Get expert advice and community support for all your questions on IDNLearn.com. Discover in-depth and reliable answers to all your questions from our knowledgeable community members who are always ready to assist.

A polynomial is factored using algebra tiles.

What are the factors of the polynomial?

A. [tex]\((x-1)\)[/tex] and [tex]\((x+3)\)[/tex]
B. [tex]\((x+1)\)[/tex] and [tex]\((x-3)\)[/tex]
C. [tex]\((x-2)\)[/tex] and [tex]\((x+3)\)[/tex]
D. [tex]\((x+2)\)[/tex] and [tex]\((x-3)\)[/tex]


Sagot :

To find the correct factor pairs of the polynomial given in the problem, we can substitute the polynomial with its likely factors based on the given options. We want to ensure that the polynomial [tex]\( x^2 - x - 6 \)[/tex] is correctly represented.

Given polynomial:
[tex]\[ x^2 - x - 6 \][/tex]

Let's rewrite our options and multiply them to check which factors produce the polynomial:

1. Factors: (x - 1) and (x + 3)

[tex]\[ (x - 1)(x + 3) = x(x + 3) - 1(x + 3) = x^2 + 3x - x - 3 = x^2 + 2x - 3 \][/tex]

2. Factors: (x + 1) and (x - 3)

[tex]\[ (x + 1)(x - 3) = x(x - 3) + 1(x - 3) = x^2 - 3x + x - 3 = x^2 - 2x - 3 \][/tex]

3. Factors: (x - 2) and (x + 3)

[tex]\[ (x - 2)(x + 3) = x(x + 3) - 2(x + 3) = x^2 + 3x - 2x - 6 = x^2 + x - 6 \][/tex]

4. Factors: (x + 2) and (x - 3)

[tex]\[ (x + 2)(x - 3) = x(x - 3) + 2(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6 \][/tex]

Now, let's see which one of these expressions matches the given polynomial [tex]\( x^2 - x - 6 \)[/tex]:

- The first pair, [tex]\((x - 1)(x + 3)\)[/tex], results in [tex]\( x^2 + 2x - 3 \)[/tex]
- The second pair, [tex]\((x + 1)(x - 3)\)[/tex], results in [tex]\( x^2 - 2x - 3 \)[/tex]
- The third pair, [tex]\((x - 2)(x + 3)\)[/tex], results in [tex]\( x^2 + x - 6 \)[/tex]
- The fourth pair, [tex]\((x + 2)(x - 3)\)[/tex], results in [tex]\( x^2 - x - 6 \)[/tex]

Thus, the correct pair of factors for the polynomial [tex]\( x^2 - x - 6 \)[/tex] is:
[tex]\[ (x + 2) \text{ and } (x - 3) \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.