217k views
1 vote
To factor the expression 2x^2 - x - 3, you need to find pairs of what numbers?

User Mits
by
7.9k points

1 Answer

3 votes

Final answer:

To factor the expression 2x^2 - x - 3, one must find two numbers that multiply to -6 and add up to -1. The numbers are -3 and +2, making the factored form (2x - 3)(x + 1). One can verify the factoring by expanding the binomials to show they equal the original expression.

Step-by-step explanation:

To factor the expression 2x^2 - x - 3, you need to find two numbers that both multiply to give the product of the quadratic term coefficient (2) and the constant term (-3), which is -6, and add up to give the linear term coefficient (-1). The process of factoring a quadratic expression involves finding two binomials that when multiplied together will give us the original quadratic expression.

In this case, we are looking for two numbers that multiply to -6 and add up to -1. The numbers that meet these criteria are -3 and +2. Therefore, the factored form of 2x^2 - x - 3 is (2x - 3)(x + 1).

We can verify this by expanding the binomials:

  • 2x * x = 2x^2
  • 2x * 1 = 2x
  • -3 * x = -3x
  • -3 * 1 = -3

Combining like terms (2x - 3x) gives us -x, so the expanded form is 2x^2 - x - 3, confirming that (2x - 3)(x + 1) is indeed the factored form.

User Ilona
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories