9x^5 -2x^3 +6x^2 + 3 and 5x^4 - 7x^2 + 6 and 3x^6 - 5x^5 -x^2\nPlease show your work and explain how you got your answer.
215985
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.
377642
(x³ + 4x²y + 2xy² + 3y³) - (5xy² -2y³ + 6x²y)\nx³ + 4x²y + 2xy² + 3y³ - 5xy² + 2y³ - 6x²y\nx³ + 4x²y - 6x²y + 2xy² - 5xy² + 3y³ + 2y³\nx³ + (4-6)x²y + (2-5)xy² + (3+2)y³\nx³ - 2x²y - 3xy² + 5y³
563868
3x^2-4x-4\n=3x^2-6x+2x-4\n=[3x+2][x-2]\n\n16x^2+56x+49\n=[4x]^2+7^2+2*7*4x\n=[4x+7]^2\n\n6x^2+13x-5=0\n6x^2-15x+2x-5=0\n[3x+1][2x-5]=0\nx=[-1/3],[5/2]
415430
(x+3)(x^2+2x+4)\n\nStart by taking the first term in the first parenthesis and multiplying it by each term in the second parenthesis:\n\nx*x^2 + x*2x + x*4 = x^3 + 2x^2 + 4x\n\nNow take the second term and multiply it by each term in the second parenthesis:\n\n3*x^2 + 3*2x + 3*4 = 3x^2 + 6x +12\n\nNow add all of that together\n\nx^3 + 2x^2 + 4x + 3x^2 + 6x +12\n\nand combine terms\n\nx^3 + 5x^2 + 10x +12
308477
I'm guessing you meant 17x^3 - 10x^2 - 6x +4 and 2x^2- 6x +2\nIf that's right, you just add like powers of x and their coefficients to get 17x^3 - 8x^2 -12x +6.
68825
(4x^2 + x + 3 ) + ( 5x^2 + 9x - 2 )\n= 4x^2 + x + 3 + 5x^2 + 9x - 2 \n= (4x^2 + 5x^2) + (x + 9x) + (3 - 2)\n= 9x^2 + 10x + 1\n= 9x^2 + 9x + x + 1\n= (9x^2 + 9x) + (x + 1)\n= 9x(x + 1) + 1(x + 1)\n= (9x+1)(x+1)\nx = -1/9 or -1\n\nEDIT: Since this is an expression, the answer is  (9x+1)(x+1). If this was an equation, the answer would be \nx = -1/9 or -1.
121920
8+9+6+(1+2+3+4+5+7)^0 = 24\n\nX^(0) = 1
456503
g(x) = x^5+5x^4+10x^3+10x^2+5x+1 = (x+1)^5\n`
556365
2x-5=6+4x\n2x-5+5=5+6+4x\n2x=11+4x\n2x-4x=11+4x-4x\n-2x=11\n-2x/-2=11/-2\nx=-5.5
505619
1.  ax + xb\n2.  21x^3 + 24x*2y\n3.  24x^2 + 31x + 10\n4.  24x^2 - 8x - 6\n5.  40x^3 + 66x^2 + 38x + 6\n6.  x^2 - 1\n7.  x^3 - 8
231686
It has been a long time, here are suggestions:\n1. 5x^3 + 11x^2 + 3x + 1  \n2. 4x^3 - 13x^2 - 8x + 7 \n3. 2x^4 - x^3\n4. 21x^2 + 26 x + 8
506271
2xy(-15x^2y^4)+8x^2)-5/-4xy^3\n(-1/2)[-15x^2y^4+8x^2-5)/y^2\n(-1/2y^2)[-15x^2y^4+8x^2-5]
628042
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
442605
.more kids homework... factoring?\n1. rewrite the middle term as the sum of two terms and then factor completely 15x^2 -21x +6\n\n3(5x^2-7x+2)\n3(5x^2-5x-2x+2)\n3(5x-2)(x-1)\n\n2. rewrite the middle term as the sum of two terms and then facto by grouping. x^2 - 14x +45 \n\nx^2-9x-5x+45\n(x-9)(x-5)\n\n3. rerewrite the middle term as the sum of two terms and then facto by grouping x^2 + 19x +90\n\nx^2-10x+9x+90\n(x+10)(x+9)\n\n4. rewrite the middle term as the sum of two terms and then facto by grouping x^2 -2x -63\n\nx^2-9x+7x-63\n(x-9)(x+7)\n\n5.solve x^2 = -6x\n\nx=-6
435310
I prefer "long" multiplication but it doesn't line up as well...\n\n3x^2 + 7x - 6\n* _____x+12\n--------------------  Multiplying term by term\n_____36x^2 + 84X - 72\n3x^3 + 7x^2 - 6x\n--------------------------------  Add term by term\n3x^3 + 43x^2 + 78x - 72   <--  final answer
409208
ill give it a shot - im not sure , anyways i got 2 answers..\n\n(1st)\n\n(3-x)x+2 = 2 (x^2-2)\n\n3x-x^2+6-2x = 2x^2-4\n\nx-x^2+6 = 2x^2-4\n\nx-1/x+6 = 2/x-4\n\nx-1+6x = 2-4x\n\nx+4x+6x = 2+1\n\n11x = 3\n\nx = 3/11\n\n\n(2nd possible answer)\n\n\n(3-x)x+2 = 2 (x^2-2)\n\n3x-x^2+6-2x = 2x^2-4\n\nx-x^2+6 = 2x^2-4\n\nx-1/x+6 = 2/x-4\n\nx-1+6/x = 2-4/x\n\n-5 = -2/x\n\n-5x = -2\n\nx = -2+5\n\nx = 3
188908
(3x^3-7x^2+x-20)/(x-3) = 3x^2+2x+7 with a remainder of 1\n         \n         3x^2+2x+7 \n     _______________\nx-3 | 3x^3-7x^2+ x-20\n      -3x^3+9x^2\n    __________\n          2x^2+ x\n         -2x^2+6x\n         ________\n              7x - 20\n             -7x + 21\n             ________\n                   1\n\nI tried to show what this would look like as a division problem but it keeps jumbling up.