Question

A trader bought 2x²–x+2 TV sets for 8x⁴+7x–6. Find the price of one TV set.

Answer 1

number of TV sets are bought by Trader = 2x² - x +2
total price of TV sets = 8x⁴ + 7x - 6

price of one TV set = total price of TV sets/number of TV sets
= (8x⁴ + 7x - 6)/(2x² - x + 2)

now, 8x⁴ + 7x - 6
= 8x⁴ - 4x³ + 8x² + 4x³ - 2x² + 4x - 6x² + 3x - 6
= 4x²(2x² - x + 2) + 2x(2x² - x + 2) - 3(2x² - x + 2)
= (4x² + 2x - 3)(2x² - x + 2)

now, price of one TV set = (4x² + 2x - 3)(2x² - x + 2)/(2x² - x + 2)
= 4x² + 2x - 3

Answer 2

Hi ,

Number of T.V sets

trader bought = 2x²-x+2 ---( 1 )

Total price of the T.V sets = 8x⁴ + 7x - 6--( 2 )

Price of each T.V = ( 2 )/( 1 )

2x²-x+2) 8x⁴ + 0 + 0 + 7x -6 (4x²+2x -3
********** 8x⁴ -4x³ + 8x²
______________________
***************4x³ - 8x² + 7x
***************4x³ -2x² + 4x
_______________________
******************* -6x² + 3x - 6
****************** - 6x² + 3x - 6
________________________
Remainder = 0

Therefore ,

Each T.V set price = 4x² + 2x -3

I hope this helps you.

; )