x cubed minus two x squared minus thirty-five x equals zero.
Part A: What is being asked in the problem and what does that mean? What plan am I going to try?
Part B: Then, solve.
Part A: The problem is asking to solve the equation "x cubed minus two x squared minus thirty-five x equals zero". This means that we need to find the values of x that make the equation true. The plan we can try is factoring the equation or using the zero product property to find the solutions.
Part B: To solve the equation, we can start by factoring out an x:
x(x^2 - 2x - 35) = 0
Next, we factor the quadratic expression in parentheses:
x(x - 7)(x + 5) = 0
Now we can use the zero product property to find the solutions:
x = 0, x - 7 = 0, x + 5 = 0
From the second equation, we find:
x = 7
From the third equation, we find:
x = -5
Therefore, the solutions to the equation x cubed minus two x squared minus thirty-five x equals zero are x = 0, x = 7, and x = -5.