Part A: The problem is asking to find the solutions to the equation x^3 - 2x^2 - 35x = 0. This means we need to find the values of x that satisfy the equation and make it true. The plan I am going to try is factoring the equation, if possible, to identify the values of x that make each factor equal to zero.
Part B: To solve the equation by factoring, we need to rewrite it as a product of factors set equal to zero. Let's start by factoring out an x from each term:
x(x^2 - 2x - 35) = 0
Now, we can attempt to further factor the quadratic expression inside the parentheses. We are looking for two numbers whose product is -35 and whose sum is -2. Based on this, the factors are -7 and 5. Therefore, the equation can be factored as:
x(x - 7)(x + 5) = 0
Now, we set each factor equal to zero and solve for x:
x = 0, x - 7 = 0 (which gives x = 7), and x + 5 = 0 (which gives x = -5)
Therefore, the solutions to the equation x^3 - 2x^2 - 35x = 0 are x = 0, x = 7, and x = -5.
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 only factoring.
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