 + 10781783/126269676. Let p = d + 3/767. Determine b, given that p*b**2 - 2/9*b - 1/3 = 0.
-1, 3
Let z(q) be the third derivative of q**6/120 + 323*q**5/5 + 208658*q**4 + 1078344544*q**3/3 + 3680*q**2. Find t, given that z(t) = 0.
-1292
Let b(n) be the first derivative of -136*n**2 + 56*n**3 + 160*n + 4/5*n**5 + 85 - 11*n**4. Determine d, given that b(d) = 0.
2, 5
Let l = -6/5321 + 10672/26605. Factor -76/5*h - 722/5 - l*h**2.
-2*(h + 19)**2/5
Determine u so that -63/5 - 30*u - 1/5*u**4 - 26/5*u**3 - 112/5*u**2 = 0.
-21, -3, -1
Suppose -7*d - 5*c + 29 = -4*d, 2*d + 4*c - 20 = 0. Suppose 7*r - 2*r - o = 12, 4*o = -d. Factor 1/3*n**3 + 7/3*n - 1 - 5/3*n**r.
(n - 3)*(n - 1)**2/3
Suppose 1838*m + 10820 = 4543*m. Factor 25/3*k**m - 23/3*k + 29/3*k**3 + 2*k**5 - k**2 - 10/3.
(k + 1)**3*(k + 2)*(6*k - 5)/3
Let c(s) = s**3 - 29*s**2 - 6*s + 51. Let n be c(31). Let v = -1785 + n. Factor -16*k**3 - 136/5*k**v - 9/5 - 69/5*k.
-(4*k + 3)**2*(5*k + 1)/5
Determine f so that -6960*f**2 + 788 - 652*f + 1001 + 2442*f + 6961*f**2 = 0.
-1789, -1
Let d(h) = 3*h**4 + 144*h**3 + 933*h**2 - 15720*h + 26250. Let t(o) = -3*o**4 - 143*o**3 - 932*o**2 + 15692*o - 26249. Let y(q) = -5*d(q) - 6*t(q). Factor y(r).
3*(r - 6)*(r - 2)*(r + 27)**2
Factor -76*w - 35 + 6*w**2 - 4*w**3 + 32*w**2 - 85 + 10*w**2 - 8*w**2.
-4*(w - 6)*(w - 5)*(w + 1)
Let x(j) be the second derivative of -2/9*j**3 + 0*j**2 + 2*j + 7/18*j**4 - 3/10*j**5 + 1/9*j**6 - 1/63*j**7 - 2. Factor x(b).
-2*b*(b - 2)*(b - 1)**3/3
Let s(q) be the third derivative of q**6/320 - 11*q**5/160 + 3*q**4/8 - 860*q**2. Factor s(w).
3*w*(w - 8)*(w - 3)/8
Let k(v) be the first derivative of 1/2*v**4 + 47*v**2 + 10*v**3 + 66*v - 133. Factor k(p).
2*(p + 1)*(p + 3)*(p + 11)
Factor 1/3*q**2 - 53*q + 314/3.
(q - 157)*(q - 2)/3
Let r(z) be the second derivative of -4/3*z**6 + 2/21*z**7 + 36/5*z**5 + 71*z - 18*z**4 + 18*z**3 + 0*z**2 + 0. Factor r(k).
4*k*(k - 3)**3*(k - 1)
Let h(g) be the second derivative of 81*g**6/40 + 513*g**5/20 + 541*g**4/4 + 380*g**3 + 600*g**2 + 139*g - 5. Find a such that h(a) = 0.
-20/9, -2
Let g(t) be the first derivative of -2*t**4 + 22*t**3/3 + 16*t**2 - 88*t - 8392. Find w such that g(w) = 0.
-2, 2, 11/4
Let y be 256/(-1040) + (1104/120)/23. Find o, given that 36/13 - y*o**2 - 6/13*o = 0.
-6, 3
Let j be ((-432)/75 - -6)/((-54)/(-990)). Solve -12 - 2/5*r**2 - j*r = 0.
-6, -5
Let s be (8/7)/(-38 + (-2840)/(-70)). Factor 1/9*n**5 + 2/3*n**3 + 1/9*n - s*n**4 - 4/9*n**2 + 0.
n*(n - 1)**4/9
Let -537*a - 1/2*a**2 - 288369/2 = 0. What is a?
-537
Let n(p) be the third derivative of 2*p**6/45 + p**5/5 + p**4/3 + 2*p**3/9 + 941*p**2 + p - 2. Let n(l) = 0. What is l?
-1, -1/4
Suppose 995 + 92*n - 778 - 1177 - 2*n**2 = 0. What is n?
