Rehman's mother has given him money to buy some boxes from the market at the rate of x^2+2x-3. The total amount of money given by his mother is represented by 4x^4+2x^3-2x^2+x-1. Out of this money he donated some amount to a child who was studying in the light of a street lamp. Find how much amount of money be must have so that he is able to buy exact and maximum number of boxes from the market.
Answers
Amount of money Rehman must have in order to buy exact and maximum number of boxes from the market is 2 (2x⁴ + x³ - x² + 31x - 33)
• Amount of money given to Rehman by his mother = 4x⁴ + 2x³ - 2x² + x - 1
• Rate of each box = x² + 2x - 3
• Therefore, total number of boxes that can be bought by Rehman = quotient of (4x⁴ + 2x³ - 2x² + x - 1) / (x² + 2x - 3)
( The division is shown in the image attached below)
• Maximum number of boxes that Rehman can buy = 4x² - 6x + 22
• Amount of money left with Rehman = Remainder = -61x + 65
• Therefore, amount of money Rehman donated to the child = -61x + 65
• Therefore, amount of money that Rehman must have to buy exact and maximum number of boxes = Amount given by his mother - Amount donated to the child
=> Required amount = (4x⁴ + 2x³ - 2x² + x - 1) - (-61x + 65)
= 4x⁴ + 2x³ - 2x² + x - 1 + 61x - 65
= 4x⁴ + 2x³ - 2x² + 62x - 66
= 2 (2x⁴ + x³ - x² + 31x - 33)
Therefore, Rehman needs 2 (2x⁴ + x³ - x² + 31x - 33) amount of money to buy exact and maximum number of boxes from the market.
