Question

If the polynomial x4
- 6x3 + 16x2
- 25x + 10 is divided by another polynomial x2
- 2x + 2m,
the remainder comes out to be (x-a), find value of ‘m’ and ‘a’.

Answer 1

Answer:

A=-5, b = 5

Step-by-step explanation:

x^4–6x^3+16x^2–25x+10

=x^2(x^2–2x+k)+2x^3-kx^2–6x^3+16x^2–25x+10.

=x^2(x^2–2x+k)-4x^3+(16-k).x^2–25x+10.

=x^2(x^2–2x+k)-4x(x^2–2x+k)-8x^2+4kx+(16-k).x^2–25x+10.

=x^2(x^2–2x+k)-4x(x^2–2x+k)+(16-k-8).x^2+(4k-25).x+10.

=x^2(x^2–2x+k)-4x(x^2–2x+k)+(8-k)x^2+(4k-25).x+10.

=x^2(x^2–2x+k)-4x(x^2–2x+k)+(8-k)(x^2–2x+k)+(16–2k).x-k(8-k)+(4k-25)x+10

=(x^2–2x+k) (x^2–4x+8-k)+(2k-9)x+(10–8k+k^2).

Here divisor =(x^2–2x+k)

Q =(x^2–4x+8-k) , R=(2k-9).x+(k^2–8k+10).

Therefore:-

x + a = (2k-9).x + (k^2–8k+10).

Equating the coeff. of x and constant term.

2k-9=1.

2k=10 => k= 5 ,

a= k^2–8k +10. , put k=5

a=25–40+10= -5 ,

a= -5 , k = 5 , Answer.