16, 30
Let j(o) be the first derivative of -o**4/24 + 4*o**3/9 - 17*o**2/12 + 5*o/3 + 3745. Find n, given that j(n) = 0.
1, 2, 5
Let n(y) be the first derivative of 6*y**4 - y**3 - 3*y**2/2 + 32*y + 58. Let d(r) be the first derivative of n(r). Solve d(b) = 0.
-1/6, 1/4
Suppose -y + 318 = 2*b + 3*y, 4*b - 2*y - 626 = 0. Let q = b - 141. Let -585*r + 200*r**2 + 0*r**3 + 405 - 4*r**3 - q*r**3 = 0. Calculate r.
1, 9/2
Factor -37/2 - 1/4*w**2 + 75/4*w.
-(w - 74)*(w - 1)/4
Let i(k) be the first derivative of -4*k**3/3 + 38*k**2 + 5264*k + 11109. Factor i(b).
-4*(b - 47)*(b + 28)
Let t(a) = 4*a - 38. Suppose 4 = 4*v - 4, -2*l + 16 = -2*v. Let h be t(l). Solve -7*o + 4*o**3 + o + 2*o - 2*o**2 - 2*o**h + 4*o**4 = 0 for o.
-1, 0, 1
Suppose 2*a - 3*o - 9 = -18, -2 = a - o. Suppose 12*t = 13*t - 3*z + 7, 12 = a*t + 2*z. Let -2/5*b**3 + 0 + 6/5*b**t + 0*b = 0. What is b?
0, 3
Let p(d) = -31*d**2 + 789*d - 51. Let l(h) = 11*h**2 - 262*h + 18. Let n(r) = -17*l(r) - 6*p(r). Factor n(b).
-b*(b + 280)
Let x(f) be the second derivative of f**6/80 + f**5/20 - f**4/4 + 32*f**3/3 + 76*f. Let h(j) be the second derivative of x(j). Factor h(d).
3*(d + 2)*(3*d - 2)/2
Let o(f) be the second derivative of -f**5/40 + 29*f**4/24 - 23*f**3/2 - 623*f. Factor o(u).
-u*(u - 23)*(u - 6)/2
Let r(l) be the second derivative of -2*l**6/15 - 36*l**5/5 + 76*l**4/3 - 102*l + 2. What is z in r(z) = 0?
-38, 0, 2
Let q = 1360273/100 - 13603. Let l = 12/25 - q. Factor 21/4*z + 9*z**2 + l.
3*(3*z + 1)*(4*z + 1)/4
Let l be ((-1200)/76 - -16)/(2/(-4)). Let i = l + 328/57. Factor -4/3 - 7/3*m**2 + i*m.
-(m - 2)*(7*m - 2)/3
Let q(a) be the third derivative of -4 - 3/25*a**5 - 9/5*a**3 - 3/5*a**4 - 7*a**2 + 0*a - 1/1575*a**7 - 1/75*a**6. Find v, given that q(v) = 0.
-3
Let d = 3/131816 - -14236113/659080. Factor -2/5*f**4 - d*f**3 - 2808/5*f - 1352/5 - 1562/5*f**2.
-2*(f + 1)**2*(f + 26)**2/5
Let f be 147/(-945)*3/(-8). Let x(n) be the third derivative of 1/300*n**5 + 0*n - f*n**4 + 13*n**2 + 1/5*n**3 + 0. What is p in x(p) = 0?
1, 6
Suppose -q + 98 = 2*q - l, 2*q - 2*l = 60. Let z(a) be the first derivative of q + 12*a**2 + a**3 - 51 - 19 + 36*a. Suppose z(n) = 0. What is n?
-6, -2
Let m = 1829 - 1827. Factor -4/7*o**3 + 0 + 2/7*o - 8/7*o**4 + 8/21*o**m - 10/21*o**5.
-2*o*(o + 1)**3*(5*o - 3)/21
Let c(k) be the second derivative of 5/54*k**4 + 0 + 68*k - 1/90*k**5 + 0*k**2 + 14/27*k**3. Factor c(g).
-2*g*(g - 7)*(g + 2)/9
Factor 273529/3*k + 0 - 1046/3*k**2 + 1/3*k**3.
k*(k - 523)**2/3
Find h, given that 20*h**2 + 107*h**3 - 134*h**3 + 11*h**3 + 4*h**4 - 8*h = 0.
0, 1, 2
Let c = -3318 - -3323. Let f(i) be the second derivative of -1/4*i**4 + 5/12*i**3 + 3/40*i**c + 0 - 4*i - 1/120*i**6 - 3/8*i**2. Solve f(l) = 0 for l.
