Solve the Cubic Equation: x³ = x² + 2x Step-by-Step

Question

$x^3=x^2+2x$

00:00 Find X

00:03 Arrange the equation so that the right side equals 0

00:11 Factor into terms with X squared

00:24 Take out the common factor from the parentheses

00:33 We want to find which solution zeros each factor in the multiplication

00:36 This is one solution

00:39 Now let's find the second solution

00:42 Factor using trinomial method, looking at the coefficients

00:45 We want to find 2 numbers whose sum equals B (-1)

00:51 And their product equals C (-2)

00:56 These are the appropriate numbers, let's substitute in the multiplication

01:03 We want to find which solution zeros each factor in the multiplication

01:16 And this is the solution to the problem

To solve the problem $x^3 = x^2 + 2x$ , follow these steps:

Step 1: Re-arrange the equation to have all terms on one side:
$x^3 - x^2 - 2x = 0$ .
Step 2: Factor out the greatest common factor (GCF), which is $x$ :
$x(x^2 - x - 2) = 0$ .
Step 3: Factor the quadratic expression $x^2 - x - 2$ :
The factors of $-2$ that add up to $-1$ are $-2$ and $1$ . Thus, $x^2 - x - 2 = (x-2)(x+1)$ .
Step 4: Combine the factored terms:
$x(x-2)(x+1) = 0$ .

Each factor can be set to zero to find the solutions:

The solutions to the equation are $x = 0, -1, 2$ .

Therefore, the correct choice from the given options is:
$x = 0, -1, 2$ .

$x=0,-1,2$