Divide the polynomial by the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible. x^5−2x^4+7/x
To divide the polynomial x^5 - 2x^4 + 7 by the monomial denominator x, we can write it as the sum of fractions:
(x^5 - 2x^4 + 7) / x = (x^5 / x) - (2x^4 / x) + (7 / x)
Simplifying each term, we get:
x^5 / x = x^(5-1) = x^4
-2x^4 / x = -2x^(4-1) = -2x^3
7 / x = 7x^0 / x = 7x^(0-1) = 7/x
Therefore, the simplified form is:
(x^5 - 2x^4 + 7) / x = x^4 - 2x^3 + 7/x