We polynomial long division to write 2 x^4+x^2- 3 x^2+4-9+x^2+x=Q x+P x/x^2+x were Q x and P (x )are polynomial what is Q(2)?

To find Q(2), we first need to perform polynomial long division on the given expression:

2x^4 + x^2 - 3x^2 + 4 - 9 / x^2 + x

First, we divide the leading term of the numerator by the leading term of the denominator:

2x^4 / x^2 = 2x^2

Next, we multiply the entire denominator by 2x^2:

2x^2 * (x^2 + x) = 2x^4 + 2x^3

Subtracting this from the original numerator gives us:

(2x^4 + x^2 - 3x^2 + 4 - 9) - (2x^4 + 2x^3) = -2x^3 - 2x^2 + 4 - 9

Next, we divide the leading term of the new numerator by the leading term of the denominator:

-2x^3 / x^2 = -2x

Multiply the entire denominator by -2x:

-2x * (x^2 + x) = -2x^3 - 2x^2

Subtracting this from the new numerator gives us:

(-2x^3 - 2x^2 + 4 - 9) - (-2x^3 - 2x^2) = 4 - 9

Since the degree of the new numerator is less than the degree of the denominator, we have our remainder as 4 - 9 = -5.

Therefore, Q(x) = 2x^2 - 2x and P(x) = -5.

To find Q(2), we substitute x = 2 into Q(x):

Q(2) = 2(2)^2 - 2(2) = 2(4) - 4 = 8 - 4 = 4

Therefore, Q(2) = 4.