Question

If polynomial x^4-8x^3-10x^2+24x-10 is divided by x^2+2x+k, the remainder comes out to be 64x+a, then find the values of k and a.

Answer 1

Through polynomial division I have solved it.
I have equated the remainder which got from polynomial
division and the remainder
given in the problem.

Answer 2

Answer:

Value of a is -35 and k is 5

Step-by-step explanation:

Given If polynomial $x^4-8x^3-10x^2+24x-10$ is divided by $x^2+2x+k$, the remainder comes out to be 64x+a, then we have to find the value of k and a.

The division is shown in figure through which the remainder comes out to be

$(24+10k-20+2k)x-(10+10k-k^2)$

 Here, remainder is given which is 64x+a

⇒ $(24+10k-20+2k)x-(10+10k-k^2)=64x+a$

⇒ 12k+4=64 ⇒ k=5

also,

$-(10+10k-k^2)=a$

⇒ -10-50+25=a

⇒ -35=a

Hence, value of a is -35 and k is 5