Letf(x)∈f[x] be a polynomial of degree n≥1 and let bars denote passage to the quotient f[x]/(f(

prove that for each g(x) there is a unique polynomial g0(x)of degree≤n−1 such that g(x) =g0(x) (equivalently, the elements1,x, . . ,xn−1are a basis of the vector spacef[x]/(f(x)) overf).

Amodel rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y = -0.04x^2 + 8.6x + 4.8, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. how far horizontally from its starting point will the rocket land? a. 0.56 m b. 215.56 m c. 431.11 m d. 215.74 m