SOLUTION: Find the greatest common factor X y, x⁴ y³, x⁴ y⁴, -x y The above should read x5y5 Factor 60m⁹ + 72m⁷ -24m³ u² -2uv – 63v²

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the greatest common factor X y, x⁴ y³, x⁴ y⁴, -x y The above should read x5y5 Factor 60m⁹ + 72m⁷ -24m³ u² -2uv – 63v²       Log On


   

Question 181788: Find the greatest common factor
X y, x⁴ y³, x⁴ y⁴, -x y
The above should read x5y5
Factor
60m⁹ + 72m⁷ -24m³
u² -2uv – 63v²
Factor by group
2x³ -4x² -3x +6
Factor completely
4x² -28x +40
y² +.02y - .015 Is the polynomial prime?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the greatest common factor
X y, x⁴ y³, x⁴ y⁴, -x y
x%5E5y%5E5%2C+x%5E4y%5E3%2C+x%5E4y%5E4%2C+-xy
It's xy, due to the last term.
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Factor
60m⁹ + 72m⁷ -24m³
60m%5E9+%2B+72m%5E7+-+24m%5E3
=12m%5E3%2A%285m%5E6+%2B+6m%5E4+-+2%29
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u² -2uv – 63v²
u%5E2+-+2uv+-+63v%5E2
=(u - 9v*(u + 7v)
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Factor by group
2x³ -4x² -3x +6
2x%5E3+-+4x%5E2+-+3x+%2B+6
=%28x-2%29%2A%282x%5E2+-+3%29
I don't know what "grouping" is.
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Factor completely
4x² -28x +40
4x%5E2+-+28x+%2B+40
=4%28x%5E2+-+7x+%2B+10%29
= 4(x-5)(x-2)
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y² +.02y - .015 Is the polynomial prime?
y%5E2+-+0.02y+-+0.015
It cannot be factored using integers. Does that make it prime?
If you multiply by 1000 to make all the coefficients integers, it's still not factorable using integers, but it can be factored using irrational numbers.
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If we look at the one above, 4(x-5)*(x-2), and divide it by 8, we get:
0.5x^2 -3.5x + 5. Is that prime? It's = (x-5)*(0.5x - 1).