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Find the greatest common factor.\newline4x3,6x24x^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.\newline4x3,6x24x^3, 6x^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 4x34x^3: First find the complete factorization of 4x34x^3.\newline4=2×24 = 2 \times 2\newlinex3=x×x×xx^3 = x \times x \times x\newline4x3=2×2×x×x×x4x^3 = 2 \times 2 \times x \times x \times x
  2. Factorization of 6x26x^2: Now, find the complete factorization of 6x26x^2. \newline6=2×36 = 2 \times 3\newlinex2=x×xx^2 = x \times x\newline6x2=2×3×x×x6x^2 = 2 \times 3 \times x \times x
  3. Find Greatest Common Factor: We found:\newline4x3=2×2×x×x×x4x^3 = 2 \times 2 \times x \times x \times x\newline6x2=2×3×x×x6x^2 = 2 \times 3 \times x \times x\newlineFind the greatest common factor of 4x34x^3 and 6x26x^2.\newlineCommon factors are 22, xx, and xx.\newline2×x×x=2x22 \times x \times x = 2x^2\newlineGreatest common factor: 2x22x^2

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