Answer :
Let's simplify the expression [tex]\(\frac{2x^9 - 6x^3}{2x^3}\)[/tex] step by step:
1. Factor the numerator: The numerator is [tex]\(2x^9 - 6x^3\)[/tex]. Notice that both terms have a common factor of [tex]\(2x^3\)[/tex]. So, you can factor out [tex]\(2x^3\)[/tex] from the numerator:
[tex]\[
2x^9 - 6x^3 = 2x^3(x^6 - 3)
\][/tex]
2. Set up the fraction: Substitute the factored form of the numerator back into the original expression:
[tex]\[
\frac{2x^3(x^6 - 3)}{2x^3}
\][/tex]
3. Cancel the common factors: In the fraction [tex]\(\frac{2x^3(x^6 - 3)}{2x^3}\)[/tex], the [tex]\(2x^3\)[/tex] in the numerator and the denominator cancel each other out:
[tex]\[
x^6 - 3
\][/tex]
Hence, the simplified expression is [tex]\(x^6 - 3\)[/tex].
Therefore, the correct answer is B. [tex]\(x^6 - 3\)[/tex].
1. Factor the numerator: The numerator is [tex]\(2x^9 - 6x^3\)[/tex]. Notice that both terms have a common factor of [tex]\(2x^3\)[/tex]. So, you can factor out [tex]\(2x^3\)[/tex] from the numerator:
[tex]\[
2x^9 - 6x^3 = 2x^3(x^6 - 3)
\][/tex]
2. Set up the fraction: Substitute the factored form of the numerator back into the original expression:
[tex]\[
\frac{2x^3(x^6 - 3)}{2x^3}
\][/tex]
3. Cancel the common factors: In the fraction [tex]\(\frac{2x^3(x^6 - 3)}{2x^3}\)[/tex], the [tex]\(2x^3\)[/tex] in the numerator and the denominator cancel each other out:
[tex]\[
x^6 - 3
\][/tex]
Hence, the simplified expression is [tex]\(x^6 - 3\)[/tex].
Therefore, the correct answer is B. [tex]\(x^6 - 3\)[/tex].
