Question 407312: Can someone please help?
Andrew factored the expression 54x^3-30x^2+15x as 5x(9x^2-6x+3). But when melissa applied the distributtive law at multiplied out 5x(9x^2-6x+3), she got 45x^3-30x^2+15x; thus, Andrews solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If prime state this.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Notice how 54 does NOT go into 5 (54 doesn't end with a 0 or a 5). So 5 is NOT part of the GCF.
Instead, the GCF of 54x^3, -30x^2 and 15x is actually 3x since this is the largest expression that goes into each term evenly. Notice how the GCF of 54, -30 and 15 is 3 and the GCF of x^3, x^2 and x is x.
So Andrew should have gotten 3x(18x^2-10x+5), which checks when you redistribute it.
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Jim
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