Solve for x.
1/2(x-2)^3+1=0
Also please teach me how to factor cubic polynomials.
(x-2)^3=-2
take the cube root of each side
x-2=-cubrt2
x=2-cubrt2
So if y=0, what would x be on the graph?
I see no y in the equation.
they meant in general i think
To solve the equation 1/2(x-2)^3 + 1 = 0, we can follow these steps:
Step 1: Eliminate the constant term by subtracting 1 from both sides of the equation:
1/2(x-2)^3 = -1
Step 2: Multiply both sides by 2 to remove the fraction:
(x-2)^3 = -2
Step 3: Take the cube root of both sides to isolate the expression (x-2):
∛(x-2)^3 = ∛(-2)
Step 4: Simplify the cube root:
x-2 = -∛2
Step 5: Finally, add 2 to both sides to solve for x:
x = 2 - ∛2
Now, moving on to factoring cubic polynomials. Factoring a cubic polynomial involves finding its roots or factors. Here's a general guide on how to factor cubic polynomials:
Step 1: Determine if there are any common factors. If there is a common factor that can be factored out, do so.
Step 2: Identify the type of cubic polynomial:
a. If the polynomial is in the form ax^3 + bx^2 + cx + d = 0, then it is a depressed cubic.
b. If the polynomial can be factored by grouping or by using a special cubic factor formula, then it is a non-depressed cubic.
Step 3: Factoring a depressed cubic:
a. Substitute a new variable to form a quadratic equation.
b. Solve the quadratic equation using factoring, the quadratic formula, or completing the square.
c. Substitute the roots back into the variable to find the factors of the original cubic polynomial.
Step 4: Factoring a non-depressed cubic:
a. Use synthetic division or long division to divide the polynomial by a factor to simplify it.
b. Repeat this process until the polynomial is reduced to a quadratic equation.
c. Use factoring, the quadratic formula, or completing the square to solve the quadratic equation.
d. Substitute the roots back into the variable to find the factors of the original cubic polynomial.
Factoring cubic polynomials can be a bit more complex compared to factoring quadratics or higher degree polynomials. It requires practice and familiarity with different factoring techniques.