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^4+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).