Questions: Divide the numerator by the monomial in the denominator. Simplify your answer. -48 x^4 + 36 x^3 - 10 x^2 / 6 x^2

Solution Steps

To solve the given polynomial division problem, we need to divide each term in the numerator by the monomial in the denominator. This involves dividing the coefficients and subtracting the exponents of like bases.

To simplify the expression \(\frac{-48x^4 + 36x^3 - 10x^2}{6x^2}\), we divide each term in the numerator by \(6x^2\).

1. \(\frac{-48x^4}{6x^2} = -8x^{4-2} = -8x^2\)
2. \(\frac{36x^3}{6x^2} = 6x^{3-2} = 6x\)
3. \(\frac{-10x^2}{6x^2} = -\frac{10}{6}x^{2-2} = -\frac{5}{3}\)

Combining the simplified terms, we get: \[ -8x^2 + 6x - \frac{5}{3} \]

Final Answer