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Find the missing factor C that makes the equality true. {:[12x^(5)=(4x^(2))(C)],[C=◻]:}

Find the missing factor C C that makes the equality true.\newline12x5=(4x2)(C)C=□ \begin{array}{l} 12 x^{5}=\left(4 x^{2}\right)(C) \\ C=\square \end{array}

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Full solution

Q. Find the missing factor C C that makes the equality true.\newline12x5=(4x2)(C)C=□ \begin{array}{l} 12 x^{5}=\left(4 x^{2}\right)(C) \\ C=\square \end{array}
  1. Isolate C in the equation: To find the missing factor C, we need to isolate C in the equation 12x5=(4x2)C12x^5 = (4x^2)C.\newlineWe can do this by dividing both sides of the equation by 4x24x^2.\newlineCalculation: C=12x54x2C = \frac{12x^5}{4x^2}
  2. Divide both sides of the equation: Now we simplify the right side of the equation by dividing the coefficients and subtracting the exponents of like bases according to the laws of exponents.\newlineCalculation: C=124⋅x(5−2) C = \frac{12}{4} \cdot x^{(5-2)}
  3. Simplify the right side of the equation: Simplify the numerical part and the exponents.\newlineCalculation: C=3×x3C = 3 \times x^3

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