If the polynomial x2−2x+k is a factor of x4−6x3+16x2−26x+10−a, then find the value of k and a.
After dividing polynomial x4−6x3+16x2−26x+10−x−a by x2−2x+k we got remainder, (−10+2k)x+(10−a−8k+k2).
Which will be equal to zero if,
−10+2k=0 and 10−a−8k+k2=0
For −10+2k=0
⇒2k=10
⇒k=5
For 10−a−8k+k2=0
⇒10−a−8×5+25=0
⇒−5−a=0
⇒a=−5
So, k=5,a=−5