-2/7, 0, 1
Let l(v) = 3*v**2 + 5*v - 47. Let q be l(6). Let 92*o**3 + 13*o**2 - q*o**3 - 17*o**2 = 0. Calculate o.
0, 4
Let d(c) be the first derivative of -1/4*c + 33/2*c**2 + 5324*c**4 - 484*c**3 - 160. Factor d(t).
(44*t - 1)**3/4
Factor 299/6*z**3 - 43/3*z**2 + 0*z + 0 + 7/6*z**4.
z**2*(z + 43)*(7*z - 2)/6
Let k = -63557 - -254303/4. Factor -27/4*c**2 + 45/4*c + k + 3/4*c**3.
3*(c - 5)**2*(c + 1)/4
Suppose 58*x - 13 - 181 = -78. Factor 31/3*n**x + 3/2*n + 17/2*n**3 - 1/3.
(n + 1)*(3*n + 1)*(17*n - 2)/6
Let n(q) = -186*q**3 + 208*q**2 + 8*q + 2. Let d(y) = -931*y**3 + 1054*y**2 + 42*y + 11. Let u(t) = -2*d(t) + 11*n(t). Find a such that u(a) = 0.
-1/46, 0, 1
Let j(p) = -11*p**2 + 469*p + 3024. Let v(u) = -u**2 - u - 1. Let w(q) = j(q) - 6*v(q). Factor w(b).
-5*(b - 101)*(b + 6)
Let l(r) = 2*r - 2. Let m(c) = -44*c - 6. Let n(q) = l(q) - m(q). Let k be n(0). Factor -16/5*t - 19/5*t**3 + 4/5 - 1/5*t**5 + 7/5*t**k + 5*t**2.
-(t - 2)**2*(t - 1)**3/5
Let i(t) be the second derivative of -13*t**6/120 + 27*t**5/40 - 73*t**4/48 + 3*t**3/2 - t**2/2 + 428*t. Suppose i(h) = 0. What is h?
2/13, 1, 2
Let z be (-17)/(102/(-36)) + -1. Let w(q) = -q**2 + 1. Let c(b) = -7*b**2 - 9*b - 12. Let u(f) = z*c(f) - 30*w(f). Factor u(h).
-5*(h + 3)*(h + 6)
Let u be (-50)/(-8) + (-4)/16. Suppose -4*h + u = 3*w - 11, 2*h + 5 = 3*w. Suppose 4*q - 7*q + 13*q**2 + q**3 - 13*q**h - 2 = 0. Calculate q.
-1, 2
Let j(i) = -29*i + 207. Let x be j(7). Let g be x/3 + 30/45. Factor -14/13*o**g - 10/13*o**3 - 4/13*o + 0.
-2*o*(o + 1)*(5*o + 2)/13
What is i in 2953*i**2 + 583696 - 18*i**3 + 107*i**2 - 3*i**3 - 586752*i + 17*i**3 = 0?
1, 382
Let x(o) = 22 - 56*o**3 + 3*o + 23*o**3 + 32*o**3 + 5*o**2. Let z be x(6). Factor -50*p + 62*p + 4*p**5 - 16*p**3 - 4*p**2 - 4*p**2 + 8*p**z.
4*p*(p - 1)**2*(p + 1)*(p + 3)
Let z(h) be the second derivative of -h**4/6 - 76*h**3/3 - 715*h**2 + 6785*h. Factor z(n).
-2*(n + 11)*(n + 65)
Let k(b) = b**3 - 14*b**2 + 16*b - 30. Let s be k(13). Solve -5*o + 2*o**3 - 18*o**5 - 7*o**4 + 10 + 6*o**2 - s + 21*o**5 = 0.
-1, 1/3, 1
Let d(v) be the third derivative of -2*v**7/735 + 3*v**6/35 - 121*v**5/105 + 60*v**4/7 - 800*v**3/21 - 2880*v**2. Factor d(f).
-4*(f - 5)**2*(f - 4)**2/7
Let v(f) = 3*f**4 + 62*f**3 - 1013*f**2 - 2512*f + 3468. Let q(d) = -8*d**4 - 187*d**3 + 3040*d**2 + 7537*d - 10404. Let j(o) = 4*q(o) + 11*v(o). Factor j(l).
(l - 34)**2*(l - 1)*(l + 3)
Suppose -503*y - 30 = -505*y - 3*k, -5*y - 3*k + 39 = 0. What is o in 2 - 4*o + o**y + 3/2*o**2 - 1/2*o**4 = 0?
-2, 1, 2
Let q be (-100)/(-1000)*(8 + -6). Factor 1/5*y**4 + 0 + q*y**5 - 3/5*y**3 - y**2 - 2/5*y.
y*(y - 2)*(y + 1)**3/5
Let f = -2284 + 2286. Let n = -263/165 + 19/11. Factor n*y**f + 0 + 2/15*y.
