307. Let y be (-25)/m + 13/6. Factor -1/10*b**y + 0*b + 0.
-b**2/10
Let h(c) be the first derivative of c**5/12 + 5*c**4/6 - 25*c**3/6 + 98*c**2 - 87. Let o(x) be the second derivative of h(x). Solve o(r) = 0.
-5, 1
Let t(o) = 209*o**3 - o - 1. Let r be t(-1). Let d be r/(-133) - (-1)/7. Let 6/7 + d*f**3 - 10/7*f - 2/7*f**4 - 4/7*f**2 - 2/7*f**5 = 0. What is f?
-3, -1, 1
Let x(u) be the first derivative of 6*u + 2/3*u**3 - 4*u**2 - 1. Determine i, given that x(i) = 0.
1, 3
Let z(y) be the first derivative of 0*y - 1/180*y**5 + 1/24*y**4 - 4*y**2 + 5 - 1/9*y**3. Let f(u) be the second derivative of z(u). What is o in f(o) = 0?
1, 2
Let l(a) = -a**3 + 11*a**2 - 107*a - 686. Let u(m) = -4*m**3 + 32*m**2 - 324*m - 2058. Let k(s) = 20*l(s) - 6*u(s). Solve k(o) = 0 for o.
-7, 7
Let u be (-16555)/(-1419) + 1*-11. Let 0*h + 0 - u*h**4 + 4/3*h**3 + 2*h**2 = 0. What is h?
-1, 0, 3
Let r(d) be the second derivative of -d**7/126 + 74*d**6/45 - 937*d**5/10 + 2701*d**4/9 - 5329*d**3/18 - 29*d - 20. Solve r(z) = 0.
0, 1, 73
Let n = 225 - 223. Suppose -161 - 5*m**n + 100*m + 86 + 180 = 0. Calculate m.
-1, 21
Let v = -835507/4 - -208877. Determine u so that 0 + v*u**2 + 1/4*u**4 + 0*u + 1/2*u**3 = 0.
-1, 0
Let w = 1211220 - 6056094/5. Suppose -2/5*x**3 + w*x**2 + 0*x - 8/5 = 0. What is x?
-1, 2
Let x(w) = -8*w**5 - 8*w**4 - 4*w**3 + 57*w**2 - 37*w. Let y(i) = -i**5 + 2*i**4 - i**3 - i**2 + i. Let q(p) = -4*x(p) + 28*y(p). Suppose q(b) = 0. What is b?
-22, -2, 0, 1
Let z(s) be the second derivative of s**5/120 + 131*s**4/24 - s**3/36 - 131*s**2/4 + s - 866. Factor z(o).
(o - 1)*(o + 1)*(o + 393)/6
Let a be (-20)/(-1710)*38 + 172/45. Factor a*y - 64/15 - 4/3*y**2 + 2/15*y**3.
2*(y - 4)**2*(y - 2)/15
Let l = 244076 + -244040. Suppose -486 + l*m - 2/3*m**2 = 0. What is m?
27
Let j(g) be the third derivative of -5*g**7/42 + 377*g**6/24 + 205*g**5/4 + 395*g**4/24 - 385*g**3/3 - 2564*g**2. Suppose j(v) = 0. Calculate v.
-1, 2/5, 77
Suppose 0 = -12*w - 90 + 222. Suppose -12 + 1 = -w*l. Find k, given that -1/3*k**2 - 2/3*k + l = 0.
-3, 1
Suppose -p = 4*h - 20, 883*p + 139 = 33*h + 888*p. Solve -x - 1/3 - x**2 - 1/3*x**h = 0 for x.
-1
Let x be (102/110 + -1)*(-2420)/220. Determine o, given that -12/5*o**3 - 4/5*o**4 + 0 + x*o**5 + 4*o**2 - 8/5*o = 0.
-2, 0, 1
Let q be 602/5 - (32/10)/8. Suppose 41*f - 37*f = q. Factor 35*y**2 + 13*y - f + 13*y + 29*y.
5*(y + 2)*(7*y - 3)
Solve 4632/11*u - 7056/11 + 218/11*u**3 + 2204/11*u**2 + 2/11*u**4 = 0.
-98, -6, 1
Let s = 913513 - 913511. Determine h, given that -282/5*h**s + 2/5*h**3 + 13254/5*h - 207646/5 = 0.
47
Solve -3/5*w**5 - 498/5*w**3 + 1782/5 + 66/5*w**4 + 1728/5*w**2 - 567*w = 0.
2, 3, 11
Let s = -158863/357 + 445. Let i = s + 347/1785. Factor 4/5 + i*p**2 + p.
