Answered

Get the information you need from a community of experts on IDNLearn.com. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.

The product of a binomial and a trinomial is [tex]$x^3 + 3x^2 - x + 2x^2 + 6x - 2$[/tex]. Which expression is equivalent to this product after it has been fully simplified?

A. [tex]$x^3 + 5x^2 + 5x - 2$[/tex]
B. [tex][tex]$x^3 + 2x^2 + 8x - 2$[/tex][/tex]
C. [tex]$x^3 + 11x^2 - 2$[/tex]
D. [tex]$x^3 + 10x^2 - 2$[/tex]

Sagot :

GinnyAnsweridn
To simplify the given polynomial [tex]\(x^3 + 3x^2 - x + 2x^2 + 6x - 2\)[/tex], follow these steps:

1. Group the like terms together:
- [tex]\(x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 + 2x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-x + 6x\)[/tex]
- Constant term: [tex]\(-2\)[/tex]

2. Combine the like terms:
- The [tex]\(x^3\)[/tex] term remains [tex]\(x^3\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 + 2x^2 = 5x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-x + 6x = 5x\)[/tex].
- The constant term remains [tex]\(-2\)[/tex].

3. Write out the simplified polynomial:
- [tex]\(x^3 + 5x^2 + 5x - 2\)[/tex]

Thus, the equivalent expression to the polynomial [tex]\(x^3 + 3x^2 - x + 2x^2 + 6x - 2\)[/tex] after full simplification is [tex]\(x^3 + 5x^2 + 5x - 2\)[/tex].

From the given options, this matches [tex]\(x^3 + 5x^2 + 5x - 2\)[/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. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.