Using Synthetic DivisionUse Synthetic Division To Find The Expression For The Area Of The Base Of A Rectangular Prism With A Height Of X + 4 X+4 X + 4 And A Volume Of X 3 + 2 X 2 − 17 X − 36 X^3+2x^2-17x-36 X 3 + 2 X 2 − 17 X − 36 .A. 2 X 2 − 9 X 2x^2-9x 2 X 2 − 9 X B. X 2 + 6 X − 24 X^2+6x-24 X 2 + 6 X − 24 C.

Introduction

Synthetic division is a method used to divide polynomials by linear factors. It is a shortcut for the long division method and is often used to find the roots of a polynomial equation. In this article, we will use synthetic division to find the expression for the area of the base of a rectangular prism with a given height and volume.

The Problem

The problem states that we have a rectangular prism with a height of $x+4$ and a volume of $x^3+2x^2-17x-36$. We need to find the expression for the area of the base of the prism.

The Formula for the Volume of a Rectangular Prism

The formula for the volume of a rectangular prism is given by:

$$V = lwh$$

where $V$ is the volume, $l$ is the length, $w$ is the width, and $h$ is the height.

The Relationship Between the Volume and the Area of the Base

Since the volume of the prism is given, we can use the formula to find the area of the base. The area of the base is given by:

$$A = lw$$

We can substitute the formula for the volume into this equation to get:

$$A = \frac{V}{h}$$

Using Synthetic Division to Find the Expression for the Area of the Base

To find the expression for the area of the base, we need to divide the volume by the height. We can use synthetic division to do this.

Step 1: Write Down the Dividend and the Divisor

The dividend is the volume of the prism, which is $x^3+2x^2-17x-36$. The divisor is the height of the prism, which is $x+4$.

Step 2: Perform the Synthetic Division

To perform the synthetic division, we need to follow these steps:

1. Write down the coefficients of the dividend in a row.
2. Bring down the first coefficient.
3. Multiply the divisor by the first coefficient and add the result to the second coefficient.
4. Multiply the divisor by the result from step 3 and add the result to the third coefficient.
5. Multiply the divisor by the result from step 4 and add the result to the fourth coefficient.

Here are the steps for our problem:

	1	2	-17	-36
		1	2	-17
			5	-9
				5

Step 3: Write Down the Result

The result of the synthetic division is $x^2+6x-24$.

Conclusion

Using synthetic division, we have found the expression for the area of the base of the rectangular prism to be $x^2+6x-24$. This is the final answer to the problem.

Discussion

Synthetic division is a powerful tool for dividing polynomials by linear factors. It is often used to find the roots of a polynomial equation and can be used to solve a wide range of problems in mathematics and science.

In this article, we used synthetic division to find the expression for the area of the base of a rectangular prism with a given height and volume. We followed the steps of synthetic division and wrote down the result.

The final answer to the problem is $x^2+6x-24$. This is the expression for the area of the base of the rectangular prism.

Final Answer

The final answer is: $\boxed{x^2+6x-24}$

Introduction

In our previous article, we used synthetic division to find the expression for the area of the base of a rectangular prism with a given height and volume. In this article, we will answer some common questions related to the topic.

Q: What is synthetic division?

A: Synthetic division is a method used to divide polynomials by linear factors. It is a shortcut for the long division method and is often used to find the roots of a polynomial equation.

Q: What is the formula for the volume of a rectangular prism?

A: The formula for the volume of a rectangular prism is given by:

$$V = lwh$$

where $V$ is the volume, $l$ is the length, $w$ is the width, and $h$ is the height.

Q: How do I use synthetic division to find the expression for the area of the base of a rectangular prism?

A: To use synthetic division to find the expression for the area of the base of a rectangular prism, you need to follow these steps:

1. Write down the coefficients of the dividend in a row.
2. Bring down the first coefficient.
3. Multiply the divisor by the first coefficient and add the result to the second coefficient.
4. Multiply the divisor by the result from step 3 and add the result to the third coefficient.
5. Multiply the divisor by the result from step 4 and add the result to the fourth coefficient.

Q: What is the result of the synthetic division for the given problem?

A: The result of the synthetic division for the given problem is $x^2+6x-24$.

Q: What is the expression for the area of the base of the rectangular prism?

A: The expression for the area of the base of the rectangular prism is $x^2+6x-24$.

Q: How do I use the result of the synthetic division to find the expression for the area of the base of the rectangular prism?

A: To use the result of the synthetic division to find the expression for the area of the base of the rectangular prism, you need to substitute the result into the formula for the area of the base:

$$A = \frac{V}{h}$$

Q: What is the final answer to the problem?

A: The final answer to the problem is $x^2+6x-24$.

Q: Can I use synthetic division to find the roots of a polynomial equation?

A: Yes, you can use synthetic division to find the roots of a polynomial equation. Synthetic division is a powerful tool for dividing polynomials by linear factors.

Q: What are some common applications of synthetic division?

A: Some common applications of synthetic division include:

• Finding the roots of a polynomial equation
• Dividing polynomials by linear factors
• Solving systems of linear equations
• Finding the expression for the area of the base of a rectangular prism

Conclusion

In this article, we have answered some common questions related to the topic of using synthetic division to find the expression for the area of the base of a rectangular prism. We have provided step-by-step instructions on how to use synthetic division and have answered some common questions related to the topic.

Final Answer

The final answer is: $\boxed{x^2+6x-24}$