Any tips for factoring polynomials?

hatjuice

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Specifically, ones that don't seem very straightforward. I've consulted my textbook, but it only gives me step-by-step examples for ones that have a GCF (such as 5x^4 + 40x). Sometimes I'm told to factor polynomials such as x^4 - 37x^2 + 36 and x^6 - 12x^4 + 48x^2 - 64 , and although I've used calculators to see what the answer would have been I can't figure out how to work it backwards... I've tried breaking up the polynomial, but that doesn't seem to work very well. :c
 
Specifically, ones that don't seem very straightforward. I've consulted my textbook, but it only gives me step-by-step examples for ones that have a GCF (such as 5x^4 + 40x). Sometimes I'm told to factor polynomials such as x^4 - 37x^2 + 36 and x^6 - 12x^4 + 48x^2 - 64 , and although I've used calculators to see what the answer would have been I can't figure out how to work it backwards... I've tried breaking up the polynomial, but that doesn't seem to work very well. :c

Only effective advice I can give you is - PRACTICE. Sometimes you need to factorize by observation:

5x4 + 40x = 5x(x3 + 23) = 5x(x + 2)(x2 - 2x + 4) This is it for factors in real domain.
 
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Hi hatjuice:

Make sure to memorize all of the special factoring patterns (eg: difference of squares, difference of cubes, sum of cubes). Subhotosh recognized a sum of cubes above; Denis used a difference of squares (twice).

Be cognizant of what's called "quadratic forms", like ax4+bx^2+c; they can be solved by substitution, as Denis did above.

Have you learned polynomial longhand-division or the "shorthand" version known as "synthetic division"? Sometimes, you can guess a factor, and then try dividing the polynomial by the guess, to see if there's no remainder. If there's no remainder, then you've got one of the factors, and you may then continue trying to factor the resulting quotient.

Have you learned the factoring method known as "factor by grouping"? It's also useful, with certain polynomials.

Google any of these topics with which you're unfamiliar.

Cheers :)
 
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