i need help solving this

Question

Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).

P(x) = 3x5 + 9x4 − 9x3 − x − 3

D(x) = x2 − 3

Answer 1

3x³ + 9 x² + 27________ ____

x² - 3 ) 3x⁵ + 9 x⁴ - 9 x³ + 0 x^2. - x - 3

3x⁵ - 9 x³

9 x⁴ + 0 x²

9 x⁴ - 27 x²

27 x² - x - 3

27 x ² -81

-x + 78 So......

3x⁵ + 9 x⁴ - 9 x³ - x - 3 = (3x³ + 9 x² + 27) (x² - 3)+ ( -x + 78 ) / (x² - 3)

Answer 2

3x^3 +9x^2 +27 = Q(x)

R(x)=-x+78

most limit synthetic division to linear divisors, but there is an extended version. it's more complicated though

probably easier to do long division on this problem