x + 1)$
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Answer 1

Question -

Divide 12x² + 11x + 2 by 4x + 1 .

Solution -

Here , we have to divide 12x² + 11x + 2 by 4x + 1 .

The dividend here is 12x² + 11x + 2 and the divisor is 4x + 1 .

This can be done in 2 methods -

1. Factorisation -

12x² + 11x + 2

=> 12x² + 8x + 3x + 2

=> 4x ( 3x + 2 ) + 1 ( 3x + 2 )

=> ( 4x + 1 )( 3x + 2 ) .

Now if we divide this by 4x + 1 , we get the quotient automatically as 3x + 2.

The remainder is 0 .

2. Long Division. ..

____________

4x + 1 ) 12x² + 11x + 2 ( 3x + 2

12x² + 3x

( - ) ( - )

________

8x + 2

8x + 2

_____

Hence , the quotient is 3x + 2 and the remainder is 0 .

This is the required answer.

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Additional Information -

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

( a + b )( a - b ) = a² - b²

( a + b )³ = a³ + 3ab ( a + b ) + b³

( a - b )³ = a³ - 3ab ( a + b ) - b³

( a + b + c )³ = a³ + b³ + c³ + 3 ( a + b )( b + c )( c + a )

a³ + b³ + c³ - 3abc = ( a + b + c )( a² + b² + c² - ab - bc - ca )

When a + b + c = 0 ,

a³ + b³ + c³ = 3abc .

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Answer 2

Given:-

⠀⠀

$\bf\implies(12 {x}^{2}+11x+2) \div (4x + 1)$

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To Find:-

⠀⠀

$\bf\implies \: The \: Solution$

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STEP BY STEP EXPLANATION:-

⠀⠀

$\bf\implies \frac{12 {x}^{2} + 11x + 2 }{4x + 1}$

⠀⠀

$\bf\implies \frac{12 {x}^{2} + 8x + 3x + 2}{4x + 1}$

⠀⠀

$\bf\implies \frac{4x \times (3x + 2) + 3x + 2}{4x + 1}$

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$\bf\implies \cancel\frac{(3x + 2) \times (4x + 1)}{4x + 1}$

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$\bf\implies3x + 2$