SOLUTION: 3x^4-9x^3y+3x^2y^2 Factor Polynomial Completely I don't understand how the steps go to this problem. I figured that the GCF is X^2 and x^2(3x^2-9xy+3y^2). Other than that I'm

Question 207313This question is from textbook Intoductory & Intermediate Algebra for College Students
: 3x^4-9x^3y+3x^2y^2
Factor Polynomial Completely
I don't understand how the steps go to this problem. I figured that the GCF is X^2 and x^2(3x^2-9xy+3y^2). Other than that I'm lost, and we are having a test with these kind of problems tomorrow. I appreciate your help.
This question is from textbook Intoductory & Intermediate Algebra for College Students

Found 2 solutions by RAY100, vleith:
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
3x^4 -9x^3*y +3x^2*y^2
.
3x^2 ( x^2 -3xy +y^2)
.
3*x*x*(x-2.62y)(x-.38y),,,,,,,need quadratic formula to solve last 2 factors
.
.
x^2 -9xy+y^2,,,,let a-1,,,b= -3,,c-1,,,,,,we'll add y^2 later
.
x=[ -(-3) +/- sqrt{ (-3)^2 -4(1)(1)}]/2(1)
.
x=[ 3 +/- sqrt{ 9-4}]/2
.
x= [ 3+/- sqrt 5 ] /2
.
x=[3+/- 2.236] / 2
.
x= 2.618, .382
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therefore ,,,(x-2.62)(x-.38)
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but we need at account for the y^2, so
.
(x-2.62y)(x-.38y)
.
check,,,FOIL above,,x^2 -3xy +1y^2,,,,ok
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
You're almost there. You can factor out a factor of 3 too

Since you can't factor the quadratic part simply, I think you are done.
And here's a helper URL for you --> http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=algebra&s2=factor&s3=basic
That URL can factor stuff - just doesn't show alot of steps. Good for checking your work though!
Hope that helps some and good luck on your test.
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