The Factor Theorem

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

Show that negative 1 is a zero of P of x = x cubed minus 5x squared + 2x + 8, find the other zeros of P, and then sketch its graph
Show that 5 is a zero of P of x = x cubed minus 19x minus 30, find the other zeros of P, and then sketch its graph
Find a fourth-degree polynomial that has zeros negative 2, 0, 2, and 4
Find a fifth-degree polynomial that has zeros negative 2, negative 1, 0, 1, and 2
Find a fifth-degree polynomial that has zeros negative 2, negative 1, 0, 1, and 2 and leading coefficient negative 4