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Find the greatest common factor.\newline9z2,6z29z^2, 6z^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.\newline9z2,6z29z^2, 6z^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 9z29z^2: First, find the complete factorization of 9z29z^2.\newline9=3×39 = 3 \times 3\newlinez2=z×zz^2 = z \times z\newlineTherefore, 9z2=3×3×z×z9z^2 = 3 \times 3 \times z \times z.
  2. Factorization of 6z26z^2: Next, find the complete factorization of 6z26z^2.\newline6=2×36 = 2 \times 3\newlinez2=z×zz^2 = z \times z\newlineTherefore, 6z2=2×3×z×z6z^2 = 2 \times 3 \times z \times z.
  3. Identifying Common Factors: Now, identify the common factors of 9z29z^2 and 6z26z^2. The common factors are 33, zz, and zz. Therefore, the greatest common factor is 3×z×z=3z23 \times z \times z = 3z^2.

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