Simplify $\frac{6x^2+20}{4}$.A. $\frac{3x^2+10}{2}$ B. $\frac{3x^2+20}{2}$ C. $6x+5$ D. $x+5$

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the expression 6x2+204\frac{6x^2+20}{4} using various methods and techniques. We will also provide step-by-step solutions and explanations to help readers understand the process.

Understanding the Expression

The given expression is 6x2+204\frac{6x^2+20}{4}. To simplify this expression, we need to understand the rules of algebraic simplification. The expression consists of two parts: the numerator and the denominator. The numerator is 6x2+206x^2+20, and the denominator is 44.

Simplifying the Expression

To simplify the expression, we can use the following techniques:

  • Factoring: We can factor out the greatest common factor (GCF) from the numerator.
  • Dividing: We can divide the numerator by the denominator.

Let's use the factoring technique to simplify the expression.

Factoring the Numerator

The numerator is 6x2+206x^2+20. We can factor out the greatest common factor (GCF) from the numerator, which is 22. Factoring out 22 from the numerator, we get:

6x2+20=2(3x2+10)6x^2+20 = 2(3x^2+10)

Now, we can rewrite the original expression as:

6x2+204=2(3x2+10)4\frac{6x^2+20}{4} = \frac{2(3x^2+10)}{4}

Dividing the Numerator by the Denominator

We can divide the numerator by the denominator by canceling out the common factors. In this case, we can cancel out the factor of 22 from the numerator and the denominator:

2(3x2+10)4=3x2+102\frac{2(3x^2+10)}{4} = \frac{3x^2+10}{2}

Therefore, the simplified expression is 3x2+102\frac{3x^2+10}{2}.

Conclusion

In this article, we simplified the expression 6x2+204\frac{6x^2+20}{4} using the factoring and dividing techniques. We factored out the greatest common factor (GCF) from the numerator and then divided the numerator by the denominator to simplify the expression. The final simplified expression is 3x2+102\frac{3x^2+10}{2}.

Answer

The correct answer is:

  • A. 3x2+102\frac{3x^2+10}{2}

Discussion

This problem requires the application of algebraic simplification techniques, including factoring and dividing. The student should be able to identify the greatest common factor (GCF) in the numerator and factor it out. Then, the student should be able to divide the numerator by the denominator to simplify the expression.

Tips and Tricks

  • Pay attention to the signs: When simplifying expressions, pay attention to the signs of the terms. In this case, the numerator has a positive sign, and the denominator has a positive sign.
  • Use the correct technique: Use the correct technique to simplify the expression. In this case, we used the factoring and dividing techniques.
  • Check your work: Check your work to ensure that the simplified expression is correct.

Practice Problems

Here are some practice problems to help you reinforce your understanding of simplifying algebraic expressions:

  1. Simplify the expression 4x2+122\frac{4x^2+12}{2}.
  2. Simplify the expression 9x2+153\frac{9x^2+15}{3}.
  3. Simplify the expression 2x2+84\frac{2x^2+8}{4}.

Answer Key

  1. 2x2+61\frac{2x^2+6}{1}
  2. 3x2+51\frac{3x^2+5}{1}
  3. x2+42\frac{x^2+4}{2}