cg^3+27c Factor Help Please

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cg^3+27c Factor Help Please

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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what can you GCF out of both terms?
c
right so now you have c(g^3+27). now you need to set it up ( )( ). what are you going to put in the front of the parenthesis?

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by front i mean the first spot in the template c(____ _____)(_____ _____)
i am really not sure how to figure that part out??
ok. so you want the variable in the first spot in each set of parenthesis (it's not a "law" but it keeps it cleaner). so, because you have an odd exponent that you cant split up evenly, one gets g^2 while the other gets g. make sense?
yes i got it
so now what does your template look like?
c(g^2______)(g_____)
right. now we need to split up 27 so that when you multiply the two numbers together, you get 27. so what are factors of 27
p and 3
9 sorry not p
also, the two numbers should add up to the middle term…in this case 0. so we need to find numbers that multiply to 27 but add to zero.
so is it 27 and 1 or 27 and 0
ok. i have a question. what math are you in because this is not the (___ ___) (___ ___) setup that we had. it's (___ ___) (___ ___ ___). this might take longer to explain
math 035
what grade is that?
i go to a community college the name of the class is fundamental of algebra 2
ok. sorry i wasnt trying to be creepy or anything. its just that we covered this in class today
no its fine
so now we are looking at the sum or difference of two cubes…which makes a lot more sense, as the cube root of both these terms is "pretty"
so the GCF is still c, but now we are looking at the setup of a^3+b^3=(a+b)(a^2-ab+b^2) otherwise known as the S.O.P. method. the first sign in the parenthesis stays the Same as the original problem the second sign is Opposite as the original, and the third is ALWAYS Positive.
if a and b represent the original terms in the equation, what fills in the parenthesis?
ok. you left but ill finish the problem in case you come back later so you can see how its done.
the first part is just the original problem because your a=g and your b=3 a=g and b=3 so your second part is (g+3) a^2 is g^2 and ab is 3g and b^2 is 9 so your third part is (g^2-3g+9) put it all together and your final answer is (g+3)(g^2-3g+9)
hope this helped
thank you so much. my internet mess up on me. I felt so rude cause i know u were really trying to help me. Thanks so much :)

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