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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(24t^2 + 36t) \div 6t$ $\newline$ ______

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Divide polynomials by monomials

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

\newline

(24t^2 + 36t) \div 6t

\newline

______

Dividing the polynomial by the monomial: We need to divide each term in the polynomial by the monomial $6t$ . $(24t^2 + 36t) \div 6t$ can be written as $(24t^2)/(6t) + (36t)/(6t)$ .
Dividing the first term: Now let's divide the first term, $24t^2$ , by $6t$ . $\newline$ $\frac{24t^2}{6t} = \frac{24}{6} \times \frac{t^2}{t} = 4t$ .
Dividing the second term: Next, we divide the second term, $36t$ , by $6t$ . $\newline$ $\frac{36t}{6t} = \frac{36}{6} \times \frac{t}{t} = 6$ .
Combining the results: Combine the results of the division of each term. $\newline$ $(24t^2 + 36t) \div 6t = \frac{24t^2}{6t} + \frac{36t}{6t} = 4t + 6$ .

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