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Find the greatest common factor.\newline8x3,6x28x^3, 6x^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_

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Full solution

Q. Find the greatest common factor.\newline8x3,6x28x^3, 6x^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Find Factorization of 8x38x^3: First, find the complete factorization of 8x38x^3.8=2×2×28 = 2 \times 2 \times 2x3=x×x×xx^3 = x \times x \times xTherefore, 8x3=2×2×2×x×x×x8x^3 = 2 \times 2 \times 2 \times x \times x \times x
  2. Find Factorization of 6x26x^2: Next, find the complete factorization of 6x26x^2. \newline6=2×36 = 2 \times 3\newlinex2=x×xx^2 = x \times x\newlineTherefore, 6x2=2×3×x×x6x^2 = 2 \times 3 \times x \times x
  3. Find Greatest Common Factor: Now, find the greatest common factor of 8x38x^3 and 6x26x^2. The common factors are 22, xx, and xx. Therefore, the greatest common factor is 2×x×x=2x22 \times x \times x = 2x^2

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