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

Divide the numerator by the monomial in the denominator. Simplify your answer. -48 x^4 + 36 x^3 - 10 x^2 / 6 x^2
Transcript text: Divide the numerator by the monomial in the denominator. Simplify your answer. \[ \frac{-48 x^{4}+36 x^{3}-10 x^{2}}{6 x^{2}} \]
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Solution

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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.

Step 1: Divide Each Term in the Numerator by the Denominator

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

Step 2: Simplify Each Term
  1. \(\frac{-48x^4}{6x^2} = -8x^{4-2} = -8x^2\)
  2. \(\frac{36x^3}{6x^2} = 6x^{3-2} = 6x\)
  3. \(\frac{-10x^2}{6x^2} = -\frac{10}{6}x^{2-2} = -\frac{5}{3}\)
Step 3: Combine the Simplified Terms

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

Final Answer

\[ \boxed{-8x^2 + 6x - \frac{5}{3}} \]

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