Create Polynomial Equations

Determine the equation of a polynomial with the roots 3, -2, and -3, which passes through (2, 10). You must type ALL THE WORK THAT leads to the final answer. You can also upload a CLEAR picture of your work here. No credits will be given if you just type the final answer.

Determine the equation of a polynomial with the roots 1, -2, and 4, which passes through (2, 24).

You must type ALL THE WORK THAT leads to the final answer. You can also upload a CLEAR picture of your work here.

No credits will be given if you just type the final answer.

Given a polynomial equation below y = a(x - 1)(x + 5) which passes through the point (3, -64). Find the value of a. (Please type the value of only)

Which of the following would create a polynomial with end behavior in which y goes upward on the left and goes downward on the right?

5.5 - Solving Polynomial Equations
Solve the equation.
$$3y^4-6y^3=-3y^2$$

Hey there! Our friends Sofia, Scott, and Nola are on a treasure hunt. They've stumbled upon an ancient door with a puzzle that needs solving to open. The puzzle is a magical polynomial equation: $$x^3 - 2x^2 - 5x + 6 = 0$$ . Can you help them unlock the door by solving this equation?

What are two solutions to the polynomial:
x²+14x=0

5.5 - Solving Polynomial Equations
Solve the equation.
$$a^3-4a^2+4a=0$$  

Solve x⁴ - 256 = 0

Hey there! Nola, Kendall, and Sofia are on a treasure hunt and stumbled upon an ancient door with a mysterious lock. To unlock it, they need to solve the polynomial equation $$x^3 - 7x + 6 = 0$$ . Can you help them find the right combination?