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When [tex]$36 x^4+12 x^8$[/tex] is divided by [tex]$12 x^4$[/tex], the result is:

A. [tex]3+12 x^8[/tex]

B. [tex]3 x+x^2[/tex]

C. [tex]3+x^4[/tex]

D. [tex]3+12 x^8[/tex]

Answer :

To solve the division

[tex]$$\frac{36x^4 + 12x^8}{12x^4},$$[/tex]

we can split the expression into two fractions:

[tex]$$
\frac{36x^4}{12x^4} + \frac{12x^8}{12x^4}.
$$[/tex]

Step 1: Divide the first term

Divide the coefficients and subtract the exponents of like bases:

[tex]$$
\frac{36x^4}{12x^4} = \frac{36}{12} \cdot \frac{x^4}{x^4} = 3 \cdot 1 = 3.
$$[/tex]

Step 2: Divide the second term

Again, divide the coefficients and subtract the exponents (using the property [tex]$x^a/x^b = x^{a-b}$[/tex]):

[tex]$$
\frac{12x^8}{12x^4} = \frac{12}{12} \cdot \frac{x^8}{x^4} = 1 \cdot x^{8-4} = x^4.
$$[/tex]

Step 3: Combine the results

Now, add the two parts together:

[tex]$$
3 + x^4.
$$[/tex]

Thus, the result of the division is

[tex]$$\boxed{3 + x^4}.$$[/tex]

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