Factoring Probs: 36k^3m+60k^2m^2+25km^3, etc

Factor competely as possible. If unfactorable, indicate that the polynomial is prime

These problems are driving me crazy, if anyone can help it'd be appriciated

36k³m+60k²m²+25km³ Okay for this one, im lost, the m in front of the K^3 competely throws me off, if it wasn't there i could do it very easily

Also

75a^4b - 108b³ Cant use difference of squares or cubes, can't even square root them, I don't even see anything that can really be done with this one, and it's really irritiating.

18m^7 - 42m^5 - 30m^2 For this one i got 3m(6m^6 - 14m^4 + 10m) and i may be wrong

These problems competely drive me nuts, im competely lost and would appriciate the help

Re: Factoring Problems

Hello, murat!

You've forgotten the simplest type of factoring: "comm factors".

Factor competely as possible.

\(\displaystyle 1)\;36k^3m\,+\,60k^2m^2\,+\,25km^3\)

Click to expand...

Factor out \(\displaystyle km:\;\;km(36k^2\,+\,60km\,+\,25m^2)\)

. . . \(\displaystyle = \;km(6k\,+\,5m)(6k\,+\,5m)\)

\(\displaystyle 2)\;75a^4b\,-\,108b^3\)

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Factor out \(\displaystyle 3b:\;\;3b(25a^4\,-\,36b^2)\) . . . difference of squares!

. . . \(\displaystyle = \;3b(5a^2\,-\,6n)(5a^2\,+\,6n)\)

\(\displaystyle 3(\;18m^7 - 42m^5 - 30m^2\)

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Hey! . . . You took out a common in this problem.
How come you didn't try on the other two problems?

Always factor out as much as possible . . .

Take out \(\displaystyle 3m^2:\;\;3m^2(6m^5\,-\,14m^3\,-10)\)

Hint: GCF.

Eliz.

murat said:

36k³m+60k²m²+25km³ Okay for this one, im lost, the m in front of the K^3 competely throws me off, if it wasn't there i could do it very easily

Click to expand...

Would it throw you off if written this way: 36mk^3 ? (same thing)

Thanks guys, im getting a bit rusty on math lately for some reason, i was never good at factoring or division just my weak point. thanks all!