Answer :
Sure! Let's work through dividing the expression step by step.
We are given the expression [tex]\(\frac{14x^8 - 4x^4 + 14x^2}{2x^2}\)[/tex]. Our goal is to divide the entire numerator by the denominator, [tex]\(2x^2\)[/tex].
Here's how you can solve it step by step:
1. Divide Each Term in the Numerator by the Denominator:
- Start with each term in the numerator: [tex]\(14x^8\)[/tex], [tex]\(-4x^4\)[/tex], and [tex]\(14x^2\)[/tex].
2. First Term:
- Divide [tex]\(14x^8\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
\frac{14x^8}{2x^2} = 7x^{8-2} = 7x^6
\][/tex]
3. Second Term:
- Divide [tex]\(-4x^4\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
\frac{-4x^4}{2x^2} = -2x^{4-2} = -2x^2
\][/tex]
4. Third Term:
- Divide [tex]\(14x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
\frac{14x^2}{2x^2} = 7x^{2-2} = 7x^0 = 7
\][/tex]
5. Combine the Results:
- Now, put it all together:
[tex]\[
7x^6 - 2x^2 + 7
\][/tex]
So, the result of dividing the expression [tex]\(\frac{14x^8 - 4x^4 + 14x^2}{2x^2}\)[/tex] is [tex]\(7x^6 - 2x^2 + 7\)[/tex]. This is the simplified form after performing the division.
We are given the expression [tex]\(\frac{14x^8 - 4x^4 + 14x^2}{2x^2}\)[/tex]. Our goal is to divide the entire numerator by the denominator, [tex]\(2x^2\)[/tex].
Here's how you can solve it step by step:
1. Divide Each Term in the Numerator by the Denominator:
- Start with each term in the numerator: [tex]\(14x^8\)[/tex], [tex]\(-4x^4\)[/tex], and [tex]\(14x^2\)[/tex].
2. First Term:
- Divide [tex]\(14x^8\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
\frac{14x^8}{2x^2} = 7x^{8-2} = 7x^6
\][/tex]
3. Second Term:
- Divide [tex]\(-4x^4\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
\frac{-4x^4}{2x^2} = -2x^{4-2} = -2x^2
\][/tex]
4. Third Term:
- Divide [tex]\(14x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
\frac{14x^2}{2x^2} = 7x^{2-2} = 7x^0 = 7
\][/tex]
5. Combine the Results:
- Now, put it all together:
[tex]\[
7x^6 - 2x^2 + 7
\][/tex]
So, the result of dividing the expression [tex]\(\frac{14x^8 - 4x^4 + 14x^2}{2x^2}\)[/tex] is [tex]\(7x^6 - 2x^2 + 7\)[/tex]. This is the simplified form after performing the division.
