Write each expression in the form: quotient +remainder divided by divisor 2x^2+4/2x?

Answer 1

I was taught to approach this the same way as long division and set it up in the following manner,
_________
2x | 2x^2 + 4

One of the things to do before launching into this problem is notice that there is no 'x' term so for clarity, add 0x term in the dividend

Like so...
____________
2x | 2x^2 + 0x + 4

Then take a 'long division' approach and consider the first term in the dividend, it's 2x^2, the divisor is 2x, so the quotient for this would be x ---> (2x)(x) = 2x^2

Our 'long division' would look like...
______ x_______
2x | 2x^2 + 0x + 4
2x^2
------

..doing the substraction of the x^2 terms and bringing down the x terms.. it looks like

______ x_______
2x | 2x^2 + 0x + 4
- 2x^2
------
0x^2 + 0x

Since the divisor has 0 constants, the long division is finished with a remainder of 4

2x^2 + 4 / 2x = x + 4

Answer 2

is that 4 over 2x or (4/2)x ?

Answer 3

2x^2 + 4/(2x)
=2x^2+2/x
=x(x^2)/x + 2/x
=(x^3 + 2)/x

Answer 4

First you must be used a clear exprimation to respect of rigors mathematics as alogebras of fundamentals of the theory of operator algebra