Which Statement Is True About The Equation { (x-4)(x+2)=16$}$?A. The Equation { X-4=16$}$ Can Be Used To Solve For A Solution Of The Given Equation.B. The Standard Form Of The Equation Is { X^2-2x-8=0$}$.C. The Factored

$$

Introduction

When dealing with algebraic equations, it's essential to understand the different forms they can take and how to manipulate them to solve for the variable. In this article, we'll examine the given equation {(x-4)(x+2)=16$}$ and determine which statement is true about it.

Understanding the Equation

The given equation is a quadratic equation in its factored form. It can be expanded to the standard form, which is {x^2-2x-8=0$}$. However, before we dive into the standard form, let's examine the first statement.

Statement A: The Equation {x-4=16$}$ Can Be Used to Solve for a Solution of the Given Equation

The first statement claims that the equation {x-4=16$}$ can be used to solve for a solution of the given equation. However, this statement is false. The equation {x-4=16$}$ is a linear equation, and it cannot be used to solve for a solution of the given quadratic equation.

To see why, let's consider the factored form of the given equation: {(x-4)(x+2)=16$}$. This equation has two solutions, which can be found by setting each factor equal to zero and solving for x. However, the equation {x-4=16$}$ only has one solution, which is x = 20. This solution does not satisfy the given equation, and therefore, the first statement is false.

Standard Form of the Equation

The second statement claims that the standard form of the equation is {x^2-2x-8=0$}$. This statement is true. The standard form of a quadratic equation is obtained by expanding the factored form and combining like terms. In this case, the factored form is {(x-4)(x+2)=16$}$, and the standard form is {x^2-2x-8=0$}$.

To see why, let's expand the factored form using the distributive property:

{(x-4)(x+2)=x(x+2)-4(x+2)$

[$=x^2+2x-4x-8$

[$=x^2-2x-8$

Therefore, the standard form of the equation is indeed [x^2-2x-8=0\$}.

Factored Form of the Equation

The third statement claims that the factored form of the equation is {(x-4)(x+2)=16$}$. This statement is true. The factored form of a quadratic equation is obtained by factoring the quadratic expression into two binomial factors. In this case, the quadratic expression is {x^2-2x-8$}$, and the factored form is {(x-4)(x+2)$].

To see why, let's consider the quadratic expression [x^2-2x-8\$}. We can factor this expression by finding two numbers whose product is -8 and whose sum is -2. These numbers are -4 and 2, so we can write the quadratic expression as:

{x^2-2x-8=(x-4)(x+2)$

Therefore, the factored form of the equation is indeed [(x-4)(x+2)=16\$}.

Conclusion

In conclusion, the true statement about the equation {(x-4)(x+2)=16$}$ is that the standard form of the equation is {x^2-2x-8=0$}$. The other two statements are false. The equation {x-4=16$}$ cannot be used to solve for a solution of the given equation, and the factored form of the equation is indeed {(x-4)(x+2)=16$}$.

Frequently Asked Questions

• What is the standard form of the equation {(x-4)(x+2)=16$}$? The standard form of the equation is {x^2-2x-8=0$}$.
• Can the equation {x-4=16$}$ be used to solve for a solution of the given equation? No, the equation {x-4=16$}$ cannot be used to solve for a solution of the given equation.
• What is the factored form of the equation {(x-4)(x+2)=16$}$? The factored form of the equation is {(x-4)(x+2)=16$}$.

Final Answer

The final answer is: B

$$

Introduction

In our previous article, we examined the equation {(x-4)(x+2)=16$}$ and determined that the standard form of the equation is {x^2-2x-8=0$}$. In this article, we'll answer some frequently asked questions about the equation and provide additional insights into its properties.

Q&A

Q: What is the standard form of the equation {(x-4)(x+2)=16$}$?

A: The standard form of the equation is {x^2-2x-8=0$}$.

Q: Can the equation {x-4=16$}$ be used to solve for a solution of the given equation?

A: No, the equation {x-4=16$}$ cannot be used to solve for a solution of the given equation.

Q: What is the factored form of the equation {(x-4)(x+2)=16$}$?

A: The factored form of the equation is {(x-4)(x+2)=16$}$.

Q: How do I solve the equation {(x-4)(x+2)=16$}$?

A: To solve the equation, you can start by expanding the factored form and combining like terms. This will give you the standard form of the equation, which is {x^2-2x-8=0$}$. You can then use the quadratic formula or factoring to solve for the solutions.

Q: What are the solutions to the equation {(x-4)(x+2)=16$}$?

A: The solutions to the equation are x = -2 and x = 6.

Q: Can I use the equation {x-4=16$}$ to find the solutions to the given equation?

A: No, the equation {x-4=16$}$ cannot be used to find the solutions to the given equation.

Q: What is the difference between the factored form and the standard form of the equation?

A: The factored form of the equation is {(x-4)(x+2)=16$}$, while the standard form is {x^2-2x-8=0$}$. The factored form is obtained by factoring the quadratic expression into two binomial factors, while the standard form is obtained by expanding the factored form and combining like terms.

Additional Insights

• The equation {(x-4)(x+2)=16$}$ is a quadratic equation in its factored form.
• The standard form of the equation is {x^2-2x-8=0$}$.
• The factored form of the equation is {(x-4)(x+2)=16$}$.
• The solutions to the equation are x = -2 and x = 6.
• The equation {x-4=16$}$ cannot be used to solve for a solution of the given equation.

Conclusion

In conclusion, the equation {(x-4)(x+2)=16$}$ is a quadratic equation in its factored form, and the standard form is {x^2-2x-8=0$}$. The factored form is obtained by factoring the quadratic expression into two binomial factors, while the standard form is obtained by expanding the factored form and combining like terms. The solutions to the equation are x = -2 and x = 6, and the equation {x-4=16$}$ cannot be used to solve for a solution of the given equation.

Frequently Asked Questions

• What is the standard form of the equation {(x-4)(x+2)=16$}$? The standard form of the equation is {x^2-2x-8=0$}$.
• Can the equation {x-4=16$}$ be used to solve for a solution of the given equation? No, the equation {x-4=16$}$ cannot be used to solve for a solution of the given equation.
• What is the factored form of the equation {(x-4)(x+2)=16$}$? The factored form of the equation is {(x-4)(x+2)=16$}$.

Final Answer

The final answer is: B