giannisdagoat
Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Factor [tex]\(x^3 + x^2 + x + 1\)[/tex] by grouping. What is the resulting expression?

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

Sagot :

GinnyAnswer
Let's factor the polynomial [tex]\(x^3 + x^2 + x + 1\)[/tex] by grouping. Here are the steps involved in the factorization process:

1. Group the terms in pairs:
[tex]\[ x^3 + x^2 + x + 1 = (x^3 + x^2) + (x + 1) \][/tex]

2. Factor out the common factors in each group:
[tex]\[ = x^2(x + 1) + 1(x + 1) \][/tex]

3. Notice that [tex]\(x + 1\)[/tex] is a common factor in both groups:
[tex]\[ = (x^2 + 1)(x + 1) \][/tex]

The polynomial [tex]\(x^3 + x^2 + x + 1\)[/tex] factors into [tex]\((x^2 + 1)(x + 1)\)[/tex].

Thus, the resulting expression is:

[tex]\[ \boxed{(x^2 + 1)(x + 1)} \][/tex]

So, from the given options, the correct answer is:
[tex]\[ \left(x^2+1\right)(x+1) \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.