Answer :
To solve this problem, we're going to divide each term in the polynomial in the numerator by the monomial in the denominator. Here's how you can do it step by step:
We start with the expression:
[tex]\[ \frac{40x^6 - 80x^5 + 45x^4}{20x^4} \][/tex]
1. Divide each term in the numerator by the denominator:
- Divide the first term:
[tex]\(\frac{40x^6}{20x^4}\)[/tex].
Simplify by dividing the coefficients and subtracting the exponents of [tex]\(x\)[/tex]:
[tex]\(\frac{40}{20} = 2\)[/tex] and [tex]\(x^{6-4} = x^2\)[/tex].
So, [tex]\(\frac{40x^6}{20x^4} = 2x^2\)[/tex].
- Divide the second term:
[tex]\(\frac{-80x^5}{20x^4}\)[/tex].
Simplify by dividing the coefficients and subtracting the exponents of [tex]\(x\)[/tex]:
[tex]\(\frac{-80}{20} = -4\)[/tex] and [tex]\(x^{5-4} = x\)[/tex].
So, [tex]\(\frac{-80x^5}{20x^4} = -4x\)[/tex].
- Divide the third term:
[tex]\(\frac{45x^4}{20x^4}\)[/tex].
Simplify by dividing the coefficients:
[tex]\(\frac{45}{20} = \frac{9}{4}\)[/tex] (since [tex]\(x^4\)[/tex] cancels out).
So, [tex]\(\frac{45x^4}{20x^4} = \frac{9}{4}\)[/tex].
2. Combine the simplified terms:
The expression simplifies to:
[tex]\[ 2x^2 - 4x + \frac{9}{4} \][/tex]
Thus, the simplified form of the given polynomial divided by the monomial is:
[tex]\[ 2x^2 - 4x + \frac{9}{4} \][/tex]
We start with the expression:
[tex]\[ \frac{40x^6 - 80x^5 + 45x^4}{20x^4} \][/tex]
1. Divide each term in the numerator by the denominator:
- Divide the first term:
[tex]\(\frac{40x^6}{20x^4}\)[/tex].
Simplify by dividing the coefficients and subtracting the exponents of [tex]\(x\)[/tex]:
[tex]\(\frac{40}{20} = 2\)[/tex] and [tex]\(x^{6-4} = x^2\)[/tex].
So, [tex]\(\frac{40x^6}{20x^4} = 2x^2\)[/tex].
- Divide the second term:
[tex]\(\frac{-80x^5}{20x^4}\)[/tex].
Simplify by dividing the coefficients and subtracting the exponents of [tex]\(x\)[/tex]:
[tex]\(\frac{-80}{20} = -4\)[/tex] and [tex]\(x^{5-4} = x\)[/tex].
So, [tex]\(\frac{-80x^5}{20x^4} = -4x\)[/tex].
- Divide the third term:
[tex]\(\frac{45x^4}{20x^4}\)[/tex].
Simplify by dividing the coefficients:
[tex]\(\frac{45}{20} = \frac{9}{4}\)[/tex] (since [tex]\(x^4\)[/tex] cancels out).
So, [tex]\(\frac{45x^4}{20x^4} = \frac{9}{4}\)[/tex].
2. Combine the simplified terms:
The expression simplifies to:
[tex]\[ 2x^2 - 4x + \frac{9}{4} \][/tex]
Thus, the simplified form of the given polynomial divided by the monomial is:
[tex]\[ 2x^2 - 4x + \frac{9}{4} \][/tex]
