Match The Trinomials With Their Factors.1. $a^2 + A - 20$2. $a^2 - 9a + 20$3. $a^2 - 8a - 20$4. A 2 − 12 A + 20 A^2 - 12a + 20 A 2 − 12 A + 20 Factors:A. ( A − 10 ) ( A − 2 (a - 10)(a - 2 ( A − 10 ) ( A − 2 ]B. ( A − 4 ) ( A + 5 (a - 4)(a + 5 ( A − 4 ) ( A + 5 ]C. ( A − 10 ) ( A + 2 (a - 10)(a + 2 ( A − 10 ) ( A + 2 ]Note: The

Introduction

In algebra, trinomials are a type of polynomial expression that consists of three terms. Factoring trinomials is an essential skill in mathematics, as it allows us to simplify complex expressions and solve equations. In this article, we will explore how to match trinomials with their factors, focusing on the given trinomials and their corresponding factors.

Understanding Trinomials and Factoring

A trinomial is a polynomial expression that consists of three terms, which can be added, subtracted, multiplied, or divided. The general form of a trinomial is:

ax^2 + bx + c

where a, b, and c are constants, and x is the variable. Factoring a trinomial involves expressing it as a product of two binomials.

The Process of Factoring Trinomials

Factoring trinomials involves several steps:

1. Identify the coefficients: Identify the coefficients of the trinomial, which are the numbers that multiply the variables.
2. Determine the signs: Determine the signs of the coefficients, which will help us decide whether the factors are positive or negative.
3. Find the factors: Find the factors of the trinomial by using the coefficients and signs.
4. Check the factors: Check the factors to ensure that they multiply to the original trinomial.

Matching Trinomials with Their Factors

Now, let's match the given trinomials with their factors.

Trinomial 1: $a^2 + a - 20$

To factor this trinomial, we need to find two numbers whose product is -20 and whose sum is 1. These numbers are 5 and -4, so we can write the trinomial as:

$(a + 5)(a - 4)$

This matches with option B. $(a - 4)(a + 5)$.

Trinomial 2: $a^2 - 9a + 20$

To factor this trinomial, we need to find two numbers whose product is 20 and whose sum is -9. These numbers are -10 and -1, so we can write the trinomial as:

$(a - 10)(a - 1)$

However, this does not match with any of the given options. We need to try again.

Let's try to factor the trinomial by grouping:

$a^2 - 9a + 20 = (a^2 - 8a) + (-a + 20)$

$= a(a - 8) - 1(a - 8)$

$= (a - 1)(a - 8)$

This matches with option C. $(a - 10)(a + 2)$ is incorrect, however, the correct option is C. $(a - 10)(a + 2)$ is incorrect, however, the correct option is C. $(a - 1)(a - 8)$.

Trinomial 3: $a^2 - 8a - 20$

To factor this trinomial, we need to find two numbers whose product is -20 and whose sum is -8. These numbers are -10 and 2, so we can write the trinomial as:

$(a - 10)(a + 2)$

This matches with option C. $(a - 10)(a + 2)$.

Trinomial 4: $a^2 - 12a + 20$

To factor this trinomial, we need to find two numbers whose product is 20 and whose sum is -12. These numbers are -10 and -2, so we can write the trinomial as:

$(a - 10)(a - 2)$

This matches with option A. $(a - 10)(a - 2)$.

Conclusion

In this article, we have matched the given trinomials with their factors. We have used the process of factoring trinomials to identify the factors of each trinomial. By following the steps of identifying the coefficients, determining the signs, finding the factors, and checking the factors, we have been able to match the trinomials with their factors.

Final Answer

The final answer is:

• Trinomial 1: $a^2 + a - 20$ matches with option B. $(a - 4)(a + 5)$.
• Trinomial 2: $a^2 - 9a + 20$ matches with option C. $(a - 1)(a - 8)$.
• Trinomial 3: $a^2 - 8a - 20$ matches with option C. $(a - 10)(a + 2)$.
• Trinomial 4: $a^2 - 12a + 20$ matches with option A. $(a - 10)(a - 2)$.

Note

Q: What is a trinomial?

A: A trinomial is a polynomial expression that consists of three terms. The general form of a trinomial is ax^2 + bx + c, where a, b, and c are constants, and x is the variable.

Q: Why is factoring trinomials important?

A: Factoring trinomials is an essential skill in mathematics, as it allows us to simplify complex expressions and solve equations. By factoring trinomials, we can identify the roots of the equation and solve for the variable.

Q: How do I factor a trinomial?

A: To factor a trinomial, you need to follow these steps:

1. Identify the coefficients: Identify the coefficients of the trinomial, which are the numbers that multiply the variables.
2. Determine the signs: Determine the signs of the coefficients, which will help us decide whether the factors are positive or negative.
3. Find the factors: Find the factors of the trinomial by using the coefficients and signs.
4. Check the factors: Check the factors to ensure that they multiply to the original trinomial.

Q: What are the common mistakes to avoid when factoring trinomials?

A: Some common mistakes to avoid when factoring trinomials include:

• Not checking the factors: Make sure to check the factors to ensure that they multiply to the original trinomial.
• Not using the correct signs: Make sure to use the correct signs for the factors, based on the coefficients and signs of the trinomial.
• Not factoring correctly: Make sure to factor the trinomial correctly, using the correct method and steps.

Q: How do I know which method to use when factoring trinomials?

A: The method to use when factoring trinomials depends on the coefficients and signs of the trinomial. Some common methods include:

• Factoring by grouping: This method involves grouping the terms of the trinomial and factoring out common factors.
• Factoring by using the quadratic formula: This method involves using the quadratic formula to find the roots of the equation and then factoring the trinomial.
• Factoring by using the difference of squares: This method involves using the difference of squares formula to factor the trinomial.

Q: Can I use a calculator to factor trinomials?

A: Yes, you can use a calculator to factor trinomials. However, it's always a good idea to check the factors by hand to ensure that they are correct.

Q: How do I check the factors of a trinomial?

A: To check the factors of a trinomial, you need to multiply the factors together and ensure that they equal the original trinomial. You can also use a calculator to check the factors.

Q: What are some common trinomials that I should know how to factor?

A: Some common trinomials that you should know how to factor include:

• a^2 + a - 20: This trinomial can be factored as (a + 5)(a - 4).
• a^2 - 9a + 20: This trinomial can be factored as (a - 1)(a - 8).
• a^2 - 8a - 20: This trinomial can be factored as (a - 10)(a + 2).
• a^2 - 12a + 20: This trinomial can be factored as (a - 10)(a - 2).

Q: How do I practice factoring trinomials?

A: To practice factoring trinomials, you can try the following:

• Practice factoring trinomials with different coefficients and signs: Try factoring trinomials with different coefficients and signs to get a feel for how the factors work.
• Use online resources: There are many online resources available that can help you practice factoring trinomials, such as worksheets and practice problems.
• Work with a tutor or teacher: Working with a tutor or teacher can help you get personalized feedback and guidance on factoring trinomials.

Conclusion

Factoring trinomials is an essential skill in mathematics, and it's used to simplify complex expressions and solve equations. By following the steps outlined in this article, you can learn how to factor trinomials and become more confident in your math skills. Remember to practice factoring trinomials regularly to get a feel for how the factors work.