Question

Prove that the sum (n^2+2n+1)^3+(n^2+8n+16)^3+(9n^2+42n+49)^3+(9n^2+48n+64)^3 is divisible by 2n^2+10n+13

Answer 1

http://cims.nyu.edu/~kiryl/teaching/aa/review1.pdf Here is how to do it.

Answer 2

should I not have expanded then?

Answer 3

what?

Answer 4

I went through and expanded all of the terms out

Answer 5

\[1460n ^{6}+21900n^{5}+137550n^{4}+463000n^{3}+880950n^{2}+898500n+383890\]

Answer 6

no you should . Then put like terms together. tell me what u get

Answer 7

@Skip2mylou426

Answer 8

@cherry18 that's what I got after adding all of the like terms

Answer 9

Oh. ok. Thats ur answer

Answer 10

After multiplying out and combining like terms from the 28 terms, I got 1460n^{6}+21900n^{5}+137550^{4}+463000n^{3}+880950n^{2}+898500n+383890. What do I do now?

Answer 11

Thats the answer. You cant simplify anymore.

Answer 12

The problem isn't asking to simplify, it's asking to divide the quantity that I just typed by the polynomial \[2n ^{2}+10n+13\]

Answer 13

@cherry18

Answer 14

Nevermind, I got it. Thank you anyway!

Answer 15

hey nice could you post the solution please

Answer 16

@rational
\[730n ^{4}+7300n^{3}+27530n^{2}+46400n+29530\]
I had to use long division