Divide. If there is a remainder, include it as a simplified fraction. (4w^3 + 13w^2 + 3w) ÷ (w + 3) ______

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Divide. If there is a remainder, include it as a simplified fraction.   (4w^3 + 13w^2 + 3w) ÷ (w + 3)    ______

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Use Polynomial Long Division: To divide the polynomial (4w^3 + 13w^2 + 3w) by the binomial (w + 3), we will use polynomial long division. First, we divide the leading term of the polynomial, 4w^3, by the leading term of the binomial, w, to get the first term of the quotient. 4w^3 ÷ w = 4w^2 Now, we multiply the entire binomial (w + 3) by this term (4w^2) and subtract the result from the original polynomial. (4w^3 + 13w^2 + 3w) - (4w^2 * (w + 3)) = (4w^3 + 13w^2 + 3w) - (4w^3 + 12w^2)Find First Quotient Term: After subtracting, we combine like terms to find the new polynomial to divide. (4w^3 + 13w^2 + 3w) - (4w^3 + 12w^2) = w^2 + 3w Now, we divide the leading term of the new polynomial, w^2, by the leading term of the binomial, w, to get the next term of the quotient. w^2 ÷ w = w We multiply the entire binomial (w + 3) by this term (w) and subtract the result from the new polynomial. (w^2 + 3w) - (w * (w + 3)) = (w^2 + 3w) - (w^2 + 3w)Subtract and Combine Like Terms: After subtracting, we find that the result is 0, which means there is no remainder. (w^2 + 3w) - (w^2 + 3w) = 0 Therefore, the division is exact, and there is no remainder to express as a fraction. The quotient we have found is 4w^2 + w.

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(4w^3 + 13w^2 + 3w) \div (w + 3)$ $\newline$ ______

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Divide. If there is a remainder, include it as a simplified fraction.\newline(4w3+13w2+3w)÷(w+3)(4w^3 + 13w^2 + 3w) \div (w + 3)(4w3+13w2+3w)÷(w+3)\newline______

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(4w^3 + 13w^2 + 3w) \div (w + 3)$ $\newline$ ______