Select The Two Binomials That Are Factors Of This Trinomial:$\[ X^2 - X - 20 \\]A. \[$ X - 2 \$\] B. \[$ X + 2 \$\] C. \[$ X + 4 \$\] D. \[$ X - 5 \$\]

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Introduction

Factoring trinomials is a fundamental concept in algebra that involves expressing a quadratic expression as a product of two binomials. In this article, we will explore the process of factoring trinomials and provide a step-by-step guide on how to select the correct binomials.

What are Trinomials?

A trinomial is a polynomial expression with three terms. It can be written in the form of ax^2 + bx + c, where a, b, and c are constants. For example, x^2 - x - 20 is a trinomial.

How to Factor Trinomials

Factoring trinomials involves finding two binomials that, when multiplied together, result in the original trinomial. To factor a trinomial, we need to find two numbers whose product is equal to the product of the coefficient of the x^2 term and the constant term, and whose sum is equal to the coefficient of the x term.

Step 1: Identify the Coefficients

The first step in factoring a trinomial is to identify the coefficients of the x^2 term, the x term, and the constant term. In the trinomial x^2 - x - 20, the coefficients are:

  • Coefficient of x^2: 1
  • Coefficient of x: -1
  • Constant term: -20

Step 2: Find the Factors

The next step is to find the factors of the product of the coefficient of the x^2 term and the constant term. In this case, the product is 1 * -20 = -20. We need to find two numbers whose product is -20 and whose sum is -1.

Step 3: List the Possible Factors

To find the possible factors, we can list all the pairs of numbers whose product is -20. These pairs are:

  • 1 and -20
  • -1 and 20
  • 2 and -10
  • -2 and 10
  • 4 and -5
  • -4 and 5

Step 4: Select the Correct Binomials

Now that we have listed the possible factors, we need to select the correct binomials. To do this, we need to check which pair of factors has a sum of -1.

  • 1 and -20: 1 + (-20) = -19 (not equal to -1)
  • -1 and 20: (-1) + 20 = 19 (not equal to -1)
  • 2 and -10: 2 + (-10) = -8 (not equal to -1)
  • -2 and 10: (-2) + 10 = 8 (not equal to -1)
  • 4 and -5: 4 + (-5) = -1 (equal to -1)
  • -4 and 5: (-4) + 5 = 1 (not equal to -1)

Therefore, the correct binomials are (x + 4) and (x - 5).

Conclusion

In this article, we have explored the process of factoring trinomials and provided a step-by-step guide on how to select the correct binomials. We have also used the trinomial x^2 - x - 20 as an example to illustrate the process. By following these steps, you can factor any trinomial and select the correct binomials.

Answer

The correct binomials that are factors of the trinomial x^2 - x - 20 are:

  • (x + 4)
  • (x - 5)

Discussion

Do you have any questions about factoring trinomials? Have you tried factoring a trinomial before? Share your experiences and ask questions in the comments below.

Related Topics

  • Factoring quadratic expressions
  • Solving quadratic equations
  • Algebraic manipulations

References

  • [1] "Algebra" by Michael Artin
  • [2] "Calculus" by Michael Spivak
  • [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
    Factoring Trinomials: A Q&A Guide =====================================

Introduction

In our previous article, we explored the process of factoring trinomials and provided a step-by-step guide on how to select the correct binomials. However, we know that practice makes perfect, and the best way to learn is by asking questions and getting answers. In this article, we will address some of the most frequently asked questions about factoring trinomials.

Q: What is the difference between factoring and simplifying a trinomial?

A: Factoring a trinomial involves expressing it as a product of two binomials, while simplifying a trinomial involves combining like terms to reduce the expression to its simplest form.

Q: How do I know which binomials to choose when factoring a trinomial?

A: To choose the correct binomials, you need to find two numbers whose product is equal to the product of the coefficient of the x^2 term and the constant term, and whose sum is equal to the coefficient of the x term.

Q: What if I have a trinomial with a negative coefficient? How do I factor it?

A: If you have a trinomial with a negative coefficient, you can factor it by using the same process as before, but with the opposite sign. For example, if you have the trinomial -x^2 - x - 20, you can factor it as (x + 4)(x - 5).

Q: Can I factor a trinomial with a zero coefficient?

A: Yes, you can factor a trinomial with a zero coefficient. For example, if you have the trinomial x^2 - 0x - 20, you can factor it as (x + 4)(x - 5).

Q: How do I factor a trinomial with a coefficient of 1?

A: If you have a trinomial with a coefficient of 1, you can factor it by using the same process as before. For example, if you have the trinomial x^2 - x - 20, you can factor it as (x + 4)(x - 5).

Q: Can I factor a trinomial with a coefficient of -1?

A: Yes, you can factor a trinomial with a coefficient of -1. For example, if you have the trinomial -x^2 + x - 20, you can factor it as (x - 4)(x + 5).

Q: How do I factor a trinomial with a coefficient of 2?

A: If you have a trinomial with a coefficient of 2, you can factor it by using the same process as before. For example, if you have the trinomial 2x^2 - 2x - 20, you can factor it as 2(x + 4)(x - 5).

Q: Can I factor a trinomial with a coefficient of -2?

A: Yes, you can factor a trinomial with a coefficient of -2. For example, if you have the trinomial -2x^2 + 2x - 20, you can factor it as -2(x - 4)(x + 5).

Conclusion

In this article, we have addressed some of the most frequently asked questions about factoring trinomials. We hope that this Q&A guide has been helpful in clarifying any doubts you may have had about factoring trinomials.

Related Topics

  • Factoring quadratic expressions
  • Solving quadratic equations
  • Algebraic manipulations

References

  • [1] "Algebra" by Michael Artin
  • [2] "Calculus" by Michael Spivak
  • [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Practice Problems

  • Factor the trinomial x^2 + 5x + 6
  • Factor the trinomial x^2 - 7x - 18
  • Factor the trinomial x^2 + 2x - 15

Answers

  • x + 3)(x + 2)
  • (x - 9)(x + 2)
  • (x + 5)(x - 3)