Answer :
We start with the expression
[tex]$$
\frac{2x^9 - 6x^3}{2x^3}.
$$[/tex]
Step 1: Factor the Numerator
Notice that both terms in the numerator have a common factor of [tex]$2x^3$[/tex]. Factoring this out, we have:
[tex]$$
2x^9 - 6x^3 = 2x^3\left(x^6 - 3\right).
$$[/tex]
Step 2: Rewrite the Expression
Substitute the factored numerator into the expression:
[tex]$$
\frac{2x^3\left(x^6 - 3\right)}{2x^3}.
$$[/tex]
Step 3: Cancel the Common Factor
The factor [tex]$2x^3$[/tex] appears in both the numerator and the denominator, so they cancel (provided that [tex]$x \neq 0$[/tex]):
[tex]$$
\frac{2x^3\left(x^6 - 3\right)}{2x^3} = x^6 - 3.
$$[/tex]
Final Answer
The simplified expression is
[tex]$$
x^6 - 3,
$$[/tex]
which corresponds to option D.
[tex]$$
\frac{2x^9 - 6x^3}{2x^3}.
$$[/tex]
Step 1: Factor the Numerator
Notice that both terms in the numerator have a common factor of [tex]$2x^3$[/tex]. Factoring this out, we have:
[tex]$$
2x^9 - 6x^3 = 2x^3\left(x^6 - 3\right).
$$[/tex]
Step 2: Rewrite the Expression
Substitute the factored numerator into the expression:
[tex]$$
\frac{2x^3\left(x^6 - 3\right)}{2x^3}.
$$[/tex]
Step 3: Cancel the Common Factor
The factor [tex]$2x^3$[/tex] appears in both the numerator and the denominator, so they cancel (provided that [tex]$x \neq 0$[/tex]):
[tex]$$
\frac{2x^3\left(x^6 - 3\right)}{2x^3} = x^6 - 3.
$$[/tex]
Final Answer
The simplified expression is
[tex]$$
x^6 - 3,
$$[/tex]
which corresponds to option D.
