Answer :
To divide the polynomial [tex]\(\frac{72x^5 - 36x^4 + 45x^2}{-9x^2}\)[/tex], we need to divide each term in the numerator by the term in the denominator, which is [tex]\(-9x^2\)[/tex].
Here's how to do it step-by-step:
1. Divide the first term:
[tex]\(\frac{72x^5}{-9x^2} = -8x^{5-2} = -8x^3\)[/tex]
2. Divide the second term:
[tex]\(\frac{-36x^4}{-9x^2} = 4x^{4-2} = 4x^2\)[/tex]
3. Divide the third term:
[tex]\(\frac{45x^2}{-9x^2} = -5x^{2-2} = -5\)[/tex]
When you simplify the expression by dividing each term in the numerator by the denominator, you end up with:
[tex]\[
-8x^3 + 4x^2 - 5
\][/tex]
Therefore, the simplified result of the division is:
[tex]\[ -8x^3 + 4x^2 - 5 \][/tex]
This polynomial is the simplest form of [tex]\(\frac{72x^5 - 36x^4 + 45x^2}{-9x^2}\)[/tex].
Here's how to do it step-by-step:
1. Divide the first term:
[tex]\(\frac{72x^5}{-9x^2} = -8x^{5-2} = -8x^3\)[/tex]
2. Divide the second term:
[tex]\(\frac{-36x^4}{-9x^2} = 4x^{4-2} = 4x^2\)[/tex]
3. Divide the third term:
[tex]\(\frac{45x^2}{-9x^2} = -5x^{2-2} = -5\)[/tex]
When you simplify the expression by dividing each term in the numerator by the denominator, you end up with:
[tex]\[
-8x^3 + 4x^2 - 5
\][/tex]
Therefore, the simplified result of the division is:
[tex]\[ -8x^3 + 4x^2 - 5 \][/tex]
This polynomial is the simplest form of [tex]\(\frac{72x^5 - 36x^4 + 45x^2}{-9x^2}\)[/tex].
