Answer:
k=5
a= -5
Step-by-step explanation:
if the polynomial x^4-6x^3+16x^2-25x+10 is divided by x^2-2x+k the remainder comes out to be x+a,find k and a
Solution
x^4-6x^3+16x^2-25x+10 / x^2-2x+k = x-a
We have,
(4k-25+16-2k)x+[10-k(8-k)] = x+a
(2k+9)x + (10-8k+k^2)=x+a
2k-9=1
2k=1+9
2k=10
Divide both sides by 2
2k/2=10/2
k=5
And
10-8k+k^2=a
10-8(5)+(5^2)=a
10-40+25=a
-5=a
Therefore, a=-5
x^4-6x^3+16x^2-25x+10 divided by x^2-2x+5 = x-5
