SOLUTION: How do I factor this? {{{m4 -38m^2n^2 + 72n^4}}} The answer is {{{(m-6n)(m+6n)(m^2-2n^2)}}} I'm confused on how they got this answer. The 38 is not a typo, either.

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Question 903823: How do I factor this?

The answer is
I'm confused on how they got this answer. The 38 is not a typo, either.

Found 3 solutions by jim_thompson5910, josgarithmetic, MathTherapy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!


Break up into (see note below)

Pair up the terms

Factor from the first group

Factor from the second group

Factor out the overall GCF

Factor (difference of squares rule)


Note: the last coefficient is 72. We need to find factors of 72 that add to -38. Put another way, we need to find two numbers that multiply to 72 AND add to -38. Those two numbers are -2 and -36. That explains how I broke up into (notice the coefficients)

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Not remembering any instruction during Introductory Algebra from so long ago that dealt with factoring degree 4 trinomial, eventually further instruction combined from Introductory and College Algebra contained enough knowledge to use polynomial division for trying to handle something like you have; including Rational Roots Theorem, although you are not interested in roots here.

There is m^4 and n^4, the n^4 term having coefficient 72. Factors of 72 are 2, 3, 6, 12, 24,36.

You would want to test DIVISORS of , , , , , , ... possibly others. Your DIVIDEND must be formed as ;

After finding the quotient with remainder of zero, you next use whatever skills you have for factoring, or you might try another polynomial division on the quotient, choosing a divisor that you believe is worth testing.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

How do I factor this?

The answer is
I'm confused on how they got this answer. The 38 is not a typo, either.



The factors of 72 that sum to 72 (a * c), and differ by 38 (b), are 36 and 2
Therefore, becomes:

-------- Factoring out GCF from each pair of binomials

-------- Factoring further
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