128
Question
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.
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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)=1 and (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=5 and a=−5
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)=1 and (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=5 and a=−5
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