Answer :
To solve the problem of dividing [tex]\(36 x^4 + 12 x^8\)[/tex] by [tex]\(12 x^4\)[/tex], we will break it down step-by-step:
1. Write down the original expression:
[tex]\[
\frac{36 x^4 + 12 x^8}{12 x^4}
\][/tex]
2. Separate the terms in the numerator:
The expression can be separated into two fractions:
[tex]\[
\frac{36 x^4}{12 x^4} + \frac{12 x^8}{12 x^4}
\][/tex]
3. Simplify each fraction individually:
- For the first fraction:
[tex]\[
\frac{36 x^4}{12 x^4} = \frac{36}{12} \cdot \frac{x^4}{x^4} = 3
\][/tex]
Here, [tex]\(\frac{36}{12} = 3\)[/tex] and [tex]\(\frac{x^4}{x^4} = 1\)[/tex].
- For the second fraction:
[tex]\[
\frac{12 x^8}{12 x^4} = \frac{12}{12} \cdot \frac{x^8}{x^4} = 1 \cdot x^{8-4} = x^4
\][/tex]
Here, [tex]\(\frac{12}{12} = 1\)[/tex] and [tex]\(x^8/x^4 = x^{8-4} = x^4\)[/tex].
4. Combine the simplified terms:
[tex]\[
3 + x^4
\][/tex]
So, after dividing [tex]\((36 x^4 + 12 x^8)\)[/tex] by [tex]\(12 x^4\)[/tex], the result is:
[tex]\[
3 + x^4
\][/tex]
Thus, the answer is:
[tex]\[
\boxed{3 + x^4}
\][/tex]
The choice that fits our result from the given options is:
[tex]\[
3 + x^4
\][/tex]
1. Write down the original expression:
[tex]\[
\frac{36 x^4 + 12 x^8}{12 x^4}
\][/tex]
2. Separate the terms in the numerator:
The expression can be separated into two fractions:
[tex]\[
\frac{36 x^4}{12 x^4} + \frac{12 x^8}{12 x^4}
\][/tex]
3. Simplify each fraction individually:
- For the first fraction:
[tex]\[
\frac{36 x^4}{12 x^4} = \frac{36}{12} \cdot \frac{x^4}{x^4} = 3
\][/tex]
Here, [tex]\(\frac{36}{12} = 3\)[/tex] and [tex]\(\frac{x^4}{x^4} = 1\)[/tex].
- For the second fraction:
[tex]\[
\frac{12 x^8}{12 x^4} = \frac{12}{12} \cdot \frac{x^8}{x^4} = 1 \cdot x^{8-4} = x^4
\][/tex]
Here, [tex]\(\frac{12}{12} = 1\)[/tex] and [tex]\(x^8/x^4 = x^{8-4} = x^4\)[/tex].
4. Combine the simplified terms:
[tex]\[
3 + x^4
\][/tex]
So, after dividing [tex]\((36 x^4 + 12 x^8)\)[/tex] by [tex]\(12 x^4\)[/tex], the result is:
[tex]\[
3 + x^4
\][/tex]
Thus, the answer is:
[tex]\[
\boxed{3 + x^4}
\][/tex]
The choice that fits our result from the given options is:
[tex]\[
3 + x^4
\][/tex]
