How do you factor 24x^2 + 4x - 21?
918752
It is not factorable in integers.  The roots of the quadratic ax^2 + bx + c are found by the formula x = (-b +- sqrt(b^2 - 4ac) / 2a, which for this quadratic simplifies to (-1 +- sqrt(127)) / 12.\n\nFor the quadratic to be factorable in integers, the roots need to be either integers, or nice fractions.  For example, if one root was exactly 3/7, the quadratic would have the factor (7x - 3).  This will only happen if (b^2 - 4ac) is a perfect square.  But the roots of this quadratic are IRRATIONAL, because of sqrt(127) - or sqrt(2032) before simplifying, as noted by a previous answerer.  Their values are 0.85578564 and -1.022452306.
718313
4w - 24 = 3w + 3 (multiplying out the brackets)\n4w-3w = 24 + 3 (moving the 'w's and numbers to seperate sides)\n\ntherefore we are left with\nw = 27\n\nAnd to check\n4(27-6) = 4(21) = 84 = 3(27 + 1) = 3*28 = 84
740569
1) L = 4W\nA = LW = 20\nSubstitute L = 4W to get 20 = 4W x W\n20 = 4W^2, divide both sides by 4 to get\n5 = W^2, take square root of both sides to get W\nW = √5\n\n20 = L x W\n20 = L x √5, divide both sides by √5 to get L\nL = 20/√5 or, when rationalized, 4√5\nFinal answer:\nL = 4√5 and W = √5\n\n----\n\n2) L = W + 4\nA = 6 = L x W, substitute L = W + 4 to get\n6 = (W + 4) x W\n6 = W^2 + 4W, substract 6 from both sides to get\n0 = W^2 + 4W - 6\nThis is not easily factored, so you'd have to use the quadratic equation to solve for W. Once you have W, just plug that in to L = W +4 to get the L value. Good luck!
588758
a.  ax + bx\nb.  21x^3 + 24x^2y\nc.  24x^2 + 31x + 10\nd.  24x^2 - 8x - 6\ne.  40x^3 + 66x^2 + 38x + 6  (I assumed that you meant 7x in the first half of the equation.  If not, this is not correct.)\nf.  x^2 -1\ng.  x^3 - 8
669578
I have corrected the expression. Well here I redo the factorization\n\nThe given expresion \n= 12x^3+60x^2y+75xy^2\n= 3x(4x^2+20xy+25y^2)\n= 3x[(2x)^2+2(2x)(5y)+(5y)^2]\n= 3x(2x+5y)^2
205892
n! =n*n-1*n-2...until you get to zero.\n\nso 4! equals 4*3*2*1\nwhich is 24
259003
Use the quadratic formula.  It works everytime!\nx = (-b plus or minus sprt(b^2 - 4ac))/2\nwhere\nax^2 + bx + c = 0\nSome of these will factor, however not all of them will.
932672
Add 20 to both sides to get a zero on the products side\n6x^2 + 19x - 10 + 20 = -20 + 20\n6x^2 + 19x  + 10 = 0\nTo factor it the basic formula is:\n(_x + _)(_x + _)\n\nNow you need to figure out the factors\nTo get six your possible factors are 1 and 6 or 2 and 3\nTo get ten your possible factors are 1 and 10, or 2 and 5\n\nTo get the middle term of 19x you'll need to play around with the numbers and orders until when you FOIL it to check yourself you get 6x^2 + 19x  + 10 = 0\n\nIt just so happens to be\n(3x + 2)(2x + 5) = 0\nAnd to check yourself:\n6x^2 + 2(2x) + 5(3x) + 10 = 0 --> 6x^2 + 4x + 15x + 10 = 0 --> 6x^2 + 19x + 10 = 0\n\nOkay now lets simplify it to find the x values\n3x +2 = 0 --> 3x = -2 --> x = -2/3\n2x + 5 = 0 --> 2x = - 5 --> x = -5/2 --> x = -2.5\nSo x can be -2/3 and - 2.5
149556
4x^3+36x^2+32x----using common factor which in this case would be 4x so, 4x(x^2+9x+8) and then u use guessing method \nand the complete factorization would be 4x(x+8)(x+1).
98369
(8+2x6)=8+12=20\n(24-20)=4\n3x4=12\n100-12+12=100\n\nYou have to calculate the inner bracket first, then the other brackets. x and / comes before + and -
729543
-24+w+8=4\n-24+24+w+8-8=4+24-8\nw=20\n\nhope this helps!
1040147
I'm guessing you mean 21/24 = x / 8\nthat's 7/8 in lowest terms\n\nx = 7
563831
4! + 4! + 4/4 =49\n\n4!= factorial(4) =24
729005
a.xa+xb\nb.21x^3+24x^2y\nc.3x(8x+5)+2(8x+5)\n=24x^2+15x+16x+10\n=24x^2+31x+10\nd.4x(2x+1)-6(2x+1)\n=8x^2+4x-12x-6\n=8x^2-8x-6\ne.8x(5x^2+7x+3)+2(5x^2+7x+3)\n=40x^3+56x^2+24x+10x^2+14x+6\n=40x^3+66x^2+38x+6\nf.x^2-1\ng.x(x^2+2x+4)-2(x^2+2x+4)\n=x^3+2x^2+4x-2x^2-4x-8\n=x^3-8
699210
Just plug in the numbers and solve for s...\ns=6^2-4^2\n    -----------\n       2(2)\ns=36-16\n     -------\n         4\n\ns=20/4\ns=5
530154
48x - 24x = (48-24)x = 24x\n48x+-13+-24x=131\n24x - 13 = 131\nAdd 13 to each side\n24x = 144\nDivide by 24\nx = 144/24\nx = 6
796585
1.factor\n(2x+1)(x-4)=0\n2.set it to 0\n2x+1=0\nor\nx-4=0\n3.solve\n{x=-1/2 or x=4} <=answer