(p + 1)*(p + 4)/5
Let a(f) = f**5 - f**4 - 5*f**3 + 5*f**2 + 4*f - 1. Let w = -3450 + 3453. Let u(r) = -2 - 1 + 4. Let q(k) = w*u(k) - a(k). Suppose q(m) = 0. What is m?
-2, -1, 1, 2
Let a(p) be the second derivative of p**4/12 + 17*p**3 + 376*p**2 + 166*p. Factor a(w).
(w + 8)*(w + 94)
Let l = 946479/2 - 473239. Suppose 2*y**2 + 5/2*y + l*y**3 + 1 = 0. Calculate y.
-2, -1
Let k(m) be the third derivative of 0*m + 0 + 12*m**2 + 2/21*m**7 - 5/336*m**8 + 0*m**4 + 0*m**5 + 0*m**3 - 1/6*m**6. Solve k(w) = 0.
0, 2
Find w, given that 2/15*w**2 + 64/5 - 44/15*w = 0.
6, 16
Let b = -25736/23 - -77231/69. Let -b*u**2 - 169/3 - 26/3*u = 0. Calculate u.
-13
Let o(a) = -3*a**2 + 85*a - 35*a + 5*a**2. Let z(s) = -4*s**2 - 52*s. Let f(i) = -3*o(i) - 2*z(i). What is g in f(g) = 0?
0, 23
Suppose -11*v - 44*v = 10*v - 390. Factor -4*q**2 + v*q + 2/3*q**3 + 0.
2*q*(q - 3)**2/3
Let h be -27 + 16 + -5 + (-6 - (0 + -27)). Determine u so that -u**4 - 2*u + 11/3*u**2 + 7/3*u**3 - 1/3*u**h - 8/3 = 0.
-4, -1, 1, 2
Let x(p) be the first derivative of -p**7/210 + 17*p**6/90 - 46*p**3/3 + 21. Let c(b) be the third derivative of x(b). Factor c(l).
-4*l**2*(l - 17)
Let v be (-4)/(-140) - 92/(-420)*9. Solve -24/5*j**4 - 312/5*j - 114/5*j**3 - 2/5*j**5 - 144/5 - 268/5*j**v = 0 for j.
-3, -2
Let j(v) be the third derivative of -2645/4*v**4 + 1 + 0*v - 17/20*v**6 + 121*v**2 + 759/20*v**5 - 12167/4*v**3 + 1/140*v**7. Determine w, given that j(w) = 0.
-1, 23
Factor 64/5*g - 4/5*g**3 - 28/5*g**2 + 448/5.
-4*(g - 4)*(g + 4)*(g + 7)/5
Let j = -29449/10 - -2945. Let q(z) be the second derivative of 9/10*z**5 + 0 + 0*z**3 + 9/4*z**4 + 0*z**2 - 26*z + j*z**6. Determine y, given that q(y) = 0.
-3, 0
Let d(u) be the second derivative of 25*u**7/42 - 7*u**6 - 29*u**5/4 + 15*u**4/2 + 1379*u. What is v in d(v) = 0?
-1, 0, 2/5, 9
Suppose 346*z**4 - 3216 - 21258*z + 1705*z - 26559*z - 2*z**5 - 14438*z**3 + 12428*z**2 - 12272 - 57838*z**2 = 0. What is z?
-1, 88
Let p be (-1530)/(-357) + (-1)/7*2. Factor 2*x**3 - 2*x**p - 9391*x - 2*x**5 + 2*x**2 + 9391*x.
-2*x**2*(x - 1)*(x + 1)**2
Find k, given that 1/2*k**2 - 43/2*k - 22 = 0.
-1, 44
Factor -58/7*j**2 + 6 + 106/7*j + 6/7*j**3.
2*(j - 7)*(j - 3)*(3*j + 1)/7
Let n(h) be the first derivative of -h**5/300 - h**4/60 - 25*h**2/2 + h - 90. Let s(c) be the second derivative of n(c). Factor s(f).
-f*(f + 2)/5
Let t(w) = -w**3 - 2*w**2 + w + 1. Let n(r) = -10*r**3 - 635*r**2 - 2435*r - 2415. Let z(l) = n(l) - 5*t(l). Factor z(q).
-5*(q + 2)**2*(q + 121)
Let n be ((-2)/44)/((-4)/144). Let q(s) = 2*s**3 + 119*s**2 - 182*s + 65. Let m be q(-61). Let 10/11*k**3 + 14/11*k + n*k**2 + 4/11 + 2/11*k**m = 0. What is k?
-2, -1
Let x(v) = v**3 + v**2 + v + 1. Let d(p) = 7 + 6*p**3 + 16*p - p**2 + 2 - 3 + 17*p**2. Let u(k) = -d(k) + 3*x(k). Solve u(b) = 0 for b.
