 Calculate n.
-76, 0, 1/3
Let c(n) be the third derivative of 0 + 0*n + 0*n**4 - 1/90*n**6 + 6*n**2 + 0*n**5 - 23/6*n**3. Let b(p) be the first derivative of c(p). Factor b(m).
-4*m**2
Let k(l) be the third derivative of 1/20*l**5 - 8 + 6*l**3 - 14*l**2 - 13/8*l**4 + 0*l. Find h such that k(h) = 0.
1, 12
Let t be (((-6)/(-385))/((-36)/(-60)))/((-1079)/91 + 12). Factor -38/11*k + 0 - t*k**2.
-2*k*(k + 19)/11
Let h be 8/(-6)*(29 + 2751/(-168) + -13). Factor 0 + 1/2*j**5 + 0*j**2 + h*j**4 - j**3 + 0*j.
j**3*(j - 1)*(j + 2)/2
Factor 4490*g + 11736 + 15405*g - 8163*g - 4*g**2.
-4*(g - 2934)*(g + 1)
Let r(o) be the first derivative of -1/20*o**5 - 5/2*o**2 - 13 + 0*o - 18*o**3 - 3/2*o**4. Let x(b) be the second derivative of r(b). Find m such that x(m) = 0.
-6
Let k(x) be the third derivative of -1/18*x**5 - 47/108*x**4 + 0 - 1/540*x**6 + 49*x**2 - 11/9*x**3 + 0*x. Determine y so that k(y) = 0.
-11, -3, -1
Let i(j) be the third derivative of -j**5/330 + 5*j**4/132 - 4*j**3/33 + 1319*j**2. Factor i(p).
-2*(p - 4)*(p - 1)/11
Let i(k) be the second derivative of -22*k - 65/6*k**3 + 5/6*k**4 - 3 + 25*k**2 + 1/4*k**5. Solve i(q) = 0.
-5, 1, 2
Let l = 27529 - 27526. Let d(x) be the second derivative of -2/3*x**l + 0 + 0*x**2 + 1/12*x**4 + 41*x. Let d(b) = 0. What is b?
0, 4
Factor -2684 - 7170*r**2 - 3879*r**3 - 4420 + 279*r**3 - 14240*r - 3550*r**2 - 460*r**4 - 2*r**5.
-2*(r + 2)**4*(r + 222)
Suppose -10*d + 255 = 75*d. Let l(g) be the first derivative of -d*g**2 - 1/5*g**3 - 15*g - 3. Factor l(j).
-3*(j + 5)**2/5
Let l(i) be the second derivative of -i**7/42 + 4*i**6/15 + 17*i**5/20 - 17*i**4 + 30*i**3 + 1680*i. Find d, given that l(d) = 0.
-5, 0, 1, 6
Suppose 14*d**2 - 79*d**2 + 19*d**2 + 55*d + 900 + 24*d**2 + 17*d**2 = 0. Calculate d.
-9, 20
Let v(q) = -q**5 - 27*q**4 + 46*q**3 + 64*q**2. Let i(z) = -9*z**4 + 15*z**3 + 21*z**2. Let g(j) = 8*i(j) - 3*v(j). Factor g(d).
3*d**2*(d - 2)*(d + 1)*(d + 4)
Find h, given that -1441*h**2 + 2758*h**2 + 258*h - 1319*h**2 = 0.
0, 129
Let t = 32962 + -428498/13. Find p such that 40/13 + 42/13*p + t*p**2 = 0.
-4, -5/4
Factor -256264/5*i - 2/15*i**4 - 254616/5 - 1244/15*i**3 - 195914/15*i**2.
-2*(i + 2)**2*(i + 309)**2/15
Suppose 3*l - 3*m = -l - 4, -4*l = 5*m - 28. Suppose 0 = 2*t - 15 + 7. Factor -n**2 - 5*n**2 + t*n + 8*n**l.
2*n*(n + 2)
Let c(q) be the third derivative of -q**5/15 + 7*q**4 + 2006*q**3/3 - 725*q**2. Factor c(r).
-4*(r - 59)*(r + 17)
Factor 2/7*u**3 + 0*u + 18/7*u**2 + 0.
2*u**2*(u + 9)/7
Suppose -5*p + 3*p = -12. Find l, given that p*l**3 - 28*l + 15*l**2 + 11*l - 3*l**4 - l = 0.
-2, 0, 1, 3
Let f(q) be the first derivative of q**3 - 3/2*q**2 + 7 - 18*q. Solve f(x) = 0 for x.
-2, 3
Let y(a) be the first derivative of a**5/100 + a**4/6 + 3*a**3/10 - 29*a - 89. Let z(o) be the first derivative of y(o). Find b, given that z(b) = 0.
