Simplify the polynomial [(6x-8)-2x]-[(12x-7)-(4x-5)]?
814352
(12x^2 +16x) - (12x-7)- (4x-5)\n12x^2 +16x -12x +7 -4x +5\n\n12x^2+12\n\nthat is what I got....\nI think you might be able to put 12 on the other side of the = sign and turn it into 12x^2 = -12 and then since both sides have 12 in common you can divide both sides by 12 and you will have x^2 = -1 then you can add 1 to both sides and you will have x^2 +1 but I think I'm getting off track by that point....it's been a while since I had to do this stuff.
714160
x^2+6x+8/x^2-4-21 / x^2-4/x^2-7x\n=x^2 + 6x +(8/x^2) - 4 - (21/x^2) - (4/x^2) - 7x\n=x^2 + 6x -4 -7x +(8/x^2) - (21/x^2) - (4/x^2) \n=x^2 + 6x -4 -7x +[8-21-4]/x^2\n=x^2 + 6x -4 -7x -17/x^2\n=(x^2)*[x^2 - x -4  -17]/x^2\n=(x^2)*(x^2) - (x^2)*(x) -4*(x^2)  -17]/x^2\n=(x^4) - (x^3) - 4(x^2)x -17]/x^2
346785
(x^2-5x+4)/(x^2-9) * \n(x^2+7x+12)/(x^2+3x-28)=\n\n[(x^2-5x+4)*(x^2+7x+12)]/\n[(x^2-9)*(x^2+3x-28)]=\n\n[(x^2-4x-x+4)*(x^2+4x+3x+12)]/\n[(x-3)(x+3)*(x^2+7x-4x-28)]=\n\n[(x(x-4)-(x-4))*(x(x+4+3(x+4)]/\n[(x-3)(x+3)*(x(x+7)-4(x+7)]=\n\n[(x-4)(x-1)*(x+4)(x+3)]/\n[(x-3)(x+3)*(x+7)*(x-4)]=\n\n[(x-1)(x+4)]/[(x-3)(x+7)]
897641
8-3x=4x-12+6\n-7x=-14\nx=2
562954
You simply divide each term in the polynomial by that integer.. For your example here it goes..\n\n(3x^2+8x-2) divided by 2 \n\n> {3(x^2)/2} + {8x/2} - {2/2}\n\n>> Answer: 1.5 x^2 + 4x -1    or   (3/2)x^2 + 4x -1
928231
8x-10x > -11-1\n\n-2x > -12\n\nx < 6
475786
Represent these binomials in Vector Notation to do the calculations. The Vector Space will be in 7 dimensions, So choose a 7 dim vestor to represent each polynomial.\n\nLet V1: 9x^5 -2x^3 +6x^2 + 3 \nLet V2: 5x^4 - 7x^2 + 6 \nLet V3: 3x^6 - 5x^5 -x^2\n\nMatix Vector Form for Vector 1=V1 etc..\nWe are in 7 space, so express our vector with (&) and seven\ndigits. Let V=V1+V2+V3\nV1= (0, 9, 0, -2, 6, 0, 3)\nV2= (0, 0, 5, 0, -7, 0, 6)\nV3= (3,-5, 0, 0, -1, 0, 0)\n\nV = (3, 4, 5, -2,-2, 0, 9)\nIn algebraic representation\nAns is:\n3x^6+ 4x^5 +5X^4 -2x^3 -2x^2 +9\n\n---\nVectors in 2 space, ex.\nV1=(x1, x2)\nV2=(y1, y2)\nV1+V2=(x1+y1, x2+y2)\nThat is what I did for the 7 space vector above. I expressed the 6 th degree binmial with a 7 dim vector,\nto make calcualting the answer faster. On paper, you could line up all of your equations so that each binomial eqs line up. All x^6 lined up under all x^6, all x^5 lined up under x^5,...etc. But using vectors makes this quicker and faster to calculate the binomials.\n\nMy sources: Two MS's in Mathematics that I received many, many years ago.
945218
[(x^2)^2]^2\n\n(x^2 -4x +4)^2\n\nmultiply      x^2  (x^2 -4x +4)^  = x^4 -4x^3 +4x^2\n\nmultiply     -4x (x^2 -4x +4)^    = -4x^3 +16x^2 -16x\n\nmultiply     4  (x^2 -4x +4)^      =  4x^2 -16x +16\n__________________________________________\n\nthe answer should be                 x^4 -8x^3 +24x^2 -32x +16\n\ni hope that helped
1106533
1) 6(x-4)(x-2)\n= 6(x^2 - 2x - 4x +8)\n= 6(x^2 - 6x + 8)\n= 6x^2 - 36x + 48\n\n2) (x+7)(x+4)-(x+3)(x+2)\n= (x^2 + 4x + 7x + 28) - (x^2 + 2x + 3x + 6)\n= (x^2 + 11x + 28) - (x^2 + 5x + 6)\n= x^2 + 11x + 28 - x^2 - 5x - 6\n= 6x + 22
11476
algebraic simplification\n\nx over 4+3 = 2x+3 over 5\nx / (4+3) = (2x+3) / 5\nx/7 = (2x+3)/5\n5x/7 = 2x+3\n9x/7 = -3\n\nx = -7/3
742127
= (x^12)/12 - (8x^11)/11 + (5x^10)/2 - (10x^9)/3 - (15x^8)/4 + 24x^7 - 49x^6 + 60x^5 - (195x^4)/4 + (80x^3)/3 - (19x^2)/2 + 2x + C
913334
x^2 + 2x + 7 Remainder 10\n\ni can add the steps if you don't think i did it by hand
321475
*(2x/(x^2-4)) + (5/2-x) - (1/2+x)\n*(2x/(x^2-4)) + (5/2-x)((2+x)/(2+x)) - (1/2+x)((2-x)/(2-x))\n*(2x/(x^2-4)) + (10+5x)/(4-x^2) - (2-x)/(4-x^2)\n*(2x/(x^2-4)) + (8+6x)/(4-x^2)\n\nyou should be able to get it from there
783870
7x^2+16x over (x-2)(x+2)(x+3)
352749
By the chain rule:\n[e^(3x^(2)-7x)]*(6x-7)
846794
2x/x^2 - 5x + 6 + 4/x - 2\n\nFirst we will simplify\n2x/x^2\n\nThe x on the top crosses out and the x^2 on the bottom becomes x.  We end up with 2/x.\n\n2/x - 5x + 6 + 4/x - 2\n\nNow we combine like terms.  All of the terms with just numbers will be added together.  Everything with something over x will be combined. \n\n(2/x + 4/x) - 5x + (6 - 2)\n\nWe have 6/x - 5x + 4\n\nNothing else can be combined so it is now in simplest form.
1053464
if you want to simplify it \n\nit is 3x - 4x + 4 = -x + 4