Answer:
(2x^3)(3x^3 +2x +5)
Step-by-step explanation:
The key words here are "greatest common factor." They have their usual English meanings. A common factor is one that is a multiplier in every term, so you need to look to see what those are. The "greatest common factor" is the largest common factor you can find.
first term: 2·3·x·x·x·x·x·x
second term: 2·2·x·x·x·x
third term: 2·5·x·x·x
A common factor is a factor that is on every list. I have shown them in bold. Once the common factor is factored out, the remaining factors are summed according to the distributive property.
6x^6 +4x^4 +10x^3 = (2x^3)(3x^3 +2x +5)
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Of course you recognize that each of the coefficient numbers is even. That means they are all divisible by 2. So, you know right away that 2 is a common factor.
There are powers of x in every term. The lowest power of x is x^3, and all the other powers are higher, so you know that x^3 will be a common factor, too. Having got this far, you can factor out 2x^3 and see if any of the remaining terms seem to have anything in common. They don't.
