Question

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

Answer 1

Answer:

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

Step-by-step 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  $x^2 - x$