Question

can someone teach me how to get the common term (the numeric) from this equation:

Answer 1

Equation is attached

Answer 2

first look at the coefficients:
1/2, -3/2,-1/2
i can divide 1/2 evenly into all 3

next look at the exponents of the variable x
k,2k,3k
i can take at most 1 k away from each of them

so we factor out 1/2x^k leaving
1/2x^k(1-3x^k-x^2k)

Answer 3

Can you give me another example please?

Answer 4

I understand the part related to the exponents. The fraction coefficients is what im confussed in

Answer 5

3/4x^2 - 3/2x^3 +1/4x^4

coefficients:
3/4, -3/2, 1/4
try to break them down into lowest fractions
3/4 = 3*1/4
3/2 = 3*1/2 = 6*1/4
1/4 = 1*1/4
now they all have something in common, the 1/4

exponents:
2,3,4
i can take away at most 2 from each exponent

factor out 1/4x^2
=1/4x^2(3 - 6x +x^2)

Answer 6

Ok it is clear for me now. One medal for you help. Thank you friend :)

Answer 7

no problem :)