To find the result of dividing [tex]\( 48a^3 + 32a^2 + 16a \)[/tex] by [tex]\( 4a \)[/tex], we can use polynomial division. The process involves dividing each term of the polynomial by [tex]\( 4a \)[/tex] separately. Let's go through each step in detail:
1. First Term: [tex]\( 48a^3 \)[/tex]
[tex]\[
\frac{48a^3}{4a} = 48 \cdot \frac{a^3}{a} = 48 \cdot a^{3-1} = 48a^2
\][/tex]
2. Second Term: [tex]\( 32a^2 \)[/tex]
[tex]\[
\frac{32a^2}{4a} = 32 \cdot \frac{a^2}{a} = 32 \cdot a^{2-1} = 32a
\][/tex]
3. Third Term: [tex]\( 16a \)[/tex]
[tex]\[
\frac{16a}{4a} = 16 \cdot \frac{a}{a} = 16 \cdot a^{1-1} = 16 \cdot a^0 = 16 \cdot 1 = 4
\][/tex]
Now, we combine the results of each division:
[tex]\[
48a^2 + 32a + 4
\][/tex]
Hence, the division yields:
[tex]\(
48a^2 + 32a + 4
\)[/tex]
The correct answer is:
D. [tex]\( 12a^2 + 8a + 4 \)[/tex]
