Question

Dvide 2x² + 3x + 1 by x +2​

Answer 1

Answer:

SEE IMAGE

Step-by-step explanation:

Answer 2

$\sf\huge {\underline{\underline{{Solution}}}}$

let f(x) = 2x²+3x+1

g(x) = x+2

Taking first two terms : 2x²+3x

In order to make x² with coefficient 2 Multiply the g(x) with 2x => 2x( x+2)= 2x²+4x

2x²+3x+1

2x²+4x

$(-)(-)$

_________

-x +1

Taking last constant : -x +1

In order to make -x Multiply the g(x) with - sign.

=> -(x+2)= -x-2

-x+1

-x-2

(+)(+)

____

3

___

let r(x) be the remainder = 3

q(x) be the quotient= 2x-1

g(x) be the Divisor= x+2

f(x) be the dividend= 2x²+3x+1

Check :

By using division algorithm

Dividend = Divisor*quotient+remainder

2x² + 3x + 1 = (x+2)*(2x-1)+3

2x² + 3x + 1 = 2x²-x+4x-2+3

2x² + 3x + 1 = 2x²+3x+1