Problem: When the polynomial x3−2x^{3}-2x3−2 is divided by the polynomial x2−2x^{2}-2x2−2, the remainder is
Answer Choices:
A. 222
B. −2-2−2
C. −2x−2-2x-2−2x−2
D. 2x+22x+22x+2
E. 2x−22x-22x−2
Solution:
xx2+0x−2x3+0x2+0x−2x3+0x2−2x2x−2=(remainder)\begin{array}{r|rrrl} & x & & & \\ \hline x^2 + 0x - 2 & x^3 & + 0x^2 & + 0x & - 2 \\ & x^3 & + 0x^2 & - 2x & \\ \hline & & & 2x & -2 = \text{(remainder)} \end{array} x2+0x−2xx3x3+0x2+0x2+0x−2x2x−2−2=(remainder)