Question

A factory has a profit fund represented by 6x4+8x3+17x2+21x+7. the fund is equally divided between each worker of the factory. each worker receives an amount of 2x2+5, while after distribution , x+2 amount is left. the management decides to use this amount to create a medical aid fund. find the number of workers who received the fund.

Answer 1

We have total fund = 6x⁴+8x³+17x²+21x+7, and after giving 2x²+5 to each worker, the amount left from the fund is x+2.
So, we will subtract x+2 from the total fund, we get
6x⁴+8x³+17x²+21x+7 - (x+2)
6x⁴+8x³+17x²+21x+7 - x - 2
6x⁴+8x³+17x²+20x+5
6x⁴+8x³+17x²+20x+5 is the amount that is distributed between the workers and each worker got 2x²+5. In other words the polynomial 6x⁴+8x³+17x²+20x+5 is divided by our divisor 2x²+5 and after division we wili zero as a remainder.
6x⁴+8x³+17x²+20x+5 ÷ 2x²+5
+ 3x²+4x+1
So, the number of workers who received the funds = 3x²+4x+1  Answer.