Question

Rams mother has given him money to buy some boxes from market at the rate of 4x²+3x-2. the total amount of money is represented by 8x⁴+14x³-2x²+7x-8. out of this money he donated some amount to child who was stufying in the light of a street lamp. find how much amount of money he donated and how many boxes he purchased from market?

Answer 1

No. of boxes he bought = the quotient
Amount he donates to the poor child = the remainder

See the attachment
Hope it helps!!!

Answer 2

Answer:

The amount he donated is $14x-10$

No. of boxes he purchased is  $2x^2+2x-1$

Step-by-step explanation:

Cost of 1 box = $4x^2+3x-2$

Ram has total amount = $8x^4+14x^3-2x^2+7x-8$

So, No. of boxes he can buy =  $\frac{8x^4+14x^3-2x^2+7x-8}{4x^2+3x-2}$

So, Dividend =  $8x^4+14x^3-2x^2+7x-8$

Divisor =  $4x^2+3x-2$

Since we know that :

$8x^4+14x^3-2x^2+7x-8 = (4x^2+3x-2 \times 2x^2)+(8x^3+2x^2+7x-8)$

$8x^4+14x^3-2x^2+7x-8 = (4x^2+3x-2 \times 2x^2+2x)+(-4x^2+11x-8)$

$8x^4+14x^3-2x^2+7x-8 = (4x^2+3x-2 \times 2x^2+2x-1)+(14x-10)$

So, The quotient is $2x^2+2x-1$

Remainder : $14x-10$

So,The amount he donated is $14x-10$

No. of boxes he purchased is  $2x^2+2x-1$