# Solving Cubic Root Algebra: Don't Know the Steps

• MHB
• STS
In summary, The equation has one rule that a cannot be equal to -1, and the second picture is the correct answer. However, the steps leading to that answer are unclear and there may be a typo in the equation.
STS
I don't understand this.
a is not suppose to be -1; this is the only rule in the equation
The answer is the second picture, I just don't know the steps that lead to that answer.
View attachment 8926

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STS said:
I don't understand this.
a is not suppose to be -1; this is the only rule in the equation
The answer is the second picture, I just don't know the steps that lead to that answer.
In order for this to be correct we would need $$\displaystyle \sqrt[3]{ 0.125 - 0.5 } = 0$$, which clearly isn't true. Is there a typo?

-Dan

Hi STS.

You probably mean the following expression:
$$\frac{4a^2-10\times\sqrt[3]{0.064}}{3a+3+{\color{red}\sqrt[3]{0.125}}-0.5}.$$

## 1. How do I solve a cubic root algebra problem when I don't know the steps?

First, identify the given cubic equation and make sure it is in the form of ax^3 + bx^2 + cx + d = 0. Then, use the rational root theorem to find possible rational roots. Next, use synthetic division to test each possible root until you find one that works. Once you have found one root, use the quadratic formula to solve for the remaining roots.

## 2. What is the rational root theorem and how does it help with solving cubic root algebra?

The rational root theorem states that any rational root of a polynomial equation will be a factor of the constant term divided by a factor of the leading coefficient. This helps by giving a list of possible rational roots to test in the equation, making it easier to find a root and solve the equation.

## 3. Can I use the quadratic formula to solve a cubic root algebra problem?

Yes, the quadratic formula can be used to solve a cubic root algebra problem, but only after one root has been found using the rational root theorem and synthetic division. The quadratic formula can then be used to solve for the remaining roots.

## 4. What is synthetic division and how does it help with solving cubic root algebra?

Synthetic division is a shortcut method for dividing polynomials by a linear factor. It helps with solving cubic root algebra by allowing you to quickly test possible rational roots and find one that works. This saves time and makes the process of solving a cubic root algebra problem more efficient.

## 5. Is there a specific order in which I should solve a cubic root algebra problem?

Yes, there is a specific order in which you should solve a cubic root algebra problem. First, use the rational root theorem to find possible rational roots. Then, use synthetic division to test each possible root until you find one that works. Once you have found one root, use the quadratic formula to solve for the remaining roots. Finally, check your solutions by plugging them back into the original equation to ensure they are correct.

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