2*y*(y + 1)/15
Let v = 1368 - 754. Factor 606*p**2 - 4*p**3 + 2*p - 6*p - v*p**2.
-4*p*(p + 1)**2
Let a = -68 - -92. Factor -29*q + 47*q - q**2 - a*q.
-q*(q + 6)
Let k(p) be the second derivative of -p**6/120 - 9*p**5/20 - 81*p**4/8 - p**3/3 + p**2 + 184*p + 1. Let v(r) be the second derivative of k(r). Factor v(y).
-3*(y + 9)**2
Let p = 515 + -487. Determine u, given that p*u**3 + 95 + 604*u - 312*u - 351*u**2 - 89*u**2 + 25 = 0.
-2/7, 1, 15
Let z(u) be the second derivative of 2/9*u**3 + 1/72*u**4 - 3*u + 7/12*u**2 + 0. Factor z(d).
(d + 1)*(d + 7)/6
Let d = 231406 - 1154158/5. Factor 686/5*j**4 + d*j + 272/5 + 10164/5*j**2 + 2450*j**3.
2*(j + 17)*(7*j + 2)**3/5
Factor -72 - 3/7*q**2 - 177/7*q.
-3*(q + 3)*(q + 56)/7
Let u = 142592 - 570319/4. Find c such that 7/2*c + u + 1/4*c**2 = 0.
-7
Let g be 2/(-11) + (-4155)/(-165). Find u, given that g*u**2 - 24*u**4 - 4*u**5 - 32*u**3 + 10*u**2 + 111 + 17 + 192*u + 29*u**2 = 0.
-2, 2
Suppose 777*z - 786*z = 0. Factor 6/7*n**3 + z*n + 0 + 2/7*n**4 + 4/7*n**2.
2*n**2*(n + 1)*(n + 2)/7
Let x = 153122/319 + -480. Let b = x - -949/1276. Factor -b - 3*s - 9/4*s**2.
-3*(s + 1)*(3*s + 1)/4
Let n(p) be the second derivative of -60*p + 0 + 0*p**3 - 1/42*p**4 + 0*p**2. Factor n(f).
-2*f**2/7
Suppose 0 = -25*v - 11 + 111. Let m(f) = f**2 + 16*f + 17. Let n be m(-15). Factor -14*l**n - 727*l**4 + 5*l - l + 733*l**4 + v*l**3.
2*l*(l - 1)*(l + 2)*(3*l - 1)
Let i be (-41 + 1)/(6/(-18)*3). Find k, given that 1510*k**3 + 390*k**2 + i - 248*k + 75*k**5 - 1715*k**3 - 80*k**4 + 28*k = 0.
-2, 2/5, 2/3, 1
Let y(r) be the first derivative of r**3/3 - 353*r**2/2 - 354*r - 8486. Factor y(k).
(k - 354)*(k + 1)
Let w(b) = 68*b - 1085. Let n be w(16). Let j(u) be the first derivative of 2 + 0*u - 2*u**4 - 4/5*u**5 + 4/3*u**n + 4*u**2. Solve j(l) = 0 for l.
-2, -1, 0, 1
Determine a, given that 0 + 2/5*a**3 + 392/5*a**2 + 776/5*a = 0.
-194, -2, 0
Let l(b) be the first derivative of -b**7/504 + b**6/24 - 5*b**5/18 + 57*b**3 + 26. Let s(y) be the third derivative of l(y). Suppose s(u) = 0. What is u?
0, 4, 5
Let u = -1032935/8 - -129117. Factor u*k - 9/8*k**3 - 1/2*k**5 + 0 - 1/8*k**2 - 11/8*k**4.
-k*(k + 1)**3*(4*k - 1)/8
Let t(y) = 16*y**2 - 714*y - 714. Let z(m) = -38*m**2 + 1429*m + 1427. Let h(l) = -5*t(l) - 2*z(l). Factor h(j).
-4*(j - 179)*(j + 1)
Let b be ((-720)/(-70))/12 + 5232/21. Let v(h) be the first derivative of -1/2*h**4 - 75*h**2 - 10*h**3 + 5 - b*h. Let v(o) = 0. What is o?
-5
Let k(l) be the third derivative of -l**8/252 + 44*l**7/105 + 37*l**6/15 - 1052*l**5/45 + 131*l**4/2 - 92*l**3 - 2*l**2 + 585*l. What is f in k(f) = 0?
-6, 1, 69
Let u be (1/4 - 0) + (-92)/(-16). Let 26*g**4 - 95*g**2 - 15*g - 2*g**3 - u*g**4 - g**3 + 90 + 3*g**3 = 0. Calculate g.
