Get the answers you've been looking for with the help of IDNLearn.com's expert community. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

Part B

When written in factored form, which two polynomials have a factor of [tex]$x + 12$[/tex]?

A. [tex]x^2 + 8x + 12[/tex]
B. [tex]x^2 - 12x + 27[/tex]
C. [tex]x^2 - 8x - 48[/tex]
D. [tex]x^2 + 10x - 24[/tex]
E. [tex]x^2 + 15x + 36[/tex]


Sagot :

Certainly! Let's determine which of the given polynomials have a factor of [tex]\(x + 12\)[/tex] by factoring each polynomial step-by-step.

### Given Polynomials:
1. [tex]\(x^2 + 8x + 12\)[/tex]
2. [tex]\(x^2 - 12x + 27\)[/tex]
3. [tex]\(x^2 - 8x - 48\)[/tex]
4. [tex]\(x^2 + 10x - 24\)[/tex]
5. [tex]\(x^2 + 15x + 36\)[/tex]

#### Factoring Each Polynomial:

1. [tex]\(x^2 + 8x + 12\)[/tex]:
[tex]\[ x^2 + 8x + 12 = (x + 2)(x + 6) \][/tex]
This polynomial factors to [tex]\((x + 2)(x + 6)\)[/tex]. Neither factor is [tex]\(x + 12\)[/tex].

2. [tex]\(x^2 - 12x + 27\)[/tex]:
[tex]\[ x^2 - 12x + 27 = (x - 3)(x - 9) \][/tex]
This polynomial factors to [tex]\((x - 3)(x - 9)\)[/tex]. Neither factor is [tex]\(x + 12\)[/tex].

3. [tex]\(x^2 - 8x - 48\)[/tex]:
[tex]\[ x^2 - 8x - 48 = (x - 12)(x + 4) \][/tex]
This polynomial factors to [tex]\((x - 12)(x + 4)\)[/tex]. Neither factor is [tex]\(x + 12\)[/tex].

4. [tex]\(x^2 + 10x - 24\)[/tex]:
[tex]\[ x^2 + 10x - 24 = (x + 12)(x - 2) \][/tex]
This polynomial factors to [tex]\((x + 12)(x - 2)\)[/tex]. One of the factors is [tex]\(x + 12\)[/tex].

5. [tex]\(x^2 + 15x + 36\)[/tex]:
[tex]\[ x^2 + 15x + 36 = (x + 3)(x + 12) \][/tex]
This polynomial factors to [tex]\((x + 3)(x + 12)\)[/tex]. One of the factors is [tex]\(x + 12\)[/tex].

### Conclusion
Among the given polynomials, the ones that have a factor of [tex]\(x + 12\)[/tex] are:
- [tex]\(x^2 + 10x - 24\)[/tex], which factors to [tex]\((x + 12)(x - 2)\)[/tex]
- [tex]\(x^2 + 15x + 36\)[/tex], which factors to [tex]\((x + 3)(x + 12)\)[/tex]

Thus, the polynomials that have a factor of [tex]\(x + 12\)[/tex] are:

[tex]\[ x^2 + 10x - 24 \][/tex]
[tex]\[ x^2 + 15x + 36 \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.