SOLUTION: Could you please help with the following problem in factoring polynomials?
Factor the common factor out of each expression.
20 − 35n^2 − 20n^3
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-> SOLUTION: Could you please help with the following problem in factoring polynomials?
Factor the common factor out of each expression.
20 − 35n^2 − 20n^3
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Question 1178745: Could you please help with the following problem in factoring polynomials?
Factor the common factor out of each expression.
20 − 35n^2 − 20n^3 Found 2 solutions by MathLover1, greenestamps:Answer by MathLover1(20850) (Show Source):
Perhaps this is from the same student as a number of other similar questions I am seeing at this forum today....
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
5(4-7n^2-4n^3) [1]
Not all the terms contain powers of the variable n, so there is no n in the GCF.
You might want to write the polynomial factor in standard form -- with decreasing powers of the variable:
5(-4n^3-7n^2+4) [2]
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:
-5(4n^2+7n^2-4) [3]
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".
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.
It might even be the case that the most useful factorization is
-5(-4+7n^2+4n^3) [4]
That one is awkward; but it is mathematically correct.
