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------------------------------------------------ What is the greatest common factor for [tex]30x^2[/tex] and [tex]45x^5[/tex]?

Answer :

Final answer:

The greatest common factor for 30x^2 and 45x^5 is 15x^2.

Explanation:

The greatest common factor (GCF) for 30x2 and 45x5 can be found by identifying the common factors and choosing the highest power of each factor.

First, factorize both expressions:

  • 30x2 = 2 × 3 × 5 × x × x
  • 45x5 = 3 × 3 × 5 × x × x × x × x × x

The common factors are 3, 5, and x2. The highest power of 3 is 3, the highest power of 5 is 1, and the highest power of x is 2. Therefore, the GCF is 3 × 5 × x2, which simplifies to 15x2.

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