-3, -1, -1/3
Let k(x) be the first derivative of x**3/12 + 119*x**2/8 + 59*x/2 - 1427. Factor k(o).
(o + 1)*(o + 118)/4
Let h(g) be the first derivative of g**9/756 + g**8/140 - g**7/105 - 2*g**6/15 - 4*g**5/15 + 20*g**3 - 7. Let o(j) be the third derivative of h(j). Factor o(a).
4*a*(a - 2)*(a + 1)*(a + 2)**2
Let u(q) be the second derivative of 0*q**3 + 61 + 1/15*q**6 - q + 0*q**2 - 4/5*q**5 + 2*q**4. Factor u(j).
2*j**2*(j - 6)*(j - 2)
Suppose 58/9*w**2 - 8/9*w + 2/9*w**3 - 232/9 = 0. What is w?
-29, -2, 2
Factor 3/4*a**3 + 783 + 795/4*a**2 + 786*a.
3*(a + 2)**2*(a + 261)/4
Let f(w) be the first derivative of 2/39*w**3 - 237 + 10/13*w**2 + 0*w. Let f(r) = 0. Calculate r.
-10, 0
Suppose 46*x + 540 = 290 + 480. What is f in -8/3*f**4 + 14/3*f**3 - 2/3*f**x + 0 + 0*f + 20/3*f**2 = 0?
-5, -1, 0, 2
Factor -130/3 + 1/9*j**3 + 59/9*j + 22/3*j**2.
(j - 2)*(j + 3)*(j + 65)/9
Suppose -118 - 26 = 4*z. Let h be (-30)/z*(-24)/(-40). Factor 5/2*m + h*m**2 + 3.
(m + 2)*(m + 3)/2
Let q(t) be the third derivative of -t**5/120 + 19*t**4/12 - 37*t**3/3 + 3277*t**2. Determine j, given that q(j) = 0.
2, 74
Let h(a) be the third derivative of 3/4*a**3 + 0 + 3/320*a**6 - 25*a**2 + 1/16*a**4 - 19/160*a**5 + 2*a. Suppose h(q) = 0. What is q?
-2/3, 1, 6
Suppose 3*m - 4*g + 10 = 0, 0 = -0*m - 5*m + 4*g - 6. Let 1445 + 7*s**2 - 10*s - 2*s**m - 160*s = 0. What is s?
17
Let y = -846 - -1471. Suppose 630 = z + y. Find j such that 10/11*j**4 + 2/11*j**3 - 6/11*j**z + 4/11*j + 0 - 10/11*j**2 = 0.
-1, 0, 2/3, 1
Let i(u) = -9*u**2 - 6*u - 6. Suppose -153*m - 259 = -106. Let x(r) = -r**2 - 1. Let o be (4/(-3))/((-4)/18). Let s(g) = m*i(g) + o*x(g). Factor s(b).
3*b*(b + 2)
Factor 296/13*h**4 - 2/13*h**5 + 485000/13*h + 220300/13*h**2 - 14402/13*h**3 + 250000/13.
-2*(h - 50)**3*(h + 1)**2/13
Let t = 281/12 + -1393/60. Let w(j) be the first derivative of -t*j**3 + 0*j**2 + 1/20*j**4 + 12 + 0*j. Find p, given that w(p) = 0.
0, 3
Factor 31*b - 4*b + 10*b**2 + 91*b**3 - 92*b**3 - 46*b**2 + 49*b.
-b*(b - 2)*(b + 38)
Let t be -1*((-555)/60 + -14). Let b(v) = v**2 - 7*v + 9. Let x be b(6). Suppose -153/4*p**x - t*p**2 - 1/2 - 81/4*p**4 - 23/4*p = 0. Calculate p.
-1, -1/3, -2/9
Suppose -2*d + 8 = -m, 2 = 5*d + 2*m - 9. Factor -50*p**2 - 2*p**3 - 220*p - 40 - 80 + 17*p**d.
5*(p - 6)*(p + 2)*(3*p + 2)
Let j(o) be the second derivative of -8*o - 2 - 6*o**3 - 39/2*o**2 + 1/4*o**4. Factor j(y).
3*(y - 13)*(y + 1)
Let t = -24167709/259 + 653193/7. Let d = t + 12/259. Solve -12/7*y**3 + 3/7*y**4 + 0 + d*y**2 + 0*y = 0.
0, 2
Suppose -2*z = 2*p + 2, -4187*p + 4189*p = -4*z + 2. Factor 0 - 1/2*c - 5/2*c**z - 2*c**3.
-c*(c + 1)*(4*c + 1)/2
Let f(o) be the first derivative o