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What is the result of dividing [tex]$48a^3 + 32a^2 + 16a$[/tex] by [tex]$4a$[/tex]?

A. [tex][tex]$12a + 8$[/tex][/tex]
B. [tex]$12a^2 + 4a + 4$[/tex]
C. [tex]$12a^2 + 4a + 8$[/tex]
D. [tex][tex]$12a^2 + 8a + 4$[/tex][/tex]

Sagot :

GinnyAnsweridn
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]
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