Add:9x^5 -2x^3 +6x^2 + 3 and 5x^4 - 7x^2 + 6 and 3x^6 - 5x^5 -x^2?
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.
772739
3(2x+3)+6=5(2x+3)\n6x+9+6=10x+15\n6x+15=10x+15\n15=4x+15\n30=4x\n30/4=x\n15/2=x or x=15/2
924177
FOIL out the first part of the expression and simplify:\n\n(x+3)^2 = x^2+6x+9\n\nTherefore, (x+3)^2-6 = x^2+6x+9-6 = x^2+6x+3\n\nTherefore using the general form, ax^2+bx+c, you can conclude that,\n\na=1, b=6, c=3\n\n----------------\n\nHope this helps
765513
do u mean 6x^2(-9x^3) = -54x^5\nmultiply the constants and add the exponents
531417
(a+b)(b^6-ab^5+a^2b^4-a^3b^3+a^4b^2-a^5b+a^6)\nGood Night, and Good Luck!
904822
Hello Dear Blue \n\n2x^3+8x^2 - 5x + 5 ÷ x-2\n\n▪ Step1\n( 2x^2 ) ( x-2 ) = 2x^3 - 4x^2 ; { let Q1 = 2x^2 }\n2x^3+8x^2 - 5x + 5 - ( 2x^3 - 4x^2 ) = \n2x^3+8x^2 - 5x + 5 - 2x^3 + 4x^2 = +12x^2 - 5x + 5 {remainder} \n\n▪ Step 2\n+12x^2 - 5x + 5 ÷ x - 2 \n(x - 2) (12x) = 12x^2 - 24x ; { let Q2 = +12x }\n+12x^2 - 5x + 5 - ( 12x^2 - 24x  ) =\n+12x^2 - 5x + 5 - 12x^2 + 24x = +19x +5 {remainder}\n\n▪ Step 3 \n19x +5 ÷ x -2\n(x -2) (+19) = +19x - 38; { let Q3 = +19}\n19x +5  - (+19x - 38) =\n19x +5  -19x + 38 = +43 {remainder}\n\n▪ Step 4\nSum Q1, Q2, Q3\nQ1 + Q2 + Q3\n2x^2 +12x +19\n\nSo;\n(2x^3+8x^2-5x+5) ÷ (x - 2)    = >\n\nQ(x) OR quotient = 2x^2 +12x +19 \nR(x) OR Remainder is + 43 \n\nGood Luck dear.
846363
3x² + 6 + 10 - (3x² - 8x - 5)\n\n3x² + 6x + 10 - 3x² + 8x + 5\n\n3x² - 3x² + 6x + 8x + 10 + 5\n\n0 + 14x + 15\n\n14x + 15\n\nThe answer is 14x + 15\n\n- - - - - - -s-
1024215
1^3 + 6^3 +8^3 = 9^3\n\n3^3+10^3+18^3 = 19^3\n4^3+17^3+22^3 = 25^3\nthere's a lot!!!
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.
142543
Polynomial= multiple terms, i.e. 3x^2+7x-3\nSo I suppose addition of them would be like\n(4x^2+7x-5)+(9x^2+9x+7+y)\n=4x^2+7x-5+9x^2+9x+7+y\n=13x^2+16x+2+y\nor\n(4x^2+7x-5)-(9x^2+9x+7+y)=\n(4x^2+7x-5)-1(9x^2+9x+7+y)=\n(4x^2+7x-5)+ (-1*(9x^2+9x+7+y))=\n(4x^2+7x-5)+(-9x^2-9x-7-y)=\n4x^2+7x-5-9x^2-9x-7-y=\n-5x^2-2x-12-y.\n\nMaybe now you can do your own.\nNote that these methods only work with adding/subtracting.
766061
p^9-q^9/p^6-q^6\n=(p^3-q^3)(p^6+p^3q^3+q^6)/(p^3+q^3)(p^3-q^3)\n=(p^6+p^3q^3+q^6)/(p^3+q^3)
780298
first u distribute the - to the stuff in the parenthesis so you have\n7x^2-3+x^2\nthen combine like terms\n8x^2-3
144536
6x^4 - 13x^3 - 9x^2 + 28x - 12
609345
The demoninator of the second term (x^2 + 7x + 6) can be factored to (x+6)(x+1), so multiply both sides by that value and watch the terms cancel out.  You get \n\n5(x+1) + 2 = 3(x+6)\n5x + 7 = 3x + 18\n2x = 11\nx = 5.5
786382
x^2-6x+9=3+9\n(x-3)^2=+/-rt12\nx-3=+/-2rt3\nx=3+/-2rt3\n\n2.2(x^2+5x)=-11\n2(x^2+5x+25/4-25/4)=-11\n2(x+5/2)^2-25/2=-22/2\n2(x+5/2)^2=3/2\n(x+5/2)^2=3/4\nx+5/2=+/-(rt3)/2\nx=-5/2+/-(rt3)/2\n=1/2[-5+/-rt3]
928591
x^2-6xy+8y^2\nx^2-6xy+9y^2-9y^2+8y^2\n(x-3y)^2-y^2\n(x-3y+y)(x-3y-y)\n(x-2y)(x-4y)\n\naliter\nx^2-4xy-2xy+8y^2\nx(x-4y)-2y(x-4y)\n(x-4y)(x-2y)
123892
3(x – 2)^2 – 3(x – 2) – 6\n3((x-2)^2 - (x-2) -2)\n3(x^2-4x+4-x+2-2)\n3(x^2-5x+4)\n\n3(x-4)(x-1)\n\nYay!!