Answered

Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.

Rewrite the following question to ensure clarity and readability. Fix any grammar or spelling errors. Remove any extraneous phrases that do not contribute to the question. Do not modify or remove LaTeX formatting. Do not translate the question or any part of it. If the question is nonsensical, rewrite it so that it makes sense.

-----

What are the prime factors?

1. [tex]16y[/tex]
a) [tex]4v[/tex]

[tex]\[
\begin{array}{c}
4 \cdot 4 = 2 \cdot 2 \cdot 2 \cdot 2 \\
\cdot 2 \cdot 2 \cdot 4 \cdot 2 \\
\downarrow \\
\frac{1 \cdot 2 \cdot 2 \cdot 2}{t}
\end{array}
\][/tex]

[tex]\[
\frac{4 \cdot 2 \cdot 2 \cdot 2 \cdot 2}{2 \cdot 2 \cdot x}
\][/tex]

[tex](2)^3[/tex]
[tex](2)^4[/tex]

4. [tex]21x^2[/tex]

Sagot :

GinnyAnsweridn
Let’s focus on simplifying the task of finding the prime factorizations step-by-step.

### 1) Prime Factorization of [tex]\( 16y \)[/tex]:
First, let's separate 16 and [tex]\( y \)[/tex]:
- The number 16 can be broken down into its prime factors.
- [tex]\( y \)[/tex] is already a prime number if it’s considered a variable.

Step-by-Step Factorization:
- We start with 16: [tex]\( 16 = 2 \times 8 \)[/tex]
- Factor 8 further: [tex]\( 8 = 2 \times 4 \)[/tex]
- Factor 4 further: [tex]\( 4 = 2 \times 2 \)[/tex]

So, combining all the factors, we get:
[tex]\[ 16 = 2 \times 2 \times 2 \times 2 = 2^4 \][/tex]

Thus, the prime factorization of [tex]\( 16y \)[/tex]:
[tex]\[ 16y = 2^4 \cdot y \][/tex]

### 2) Prime Factorization of [tex]\( 4v \)[/tex]:
First, let's separate 4 and [tex]\( v \)[/tex]:
- The number 4 can be broken down into its prime factors.
- [tex]\( v \)[/tex] is a prime number if it's considered a variable.

Step-by-Step Factorization:
- We start with 4: [tex]\( 4 = 2 \times 2 \)[/tex]

Thus, the prime factorization of [tex]\( 4v \)[/tex]:
[tex]\[ 4v = 2^2 \cdot v \][/tex]

### 3) Interpret and Correct Provided Expressions:
The given expressions seem disjointed and possibly incorrect, making it hard to interpret directly. However, let's confirm known prime factorizations before moving on to specific needs.

### 4) Prime Factorization of [tex]\( 21x^2 \)[/tex]:
First, let's separate 21 and [tex]\( x^2 \)[/tex]:
- The number 21 can be broken down into its prime factors.
- [tex]\( x^2 \)[/tex] is considered as [tex]\( x \cdot x \)[/tex].

Step-by-Step Factorization:
- We start with 21: [tex]\( 21 = 3 \times 7 \)[/tex]

Thus, the prime factorization of [tex]\( 21x^2 \)[/tex]:
[tex]\[ 21x^2 = 3 \times 7 \times x \times x \][/tex]

Recap of all the prime factorizations:

1. [tex]\( 16y = 2^4 \cdot y \)[/tex]
2. [tex]\( 4v = 2^2 \cdot v \)[/tex]
3. [tex]\( 21x^2 = 3 \times 7 \times x^2 \)[/tex]

Now, the problem seems to involve manipulation beyond basic prime factorization, potentially leading us to algebraic simplifications or fraction forms. But with the given terms taken into account, we reiterate:
- Factor each numeric element distinctly.
- Maintain each distinct algebraic element alongside to convey full intentions.

Let me know if you need specific breakdowns or assistance across further equations from initial expressions!
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.