Question

If is 5x2y4 one of the factors of 10x3y4-25x2y5, what is the other factor?

Answer 1

Answer:

Solution: 24 x 35 x 104 = 2^4×3^5×(2^4×5^4 )=2^8×3^5×5^4 

Perfect square factors of the number will be of the form 2^a×3^b×5^c 

Where a can be 0, 2, 4, 6 or 8 . b can be 0, 2 or 4 and c can be 0, 2 or 4 

So total number of square factors = 5*3*3 = 45 

But when a=b=c =0 factor will be 1. 

Thus perfect squares which are greater than 1= 45 -1 = 44