Question

please answer and give explanation ​

Answer 1

Answer:

i)

$\sqrt[x + 3]{2 {x}^{2} + x - 7}$

$= > \sqrt[x + 3]{ \binom{2 {x}^{2} +x - 7}{ - 2 {x}^{2} {- 6x } \: \: \: \: \: \: } } \: \: \: \: (2x) \\ = > \sqrt[x + 3]{ \binom{ - 5x - 7}{5 + 15} } \: \: \: (2x - 5) \\ = > \sqrt[x + 3]{8} \: \: \: \: (2x - 5)$

Here the term in the brackets outside the root is the quotient in each step and '8' is the remainder, so clearly -

Dividend = 2x^2 + x - 7

Divisor = x+3

Quotient = 2x - 5

Remainder = 8

So -

Dividend = 2x^2 + x - 7

and, Divisor × Quotient + Remainder

= (x+3) × (2x-5) + 8

= 2x^2 - 5x + 6x - 15 +8

= 2x^2 + x - 7 = Dividend

Hence, Dividend = Divisor × Quotient + Remainder

Similarly to do in part ii)