Select the answer that best completes the given statement

Question

Because 2x^3-x+5 divided by x+1 equals 2x^2-2x+1 with a remainder 4, it follows 2x^3-x+5=

Answer 1

(x+1) (2x² - 2x + 1)  +  4/(x+1)

Answer 2

I agree with David's comment that you should post the entire question.  Nonetheless, it seems pretty obvious that they are looking for you to make the connection that division problems with polynomials can be "put back together" just like problems without variables.

 

For example:

     7/3 = 2 (mod 1)

which means

     3*2+1 = 7

 

In your case:

     (2x^3-x+5)/(x+1) = 2x^2-2x+1 (mod 4)

means

     (x+1)*(2x^2-2x+1) + 4 = 2x^3-x+5

 

BTW, (mod x) is how remainders are written in formal math.