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Divide. If there is a remainder, include it as a simplified fraction.\newline(−6x3+3x2)÷3x2(-6x^3 + 3x^2) \div 3x^2

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Full solution

Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(−6x3+3x2)÷3x2(-6x^3 + 3x^2) \div 3x^2
  1. Separate and Divide Terms: We have the expression (−6x3+3x2)÷3x2(-6x^3 + 3x^2) \div 3x^2. To divide, we will separate the terms and divide each by 3x23x^2.(−6x3+3x2)÷3x2=−6x33x2+3x23x2(-6x^3 + 3x^2) \div 3x^2 = \frac{-6x^3}{3x^2} + \frac{3x^2}{3x^2}
  2. Divide First Term: Now let's divide the first term (−6x3)(-6x^3) by 3x23x^2.−6x33x2=−63×x3x2=−2×x3−2=−2x\frac{-6x^3}{3x^2} = \frac{-6}{3} \times \frac{x^3}{x^2} = -2 \times x^{3-2} = -2x
  3. Divide Second Term: Next, we divide the second term 3x23x^2 by 3x23x^2.3x23x2=33×x2x2=1×x2−2=1\frac{3x^2}{3x^2} = \frac{3}{3} \times \frac{x^2}{x^2} = 1 \times x^{2-2} = 1
  4. Combine Results: Combine the results of the division of each term.\newline(−6x3+3x2)÷3x2=−6x33x2+3x23x2=−2x+1(-6x^3 + 3x^2) \div 3x^2 = \frac{-6x^3}{3x^2} + \frac{3x^2}{3x^2} = -2x + 1

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