What must be added to polynomial f(x) = x4 + 2x2 – 2x2 + x – 1 so that
resulting polynomial is exactly divisible by x2 + 2x – 3?
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ANSWER
We divide the polynomial x
4
+2x
3
−2x
2
+x−1 by x
2
+2x−3 as shown in the above image:
From the above division, we conclude that the quotient is x
2
+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 x
2
+2x−3.
Hence, (x−2) must be added to the polynomial x
4
+2x
3
−2x
2
+x−1 so that the resulting polynomial is exactly divisible by x
2
+2x−3.
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