Determine all n for which x^n + y^n factors.?
925677
x^n + y^n has factors when n is not a power of 2: n = 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ...\n\nIf n is odd then ( x + y ) is a factor, by the factor theorem: put y = -x.\n\nIf n has an odd factor n = p q where p is odd, then x^(pq) = (x^q)^p. So, x^n + y^n = (x^q)^p + (y^q)^p can be factored. Example: x^44 + y^44 = (x^4)^11 + (y^4)^11 has x^4 + y^4 as a factor.\n\nThat only leaves x^(2^n) + y^(2^n): x^2 + y^2, x^4 + y^4, x^8 + y^8, ... None of these can be factored, using Eisenstein's criteria.\n\nIn the above I assume that all coefficients are integers. If not, note that\n\nx^4 + y^4 = ( x² + √2 x + 1 ) ( x² - √2 x + 1 )\n\nand similar results for other powers of 2.
958614
#1.)-----------------------------------\n  \n25b^ -20by + 4y^\n\nMultiply 1st and 3rd term together to get 100b^y^.\n\nFactor 100b^y^ into two factors whose sum = the middle term of -20by.\n\n1by   X 100by\n2by   X 50by\n4by   X 25by\n5by   X 20by\n10by X 10 by   ....................BINGO!\n\n-10by + (-10by) = - 20by   &   (-10by)(-10by) = 100by\n\nThis is a really kewl factor by grouping trick, I LOVE it!\n\nBring down the first term of: (25b^)\n\nNext, write the SMALLER of the two factors 1st.  Followed by the LARGER of the two factors.  In this case, they're both the same, so it doesn't matter which one goes first: (-10by)\n\nFinally, bring down the third term of: (+4y^)\n\n25b^ -10by -10by + 4y^\n\nNow, lets factor by grouping! \nFactor out the GCFs.\nGCF#1 = 5b\nGCF#2 = -2y\n\n(25b^ -10by) + (-10by +4y^)\n5b(5b - 2y) -2y(5b - 2y)\n\nGCF#3 = (5b - 2y)\n\n(5b - 2y)(5b - 2y)\n\nSimplifies further as: (5b - 2y)^   ....Whatdayaknow?! \n.......................................................................................................It's a Perfect Square Trinomial.\n\n#2.)------------------------------------------------------------------\n\n100 - 9b^\n\nAh, the difference of two perfect squares.\n\n---------------------------------------------\n\nFORMULA:\na^ - b^ = (a-b)(a+b)\n\n---------------------------------\n\nSOLUTION:\n100 - 9b^\n(10)^ - (3b)^\n\n-----------------------\n\nANSWER:\n(10-3b)(10+3b)
1029303
if you are asking for the factors,it is\n(x-15y)*(x+15y)
745882
C is correct but not complete... only the 3 is factored out... the real answer would be:\n\n3(x-1)(x+4)
896751
are you solving for y or n?
18182
2x^2 + 5x + 20x + 50\n2x^2 + 25x + 50
239852
Use the guess and check method.\n\nFirst, find all the factors of the number at the far right (example: in the 1st exercise, it is 25, so...\n\n25=1*25, 5*5\nNext, find those factors that together add up to the number in the middle.(10, in this case) . That would be: 5*5=25 and 5+5=10. So you write...\n(a+5)(a+5). \nDo this with all the rest.However, this sadly doesnt work with trinomials that have its largest exponent be bigger than 2. Also the term with the largest exponent (remember:it has to be 2) cannot have a coefficient.\n\nNote:this method works with the following exercises:1,2,3,4,5,6,and 7. I'm pretty sure. :)
600427
It is already factored, you can write it more concisely as (x-y)^2.\n\nThe EXPANDED form is x^2-2xy+y^2.
930643
factor:\n\n(2x^2+x-6)/(2x+4)=\n\n(2x-3)(x+2) / 2(x+2)\n\nthe (x+2)s cancel out leaving\n\n(2x-3)/2
168995
plynomial expression could be factorized as the product of \n(x-r) where r is a root (a zero) of the polynomial soyou must get the roots first\nMany numerical methods exists
699742
-(3x+y)(3x-y)\n-(9x^2-y^2)\ny^2-9x^2
547775
f(x)= x^3+x^2-22x-40\nf(x)= (x+4)(ax^2 + bx + c)\n\nComparing coefficients,\nx^3: 1=a\nconstant: -40=4c => c=-10\nx^2: 1=b+4a => 1=b+4 => b=-3\n\nf(x) = (x+4)(x^2-3x-10) = (x+4)(x+2)(x-5)\n\nThe other factors are (x+2) and (x-5).
683580
y^2 + 7y + 3y + 21\ny^2 + (7 + 3)y + 21\ny^2 + 10y + 21\n(y + 7)*(y + 3)
1002101
factor 9x^2y^2-9y^2\n9y^2(x^2-1)\n9y^2(x+1)(x-1)
956461
factors of 24\n1, 2, 3, 4, 6, 8, 12, 24
1033909
14x^4y^4/18x^2y^5\n\nSince x^1 and y^1 must remain in any reduction, at lowest terms this would be:\n\n7x^3y/9xy^2\n\nRead: seven x cubed y over nine x y squared
919015
(8X^6/7) * (56/24)\n8X^6/3\n\n(Hint:  X^m/X^n = X^(m-n)