Question 1178745
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Perhaps this is from the same student as a number of other similar questions I am seeing at this forum today....<br>
In this expression, the coefficients are all multiples of 5, so 5 can be part of the greatest common factor (GCF).  So the expression can be factored as<br>
5(4-7n^2-4n^3)  [1]<br>
Not all the terms contain powers of the variable n, so there is no n in the GCF.<br>
You might want to write the polynomial factor in standard form -- with decreasing powers of the variable:<br>
5(-4n^3-7n^2+4)  [2]<br>
And you might want to include the negative sign as part of the GCF, so that the leading coefficient of the polynomial factor is positive:<br>
-5(4n^2+7n^2-4)  [3]<br>
Those three factorizations are equivalent; it is BAD TEACHING to say that any of them is wrong, or that only one of them is "correct".<br>
The act of factoring an expression is never the end goal in solving a problem; it is a step in the process of solving a bigger problem.  In a particular problem, any one of the forms shown might be the best one to use, in terms of making the solution of the overall problem as simple as possible.<br>
It might even be the case that the most useful factorization is<br>
-5(-4+7n^2+4n^3)  [4]<br>
That one is awkward; but it is mathematically correct.<br>