Question

If the polynomial `x^(4)-6x^(3)+16x^(2)-25x+10` is divided by another polynomial `x^(2)-2x+k`, the remainder comes out to be (x-a). Find k and a.

Answer 1

When given polynomial is divisible by another polynomial then remainder is x+a.
It means, coefficient of x must be 1 and constant term is a.
`therefore 2k-9=1 " and" k^(2)-8k+10=a`
`implies k=5 `
`therefore (5)^(2)-8(5)+10=a implies a= -5`
`therefore k=5 " and" a=-5`