3. Let P, be the vector space of polynomials of degree at most 2. Define a map D : P2 → P, it sends a polynomial to its derivative. (a) Show that D is linear. (b) Find the matrix of D with respect to the basis {1 – z,1+ 3r², 2+ z – r*}.

I need to find all the expressions equivalent to 6x^2-5x+3

which of the follwoing is a solution to the equation x^2 +24=14-x^2

Suppose you are given a Rectangular piece of cardboard having length 3x-7 inches and width 5x+2 inches. Then you cut out a square from this piece of cardboard having side length x inches. Find the area of the remaining piece of cardboard expressed in terms of x. Please provide steps in detail and how you are thinking to get to a solution.  Thank you