Question

divide. if there is a remainder, include it as a simplified fraction\\((-8c^{2}+28c - 8)div4c\\)

Explanation:

Step1: Divide each term by \(4c\)

We can split the division of the polynomial by the monomial into dividing each term of the polynomial by the monomial. So we have:
\(\frac{-8c^{2}}{4c}+\frac{28c}{4c}-\frac{8}{4c}\)

Step2: Simplify each term

• For the first term \(\frac{-8c^{2}}{4c}\), we divide the coefficients and subtract the exponents of \(c\) (using the rule \(\frac{a^{m}}{a^{n}}=a^{m - n}\)). The coefficient \(\frac{-8}{4}=-2\) and the exponent of \(c\) is \(2-1 = 1\), so this term simplifies to \(-2c\).
• For the second term \(\frac{28c}{4c}\), the \(c\) terms cancel out and \(\frac{28}{4}=7\), so this term simplifies to \(7\).
• For the third term \(\frac{-8}{4c}\), we simplify the coefficient \(\frac{-8}{4}=-2\), so this term simplifies to \(-\frac{2}{c}\).

Answer:

\(-2c + 7-\frac{2}{c}\)