Determine the equation of the polynomial function y=f(x) shown.

Express your answer in factored form.

Factor fully.

\displaystyle 2x^3 -x^2 -145x - 72

Factor fully.

\displaystyle (x - 7)^3 -(2x + 3)^3

If you have g(x) = x^3 -4x^2 and then vertically translate it by 1 unit, does the resulting graph have fewer zeros, the same number of zeros, or more zeros than g(x)?

During which intervals of x is the graph of the function

\displaystyle f(x) = -(x+ 3)(x + 5)(x - 1) below the x-axis?

Divide 6x^3 + x^2 -12x + 5 by 2x -1. Is 2x -1 a factor?

The function y =x^3 has been vertidcally stretched by a factor of 5, horizontally compressed by a factor of \frac{1}{2}, horizontally translated 21 units to the right, and vertically translated 4 units up.

a) Write the equation of the transformed function.

b) The point (1, 1) is on the parent function. Determine the new coordinates of the transformed function.

Ellie divided x^4s+3x^3 -9x^2 +6 by a polynomial. Her answer was x^3 -2x^2 +x - 5, with a remainder of 31. What polynomial did Ellie divide by?

The function f(x) = ax^4 + 8x^2 has three turning points, an absolute maximum of 8, and one of its zeros at x =2. Determine the value of a and the location of the other zeros. Then sketch the graph of f(x).