Answer :
To simplify the expression [tex]\(\frac{2x^9 - 14x^{16}}{x^2 - 7x^9}\)[/tex], let's proceed with factoring both the numerator and the denominator:
1. Factor the numerator, [tex]\(2x^9 - 14x^{16}\)[/tex]:
- Notice that both terms in the numerator have a common factor. We can factor out the greatest common factor (GCF), which is [tex]\(2x^9\)[/tex].
- This gives us:
[tex]\[
2x^9 - 14x^{16} = 2x^9(1 - 7x^7)
\][/tex]
2. Factor the denominator, [tex]\(x^2 - 7x^9\)[/tex]:
- Similarly, both terms in the denominator have a common factor. We can factor out the GCF, which is [tex]\(x^2\)[/tex].
- This gives us:
[tex]\[
x^2 - 7x^9 = x^2(1 - 7x^7)
\][/tex]
3. Simplify the whole expression:
- Now, substitute the factored forms back into the original expression:
[tex]\[
\frac{2x^9(1 - 7x^7)}{x^2(1 - 7x^7)}
\][/tex]
- Notice that [tex]\((1 - 7x^7)\)[/tex] is a common factor in both the numerator and the denominator. These can be canceled out (as long as [tex]\(1 - 7x^7 \neq 0\)[/tex]):
[tex]\[
\frac{2x^9}{x^2}
\][/tex]
4. Final simplification:
- Dividing [tex]\(2x^9\)[/tex] by [tex]\(x^2\)[/tex], we subtract the exponents:
[tex]\[
2x^{9 - 2} = 2x^7
\][/tex]
So, the simplified expression is [tex]\(2x^7\)[/tex].
The correct answer is B. [tex]\(2x^7\)[/tex].
1. Factor the numerator, [tex]\(2x^9 - 14x^{16}\)[/tex]:
- Notice that both terms in the numerator have a common factor. We can factor out the greatest common factor (GCF), which is [tex]\(2x^9\)[/tex].
- This gives us:
[tex]\[
2x^9 - 14x^{16} = 2x^9(1 - 7x^7)
\][/tex]
2. Factor the denominator, [tex]\(x^2 - 7x^9\)[/tex]:
- Similarly, both terms in the denominator have a common factor. We can factor out the GCF, which is [tex]\(x^2\)[/tex].
- This gives us:
[tex]\[
x^2 - 7x^9 = x^2(1 - 7x^7)
\][/tex]
3. Simplify the whole expression:
- Now, substitute the factored forms back into the original expression:
[tex]\[
\frac{2x^9(1 - 7x^7)}{x^2(1 - 7x^7)}
\][/tex]
- Notice that [tex]\((1 - 7x^7)\)[/tex] is a common factor in both the numerator and the denominator. These can be canceled out (as long as [tex]\(1 - 7x^7 \neq 0\)[/tex]):
[tex]\[
\frac{2x^9}{x^2}
\][/tex]
4. Final simplification:
- Dividing [tex]\(2x^9\)[/tex] by [tex]\(x^2\)[/tex], we subtract the exponents:
[tex]\[
2x^{9 - 2} = 2x^7
\][/tex]
So, the simplified expression is [tex]\(2x^7\)[/tex].
The correct answer is B. [tex]\(2x^7\)[/tex].
