If the polynomial x4−6x3+16x2−25x+10 is divided by another polynomial x2−2x+k, the remainder comes out to be x+a, find k and a.
Open in App
Solution
To get the value of k and a, equate the obtained remainder with x+a.
It can be observed that (−9+2k)x+(10−8k+k2)=x+a .
By equating the coefficient of x and constant terms, we get
Therefore, (−9+2k)=1and (10−8k+k2)=a
For (−9+2k)=1, 2k=10 k=5
For (10−8k+k2)=a 10−8×5+25=a −5=a
Therefore, a=−5.
Hence, k=5and a=−5