If the polynomial - 6 + 16 - 25x + 10 is divided by - 2x + k, the remainder comes out to be x + a, find k and a

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

just sum

10 + 10 = 20