Question

what must the polynomial x^4 + 2x^3 - 2x^2 + x -1 so that the resulting polynomialis exactly divided by x^2 + 2x - 3​

Answer 1

Answer:

answer is x2+2×-3

Step-by-step explanation:

We divide the polynomial x4+2x3−2x2+x−1 by x2+2x−3 as shown in the above image:

From the above division, we conclude that the quotient is x2+1 and the remainder is −x+2.

Therefore, −(−x+2) that is x−2 must be added to the given polynomial  so that the resulting polynomial is exactly divisible by  x2+2x−3.

Hence, (x−2) must be added to the polynomial x4+2x3−2x2+x−1 so that the resulting polynomial is exactly divisible by x2+2x−3.