SOLUTION: Factor this polynomial, please! 250-16x^3 thank you!

Question 24637: Factor this polynomial, please!
250-16x^3
thank you!
Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You have to know the following:
a^3-b^3 = (a-b)(a^+ab+b^2)
Your Problem fits this pattern after factoring
out a "2" to get:
2(125-8x^3) = 2 (5^3-(2x)^3)
= 2 (5-2x)(5^2+(5)(2x)+(2x)^2)
= 2 (5-2x)(25+10x+4x^2)
Cheers,
stan H.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
First, take out the common factor of 2

Next, recognize the perfect cube numbers of 125 and 8. This is the difference of two cubes, which can be factored into a product of a binomial (5-2x) times a trinomial that can be either built from the binomial or from the formula you may have memorized:

If you need additional explanation of this, go to my webpage that has an entire explanation on this and other topics of factoring at this level. You can go to my webpage by clicking on my tutor name "rapaljer" anywhere in algebra.com, then go to Math in Living Color, and then under Intermediate Algebra, the very first topic is Factoring, Factoring, Factoring. This is a LONG explanation of factoring, with explanation, examples, exercises, and answers to ALL the exercises!!

R^2 at SCC

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