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7n^5 7n^4-3n^2-6n-3

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need to "factor completely" this is for a lesson about grouping to factor

Mar 27th, 2015

7n^5 + 7n^4 - 3n^2 - 6n - 3 =                        group the terms 

(7n^5 + 7n^4) - (3n^2 + 3n) - (3n + 3) =       take out the greatest common factors

7n^4 (n + 1) - 3n (n + 1) - 3 (n + 1) =            factor the polynomial

(n + 1)(7 n^4 - 3n - 3)     

Note that rational zeros of the factor 7 n^4 - 3 n - 3 could be only +/-1 or +/- 3, that is, divisors of the constant term. However, none of them is a zero of this polynomial ( 7*1^4 - 3*1 - 3 = 1 not = 0, etc.) and the obtained factoring is complete. 

Mar 26th, 2015

Thank you for your help.  I do not understand how you got the second half of line 2 from the negative sign and after.

Mar 26th, 2015

group - 3n^2 - 3n -3n - 3 =                                      note that -6n = -3n  -3n

-3n(n+1) - 3(n+1)                                                    note that when the parantheses are opened, the minus sign

                                                                                will be put at both terms: - 3n(n+1) = -3n^2 - 3n      

Mar 26th, 2015

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Mar 27th, 2015
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Mar 27th, 2015
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