Question

What polynomial should be subtracted from 7x2−6x+5 to get the difference equal to x2−x.

Answer 1

`(6x^2- 5x + 5)` should be subtracted from
`7x^2- 6x+5` to get the difference equal to
`x^2 - x`

Explanation:

Here, the given polynomial
`P(x) = 7x^2- 6x+5`

And, The other Polynomial
`R(x)  = x^2 - x`

Let us assume there exists a polynomial Q(x) such that the difference of P(x) and Q(x) is R (x):

⇒P(x) - Q(x) = R (x)

`\implies  (7x^2- 6x+5) - Q(x) = (x^2 - x)`

`\implies Q(x) = (7x^2- 6x+5) - (x^2 -x)  = 7x^2- 6x+5 - x^2 + x =  6x^2- 5x + 5\\\implies Q(x) = (6x^2- 5x + 5)`

Hence,
`(6x^2- 5x + 5)` should be subtracted from
`7x^2- 6x+5` to get the difference equal to
`x^2 - x`