Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Use the grouping method to factor the polynomial below completely.

[tex]\[ x^3 + 2x^2 + 3x + 6 \][/tex]

A. [tex]\(\left(x^2 + 2\right)(x + 3)\)[/tex]

B. [tex]\(\left(x^2 + 2\right)(x + 2)\)[/tex]

C. [tex]\(\left(x^2 + 3\right)(x + 3)\)[/tex]

D. [tex]\(\left(x^2 + 3\right)(x + 2)\)[/tex]

Sagot :

GinnyAnswer
To factor the polynomial [tex]\( x^3 + 2x^2 + 3x + 6 \)[/tex] completely using the grouping method, follow these detailed steps:

1. Group the terms: Split the polynomial into two groups.
[tex]\[ x^3 + 2x^2 + 3x + 6 = (x^3 + 2x^2) + (3x + 6) \][/tex]

2. Factor out the greatest common factor (GCF) in each group:
- In the first group, [tex]\( x^3 + 2x^2 \)[/tex], the GCF is [tex]\( x^2 \)[/tex].
- In the second group, [tex]\( 3x + 6 \)[/tex], the GCF is [tex]\( 3 \)[/tex].

Factoring out the GCF from each group:
[tex]\[ x^2(x + 2) + 3(x + 2) \][/tex]

3. Factor out the common binomial factor: Notice that both terms have a common factor of [tex]\( (x + 2) \)[/tex].
[tex]\[ x^2(x + 2) + 3(x + 2) = (x + 2)(x^2 + 3) \][/tex]

Thus, the factored form of the polynomial [tex]\( x^3 + 2x^2 + 3x + 6 \)[/tex] is:
[tex]\[ (x + 2)(x^2 + 3) \][/tex]

Therefore, the correct answer is:

D. [tex]\( (x^2 + 3)(x + 2) \)[/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.