A is false because for 2x+5 to be a factor, the 
remainder would have to be 0, not 5.

B is true because 

where P(x) is the polynomial, Q(x) is the quotient,
D(x) is the divisor, and R(x) is the remainder.

C as you have typed it is false because you have typed
it incorrectly.  When algebra must be typed all on one 
line, you MUST put parentheses around any numerator or 
denominator that contains any addition, subtraction, 
multiplication or division.  

This is what you should have typed for C:

C. (2x^3-x^2-13x+10)/(2x+5)=x^2-3x+1+5/(2x+5) <--CORRECT

for when we don't have to write it all on one line, it
means this:

C. 
 
It is not this, which you typed: 

C. 2x^3-x^2-13x+10/2x+5=x^2-3x+1+5/2x+5

for, according to PEMDAS, that means this

C.    <--INCORRECT

which is not at all what you meant.

Anyway C when typed correctly is true because 

 

But in the future, always be careful when typing algebra 
all on one line to put parentheses around any numerator 
or any denominator which contains any addition, subtraction, 
multiplication or division.

Edwin