The Polynomial 10 X 3 + 35 X 2 − 4 X − 14 10x^3 + 35x^2 - 4x - 14 10 X 3 + 35 X 2 − 4 X − 14 Is Factored By Grouping: 10 X 3 + 35 X 2 − 4 X − 14 10x^3 + 35x^2 - 4x - 14 10 X 3 + 35 X 2 − 4 X − 14 $5x^2(\ \ ) - 2(\ \ $]What Is The Common Factor That Is Missing From Both Sets Of Parentheses?A. − 2 X − 7 -2x - 7 − 2 X − 7 B. $2x +

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Introduction

Factoring polynomials is a crucial concept in algebra that helps us simplify complex expressions and solve equations. One of the methods used to factor polynomials is the grouping method, which involves grouping terms in a way that allows us to factor out common factors. In this article, we will explore the polynomial 10x3+35x2−4x−1410x^3 + 35x^2 - 4x - 14 and factor it by grouping.

The Grouping Method

The grouping method involves grouping terms in a polynomial in such a way that we can factor out common factors. To do this, we need to identify the common factors in each group of terms. Let's start by looking at the given polynomial:

10x3+35x2−4x−1410x^3 + 35x^2 - 4x - 14

We can see that the first two terms have a common factor of 5x25x^2, and the last two terms have a common factor of −2-2. However, we need to find the common factor that is missing from both sets of parentheses.

Finding the Common Factor

To find the common factor, we need to look at the terms in each group and identify the common factors. Let's start with the first group:

5x2(  )5x^2(\ \ )

We can see that the term 10x310x^3 has a factor of 5x25x^2, so we can write it as:

5x2(2x)5x^2(2x)

Now, let's look at the second group:

−2(  )-2(\ \ )

We can see that the term −4x-4x has a factor of −2-2, so we can write it as:

−2(2x)-2(2x)

Now, we can see that both groups have a common factor of 2x2x. Therefore, the common factor that is missing from both sets of parentheses is:

2x2x

Conclusion

In this article, we have explored the polynomial 10x3+35x2−4x−1410x^3 + 35x^2 - 4x - 14 and factored it by grouping. We have identified the common factor that is missing from both sets of parentheses as 2x2x. This is a crucial concept in algebra that helps us simplify complex expressions and solve equations.

Final Answer

The final answer is: 2x\boxed{2x}

Discussion

The polynomial factoring by grouping method is a powerful tool that helps us simplify complex expressions and solve equations. By identifying the common factors in each group of terms, we can factor out common factors and simplify the expression. In this article, we have seen how to apply this method to the polynomial 10x3+35x2−4x−1410x^3 + 35x^2 - 4x - 14 and find the common factor that is missing from both sets of parentheses.

Related Topics

  • Factoring polynomials
  • Grouping method
  • Common factors
  • Algebra

References

Further Reading

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Introduction

In our previous article, we explored the polynomial 10x3+35x2−4x−1410x^3 + 35x^2 - 4x - 14 and factored it by grouping. We identified the common factor that is missing from both sets of parentheses as 2x2x. In this article, we will answer some of the most frequently asked questions about the polynomial factoring by grouping method.

Q&A

Q: What is the polynomial factoring by grouping method?

A: The polynomial factoring by grouping method is a technique used to factor polynomials by grouping terms in a way that allows us to factor out common factors.

Q: How do I apply the polynomial factoring by grouping method?

A: To apply the polynomial factoring by grouping method, you need to identify the common factors in each group of terms. You can do this by looking at the terms in each group and identifying the common factors.

Q: What are some common mistakes to avoid when using the polynomial factoring by grouping method?

A: Some common mistakes to avoid when using the polynomial factoring by grouping method include:

  • Not identifying the common factors in each group of terms
  • Not factoring out the common factors correctly
  • Not checking for any remaining factors

Q: Can I use the polynomial factoring by grouping method to factor any polynomial?

A: No, you cannot use the polynomial factoring by grouping method to factor any polynomial. This method is only suitable for polynomials that can be factored by grouping.

Q: How do I know if a polynomial can be factored by grouping?

A: You can determine if a polynomial can be factored by grouping by looking at the terms in the polynomial. If the terms can be grouped in a way that allows you to factor out common factors, then the polynomial can be factored by grouping.

Q: What are some examples of polynomials that can be factored by grouping?

A: Some examples of polynomials that can be factored by grouping include:

  • 10x3+35x2−4x−1410x^3 + 35x^2 - 4x - 14
  • x2+5x+6x^2 + 5x + 6
  • x2−7x+12x^2 - 7x + 12

Q: Can I use the polynomial factoring by grouping method to solve equations?

A: Yes, you can use the polynomial factoring by grouping method to solve equations. By factoring the polynomial, you can set each factor equal to zero and solve for the variable.

Q: How do I use the polynomial factoring by grouping method to solve equations?

A: To use the polynomial factoring by grouping method to solve equations, you need to follow these steps:

  1. Factor the polynomial using the polynomial factoring by grouping method
  2. Set each factor equal to zero
  3. Solve for the variable

Conclusion

In this article, we have answered some of the most frequently asked questions about the polynomial factoring by grouping method. We have discussed how to apply the method, common mistakes to avoid, and how to use it to solve equations. By following the steps outlined in this article, you can master the polynomial factoring by grouping method and use it to simplify complex expressions and solve equations.

Final Answer

The final answer is: 2x\boxed{2x}

Discussion

The polynomial factoring by grouping method is a powerful tool that helps us simplify complex expressions and solve equations. By identifying the common factors in each group of terms, we can factor out common factors and simplify the expression. In this article, we have seen how to apply this method to the polynomial 10x3+35x2−4x−1410x^3 + 35x^2 - 4x - 14 and find the common factor that is missing from both sets of parentheses.

Related Topics

  • Factoring polynomials
  • Grouping method
  • Common factors
  • Algebra

References

Further Reading