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 remainder 4, it follows that 2x^3-x+5=?

(a) (x+1+4)x(2x^2-2x+1.

(b) 4 x (2x^2-2x+1+x+1.

(c) (x+1) x 2x^2+2x+1)+4.

(d) (x+1) x (2x^2 - 2x+1+4.

Answer 1

When it says that   2x³ - x + 5   divided by   x + 1   equals   2x² - 2x + 1 with a remainder of   4 ,   this means the following:  

  (2x³ - x + 5)/(x + 1) = 2x² - 2x + 1 + (4/(x + 1))

To solve for    2x³ - x + 5 ,   we need to isolate this expression on one side of the equation. To do so, we simply multiply both sides of the equation by   x + 1 :

     [(2x³ - x + 5)/(x + 1)]·(x + 1) = [(2x² - 2x + 1 + (4/(x + 1)))]·(x + 1)

     ((2x³ - x + 5)(x + 1))/(x + 1) = ((2x² - 2x + 1)(x + 1)) + (4/(x + 1))(x + 1)

     2x³ - x + 5 = ((2x² - 2x + 1)(x + 1)) + (4(x + 1)/(x + 1))

     2x³ - x + 5 = ((2x² - 2x + 1)(x + 1)) + 4

It looks like answer choice 'c' satisfies this solution