Answer :
To solve the problem of dividing the expression [tex]\(36x^4 + 12x^4\)[/tex] by [tex]\(12x^4\)[/tex] and obtaining one of the given results, follow these steps:
1. Combine Like Terms:
- Start with the expression [tex]\(36x^4 + 12x^4\)[/tex].
- Combine the like terms: [tex]\(36x^4 + 12x^4 = 48x^4\)[/tex].
2. Divide by the Given Divisor:
- The divisor is [tex]\(12x^4\)[/tex].
- Divide the combined expression [tex]\(48x^4\)[/tex] by [tex]\(12x^4\)[/tex]:
[tex]\[
\frac{48x^4}{12x^4} = 4
\][/tex]
3. Interpret the Result:
- The result of the division is [tex]\(4\)[/tex].
- Compare this result with the possible answers: the choices were [tex]\(3x + x^\prime\)[/tex], [tex]\(3 + 12x\)[/tex], [tex]\(3 + x^2\)[/tex], and [tex]\(3 + 12x\)[/tex].
- The result [tex]\(4\)[/tex] does not explicitly match any of the given options without clarification or adjustment, which suggests there might be a typographical error or misunderstanding in the options.
Therefore, the correct simplified result of dividing the expression [tex]\(36x^4 + 12x^4\)[/tex] by [tex]\(12x^4\)[/tex] is indeed [tex]\(4\)[/tex].
1. Combine Like Terms:
- Start with the expression [tex]\(36x^4 + 12x^4\)[/tex].
- Combine the like terms: [tex]\(36x^4 + 12x^4 = 48x^4\)[/tex].
2. Divide by the Given Divisor:
- The divisor is [tex]\(12x^4\)[/tex].
- Divide the combined expression [tex]\(48x^4\)[/tex] by [tex]\(12x^4\)[/tex]:
[tex]\[
\frac{48x^4}{12x^4} = 4
\][/tex]
3. Interpret the Result:
- The result of the division is [tex]\(4\)[/tex].
- Compare this result with the possible answers: the choices were [tex]\(3x + x^\prime\)[/tex], [tex]\(3 + 12x\)[/tex], [tex]\(3 + x^2\)[/tex], and [tex]\(3 + 12x\)[/tex].
- The result [tex]\(4\)[/tex] does not explicitly match any of the given options without clarification or adjustment, which suggests there might be a typographical error or misunderstanding in the options.
Therefore, the correct simplified result of dividing the expression [tex]\(36x^4 + 12x^4\)[/tex] by [tex]\(12x^4\)[/tex] is indeed [tex]\(4\)[/tex].
