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Answer :
To solve the problem of dividing the expression [tex]\(36x^4 + 12x^8\)[/tex] by [tex]\(12x^4\)[/tex], let's break it down into steps:
1. Separate the Terms: The expression in the numerator, [tex]\(36x^4 + 12x^8\)[/tex], can be divided term by term by the denominator, [tex]\(12x^4\)[/tex].
2. Divide Each Term:
- First, take the term [tex]\(36x^4\)[/tex] and divide it by [tex]\(12x^4\)[/tex]:
[tex]\[
\frac{36x^4}{12x^4} = \frac{36}{12} \cdot \frac{x^4}{x^4} = 3 \cdot 1 = 3
\][/tex]
- Next, take the term [tex]\(12x^8\)[/tex] and divide it by [tex]\(12x^4\)[/tex]:
[tex]\[
\frac{12x^8}{12x^4} = \frac{12}{12} \cdot \frac{x^8}{x^4} = 1 \cdot x^{8-4} = x^4
\][/tex]
3. Combine the Results: Add the results of the divisions together:
[tex]\[
3 + x^4
\][/tex]
Thus, when [tex]\(36x^4 + 12x^8\)[/tex] is divided by [tex]\(12x^4\)[/tex], the result is [tex]\(3 + x^4\)[/tex].
Therefore, the correct expression to fit into the blank is [tex]\(3 + x^4\)[/tex].
1. Separate the Terms: The expression in the numerator, [tex]\(36x^4 + 12x^8\)[/tex], can be divided term by term by the denominator, [tex]\(12x^4\)[/tex].
2. Divide Each Term:
- First, take the term [tex]\(36x^4\)[/tex] and divide it by [tex]\(12x^4\)[/tex]:
[tex]\[
\frac{36x^4}{12x^4} = \frac{36}{12} \cdot \frac{x^4}{x^4} = 3 \cdot 1 = 3
\][/tex]
- Next, take the term [tex]\(12x^8\)[/tex] and divide it by [tex]\(12x^4\)[/tex]:
[tex]\[
\frac{12x^8}{12x^4} = \frac{12}{12} \cdot \frac{x^8}{x^4} = 1 \cdot x^{8-4} = x^4
\][/tex]
3. Combine the Results: Add the results of the divisions together:
[tex]\[
3 + x^4
\][/tex]
Thus, when [tex]\(36x^4 + 12x^8\)[/tex] is divided by [tex]\(12x^4\)[/tex], the result is [tex]\(3 + x^4\)[/tex].
Therefore, the correct expression to fit into the blank is [tex]\(3 + x^4\)[/tex].
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