-3/2, 1, 2
Suppose -z = -680*h + 683*h - 12, 4*z = 5*h - 20. Factor -2/3*b**3 - 14/3*b**2 + z - 8*b.
-2*b*(b + 3)*(b + 4)/3
Suppose 2*m = 2*a - 46, -14*a + 2*m + 28 = -13*a. Suppose 25*q = 32 + a. Factor 0 + 2/3*h**q + 4/3*h.
2*h*(h + 2)/3
Let w(f) = 155*f**4 - 155*f**3 - 420*f**2 + 365*f + 305. Let a(d) = -11*d**4 + 11*d**3 + 30*d**2 - 26*d - 22. Let p(y) = -85*a(y) - 6*w(y). Factor p(v).
5*(v - 2)**2*(v + 1)*(v + 2)
Let n be (-25090)/2316 - 1*-12. Suppose -m - 4*j = 14, -5*m - 3*j + 0 = 2. Factor -1/6*r**m + n - r.
-(r - 1)*(r + 7)/6
Suppose -4312/5 + 1428/5*x - 144/5*x**2 + 4/5*x**3 = 0. Calculate x.
7, 22
Find q such that -50*q**4 - 22*q**5 - 252 + 294*q**2 + 186*q**3 + 17*q**5 - 189*q + 8*q**5 + 9 - q**4 = 0.
-1, 1, 9
Let d = -11373 + 955333/84. Let b(f) be the third derivative of -1/5*f**5 + 41*f**2 + 0*f + 0*f**4 + d*f**8 - 2/105*f**7 - 1/6*f**6 + 0 + 0*f**3. Factor b(c).
4*c**2*(c - 3)*(c + 1)**2
Let m(w) = -w**3 - 30*w**2 - 2*w + 3. Let z be m(-30). Factor z - 132*a - a**3 + 133 + 6*a**2 + 23*a**2 - 92*a.
-(a - 14)**2*(a - 1)
Let f = 439 + -346. Suppose 105 + f = 22*c. Factor -3/2*b**2 - 12 - c*b.
-3*(b + 2)*(b + 4)/2
Let a be 9530/56 - 1 - (-15)/(-35). Suppose -4*r + 2*r + 4*w + 14 = 0, 3*w = -r - 3. What is p in -a*p**r - 3*p + 0 + 45*p**2 = 0?
0, 2/15
Let f be 12 - (-2)/48*-285. Let c(a) be the first derivative of 0*a - 1/3*a**3 + 1/4*a**2 - 9 + f*a**4. Factor c(n).
n*(n - 1)**2/2
Let v(u) be the third derivative of u**7/105 + 17*u**6/20 - u**5/10 - 151*u**4/12 + 34*u**3 - 388*u**2 + 1. Factor v(c).
2*(c - 1)**2*(c + 2)*(c + 51)
Let s(f) be the first derivative of f**6/80 + 7*f**5/40 + 11*f**4/16 + 5*f**3/4 + 4*f**2 + 4*f + 69. Let z(v) be the second derivative of s(v). Factor z(w).
3*(w + 1)**2*(w + 5)/2
Let b(r) be the first derivative of r**4/5 + 36*r**3/5 + 462*r**2/5 + 484*r - 394. Factor b(v).
4*(v + 5)*(v + 11)**2/5
Let f(l) = 8*l**3 - 1244*l**2 + 2152*l - 1124. Let w(k) = k**3 - 139*k**2 + 239*k - 125. Let o(c) = 6*f(c) - 52*w(c). Factor o(n).
-4*(n - 1)**2*(n + 61)
Let v(c) be the first derivative of -42 + 1/2*c**2 + 3/4*c + 1/12*c**3. Factor v(t).
(t + 1)*(t + 3)/4
Let t(x) be the third derivative of -x**5/330 + 109*x**4/33 - 433*x**3/11 - 2*x**2 - 5579*x. Factor t(d).
-2*(d - 433)*(d - 3)/11
Let l(a) be the third derivative of a**8/23520 - a**7/8820 - 8*a**4/3 + 69*a**2. Let w(f) be the second derivative of l(f). Factor w(q).
2*q**2*(q - 1)/7
Let d be -3 - ((-20)/(-30))/((-6)/(-30) - 286/930). Let -2/5*q**5 + 68/5*q**2 - 46/5*q - 48/5*q**3 + 12/5 + d*q**4 = 0. Calculate q.
1, 2, 3
Let p(w) be the first derivative of -w**6/120 - 3*w**5/40 - w**4/4 + 21*w**3 - 7. Let l(a) be the third derivative of p(a). Determine x, given that l(x) = 0.
-2, -1
Let w = -1546 - -2326. Determine q so that -