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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(7g^2 - 5g) \div g$

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Divide polynomials by monomials

Full solution

Q. Divide. If there is a remainder, include it as a simplified fraction.

\newline

(7g^2 - 5g) \div g

Divide by $g$ : We have the expression to divide: $\newline$ $(7g^2 - 5g) \div g$ $\newline$ First, we will divide each term in the polynomial by the monomial $g$ . $\newline$ $(7g^2 - 5g) \div g = (\frac{7g^2}{g}) - (\frac{5g}{g})$
Divide $7g^2$ by $g$ : Now let's divide $7g^2$ by $g$ : $\frac{7g^2}{g} = 7g^{2-1} = 7g$
Divide $5g$ by $g$ : Next, we divide $5g$ by $g$ : $(5g)/g = 5g^{(1-1)} = 5$
Combine results: Combine the results of the division of each term: $\newline$ $(7g^2 - 5g) \div g = \left(\frac{7g^2}{g}\right) - \left(\frac{5g}{g}\right) = 7g - 5$

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