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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(4w^3 + 10w^2) \div 2w^2$

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Divide polynomials by monomials

Full solution

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

\newline

(4w^3 + 10w^2) \div 2w^2

Divide Expression: We have the expression to divide: $\newline$ $(4w^3 + 10w^2) \div 2w^2$ $\newline$ First, we will divide each term in the polynomial by the monomial $2w^2$ . $\newline$ $(4w^3 + 10w^2) \div 2w^2$ $\newline$ = $(4w^3)/(2w^2) + (10w^2)/(2w^2)$
Divide First Term: Now let's divide the first term: $\newline$ $(4w^3)/(2w^2)$ $\newline$ = $4/2 \times w^3/w^2$ $\newline$ = $2 \times w^{3-2}$ $\newline$ = $2w$
Divide Second Term: Next, we divide the second term: $\newline$ $(10w^2)/(2w^2)$ $\newline$ = $10/2 \times w^2/w^2$ $\newline$ = $5 \times 1$ $\newline$ = $5$
Combine Results: Combine the results of the division of each term: $\newline$ $(4w^3 + 10w^2) \div 2w^2$ $\newline$ = $\frac{4w^3}{2w^2} + \frac{10w^2}{2w^2}$ $\newline$ = $2w + 5$

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