Question

Divide $\large\sf\frac{(2 + 2x²)}{(x + 2)}$ and write the answer in the given form
Dividend = Divisor X Quotient + Remainder​

Answer 1

correct question :-

Divide $\large\sf\frac{(2 + 2x^2)}{(x + 2)}$ and write the answer in the given form Dividend = Divisor X Quotient + Remainder

solution : -

Linear method of division:

Divide $\large\sf\frac{(2 + 2x^2)}{(x + 2)}$

To get the term 2x² multiply (x + 2) by 2x and subtract 4x.

2x (x + 2) - 4x = 2x²

Dividend = 2x² +2= 2x(x+2) - 4x +2. ( i )

get the term-4x multiply (x+2) by -4 and add 8.

-4 (x+2) + 8 = -4x

(2x²+2)= 2x(x+2) - 4(x+2) + 8 + 2 ... from ( ii )

(2x²+2) = (x + 2) (2x - 4) + 10

Dividend = divisor x quotient + remainder.

Answer 2

$\large\underline{\sf Correct\: Question :}$

Divide $\sf\dfrac{(2 + 2x^2)}{(x + 2)}$ and write the answer in the given form

Dividend = Divisor × Quotient + Remainder

$\rule{100}{0.8}$

$\large\underline{\sf Answer :}$

To Divide : (2 + 2x²) by (x + 2)

We can write Dividend as (2x² + 2)

⠀

$\underline{\bigstar\:\sf{According\:to\:the\:Question :}}$

$:\implies\sf \large\dfrac{(2+2x^2)}{(x+2)}\\\\\\:\implies\sf Dividend=(Divisor \times Quotient) + Remainder\\\\\\:\implies\underline{\boxed{\sf (2+2x^2) = [(x + 2) \times (2x - 4)] + 10}}$

$\rule{150}{1.5}$

⠀⠀⠀⠀Polynomial Division

$\boxed{\begin{array}{l | n | r}\sf x+2&\sf 2x^2+2&\sf2x-4\\ &\sf2x^2+4x\\ & ( - )\:( - )\\&\rule{55}{0.8}\\&\sf\qquad-4x+2\\ &\sf\qquad-4x-8\\ &\qquad( + )\:\:( + )\\&\quad\rule{60}{0.8}\\&\qquad\qquad\sf10\end{array}}$