1, 3
Let n = -64 + 68. Suppose n*i + 8 = -g, -g + 2*i + 14 = g. Factor 20*t + 3*t**2 + 1 + g*t**2 + 23 - 3*t**2.
4*(t + 2)*(t + 3)
Suppose 0 = -5*b + q - 295, -q - 80 = 5*b + 215. Let j = 73 + b. Factor j + 13 - 10*f + 35*f**2 - 20*f**3 - 32.
-5*(f - 1)**2*(4*f + 1)
Let j(i) = -5*i + 39. Let d be j(-5). Suppose 0 = -68*o + d*o + 92. What is y in 16 - o*y**3 - 28*y - 18*y**3 + 45*y**3 + 8*y**2 = 0?
-4, 1
Let y(m) be the third derivative of -m**6/60 + 3*m**5/10 - 13*m**4/6 + 8*m**3 + 165*m**2 + 3*m. Suppose y(z) = 0. What is z?
2, 3, 4
Let u(f) be the third derivative of f**5/70 + 113*f**4/28 + 222*f**3/7 + f**2 - 98. Suppose u(x) = 0. Calculate x.
-111, -2
Suppose 0 = -5*g + 4*w + 7, -5*g + 5*w + 13 = 4*w. Factor -12*f**g - 12*f**4 + 11*f**2 - 8*f**2 - 6*f**2 - f**2 - 4*f**5.
-4*f**2*(f + 1)**3
Let n(c) be the first derivative of -3*c**5/25 - 1599*c**4/20 - 70218*c**3/5 + 64320*c**2 - 430944*c/5 + 318. Let n(p) = 0. Calculate p.
-268, 1, 2
Factor -308*v**2 - 1960/3*v + 5488 - 26*v**3 - 2/3*v**4.
-2*(v - 3)*(v + 14)**3/3
Let l be 52 - 55822/1140 - (-33)/(-18). Find p, given that -3/5*p**4 + l*p**3 + 9/5*p**2 + 0 + 0*p = 0.
-1, 0, 3
Suppose 5*d**5 - 490*d**3 + 389*d**4 + 5081 - 5081 - 354*d**4 = 0. Calculate d.
-14, 0, 7
Let x be -2*1/(8/(-116)). Let 26*j - 13*j**2 - 251*j - 3*j**3 + 375 + x*j**2 + 29*j**2 = 0. Calculate j.
5
Let u(p) be the second derivative of 0 - 5/9*p**4 - 205*p - 32/9*p**2 - 7/3*p**3 + 1/90*p**5. Determine k so that u(k) = 0.
-1, 32
Let z(w) = -46*w**4 - 40*w**3 - 91*w**2 + 14*w + 7. Let k(b) = -40*b**4 - 40*b**3 - 90*b**2 + 12*b + 6. Let t(j) = -7*k(j) + 6*z(j). Factor t(o).
4*o**2*(o + 3)*(o + 7)
Let v(c) be the first derivative of -3*c**5/25 - 12*c**4 - 1518*c**3/5 + 984*c**2 - 5043*c/5 + 1380. Let v(r) = 0. Calculate r.
-41, 1
Let y(w) be the first derivative of w**7/1260 - w**6/540 - 4*w**5/45 - 5*w**4/9 + 64*w**3/3 + 2*w + 134. Let s(k) be the third derivative of y(k). Factor s(u).
2*(u - 5)*(u + 2)**2/3
Solve 99/4 + 3/2*f**5 + 147/2*f**3 - 75*f - 207/4*f**4 + 27*f**2 = 0.
-1, 1/2, 1, 33
Let n(o) be the second derivative of o**4/3 - 14*o**3/3 + 24*o**2 + 8*o + 106. Let n(w) = 0. What is w?
3, 4
Let t(m) be the third derivative of -m**7/70 - 149*m**6/40 + 151*m**5/20 + 149*m**4/8 - 75*m**3 - 4666*m**2. Suppose t(x) = 0. What is x?
-150, -1, 1
Let w(v) = 13*v**2 + 201*v - 46. Let s(m) = -119*m**2 - 1816*m + 416. Let g(b) = -2*s(b) - 19*w(b). Factor g(d).
-(d + 21)*(9*d - 2)
Let k = -2/198301 - -56317494/991505. Let 276/5*g**2 + 96/5 - 4/5*g**4 - k*g - 84/5*g**3 = 0. What is g?
-24, 1
Let m(h) be the first derivative of h**6/10 + 62*h**5/5 - 52*h**4/5 - 3759. Factor m(q).
q**3*(q + 104)*(3*q - 2)/5
Let f = -12039 - -12042. Let y(w) be the second derivative of 5/12*w**4 + 0 - 15*w**f - 25