Question

if the polynomial x4-6x3+16x2-25x+10 is divided by x2-2x+k the remainder comes out to be x+a,find k and a

Answer 1

Ho it helps............

Answer 2

Answer:

The value of k and a is 5 and -5 respectively.

Step-by-step explanation:

$\frac{\left[x^{4}-6 x^{3}+16 x^{2}-25 x+10\right]}{\left[x^{2}-2 x+k\right]}$ and reminder = x+a

On diving the above given equation, we get ,

Given the reminder is (x+a)

(4k-25+16-2k)x+[10-k(8-k)] = x+a

$(2 k-9) x+\left[10-8 k+k^{2}\right]=x+a$

On comparing on both sides, we get

2k-9=1

2k=10

Therefore, k=5

Also,  $10-8 k+k^{2}=a$

$10-8(5)-5^{2}=a$

10-40+25=a

Therefore, a=-5