-9, -1, 0
Let -64*r**2 + 119*r - 958*r - 4*r**2 + 84*r**2 - 840 - 15*r**2 = 0. Calculate r.
-1, 840
Suppose 2*a - 10 = 3*n, -6*n = -n + 10. Suppose -a*f + 7*f = 40. Suppose -6*k**2 + 4*k + 8*k**2 - 14 + 0 + f*k = 0. Calculate k.
-7, 1
Factor 760*g + 69*g**3 + 63*g**3 - 207*g**3 + 73*g**3 - 42*g**2 - 14*g**2.
-2*g*(g - 10)*(g + 38)
Let z(v) = v**2 + 22*v - 95. Let g be z(-30). Let w = 148 - g. Suppose 3/5*o**2 - 1/5*o**4 + 1/5*o**w - 2/5 - 1/5*o = 0. What is o?
-1, 1, 2
Let m(h) be the third derivative of -52*h**2 - 3*h + 0 + 0*h**3 - 19/20*h**5 + 1/2*h**4. Factor m(g).
-3*g*(19*g - 4)
Solve -4/3*l**4 - 572/3*l**3 + 40328/3 - 19028/3*l - 6908*l**2 = 0 for l.
-71, -2, 1
Let q = -1177057/20 + 294661/5. Let s = -378/5 + q. Determine o so that 5/4*o**2 + 0 - s*o = 0.
0, 3
Let q be 174/357 - 106/1802. Find f, given that 3*f + q*f**2 - 24/7 = 0.
-8, 1
Let b(a) be the third derivative of a**6/280 + 521*a**5/70 + 2081*a**4/56 + 520*a**3/7 + 842*a**2. Determine x, given that b(x) = 0.
-1040, -1
Let c = -335903 - -1679521/5. Find d, given that c*d - 6/5*d**3 + 16/5*d**2 + 0 = 0.
-1/3, 0, 3
Let h(a) be the first derivative of -a**6/360 + 2*a**5/3 - 200*a**4/3 - 25*a**3/3 - 114. Let u(t) be the third derivative of h(t). Find q such that u(q) = 0.
40
Let f(l) = 5*l**3 + 56*l**2 + 68*l - 120. Let i(z) = -115*z**3 - 1290*z**2 - 1565*z + 2760. Let b(r) = -70*f(r) - 3*i(r). Find k such that b(k) = 0.
-8, -3, 1
Let s(j) be the second derivative of -2*j + 132 + 1/70*j**7 + 3/10*j**2 - 3/50*j**5 + 1/10*j**3 - 1/10*j**4 + 1/50*j**6. Factor s(r).
3*(r - 1)**2*(r + 1)**3/5
Factor 11/2*x - 1/6*x**3 + 0 - 16/3*x**2.
-x*(x - 1)*(x + 33)/6
Let f = 526731318/237083 - 90/33869. Factor 373248/7 + 216/7*u**2 + 1/7*u**3 + f*u.
(u + 72)**3/7
Let q(p) be the third derivative of p**7/280 - 37*p**6/160 - 79*p**5/80 + 37*p**4/32 + 39*p**3/4 - 844*p**2. Let q(b) = 0. Calculate b.
-2, -1, 1, 39
Let u be (19 + 36)/(-110)*-31. Factor -961/4 - u*x - 1/4*x**2.
-(x + 31)**2/4
Let z be (-14872)/396 + 19 + 19. Let u = -89 - -803/9. Suppose -2/3*n - z - u*n**2 = 0. Calculate n.
-2, -1
Suppose d = -0*h + 5*h + 59, -2*d - 2*h = -58. Let l = d - 4. Factor -l*p**2 + 27*p**2 + 1 + 2.
-3*(p - 1)*(p + 1)
Let h be (-46)/(-7) - (-28)/(-49). Let k(v) = -4*v**2 + 17*v. Let r(x) = -32*x**2 + 137*x - 2. Let m(g) = h*r(g) - 51*k(g). Determine t so that m(t) = 0.
-1/4, 4
Let m(f) = 10*f**4 - 205*f**3 + 880*f**2 - 930*f + 870. Let a(d) = -d**3 + d + 29. Let x(k) = 30*a(k) - m(k). Factor x(w).
-5*w*(w - 8)**2*(2*w - 3)
Let h(s) be the first derivative of s**3/4 - 57*s**2/4 + 1083*s/4 - 1313. Factor h(z).
3*(z - 19)**2/4
Suppose -3*s = -4*w - 25, s + 1331 = -2*w + 1346. Factor 16/13*p**w + 0*p + 2/13*p**3 + 0.
2*p**2*(p + 8)/13
Let i be 17*(-1)/136*0. Determine z, given that -25/4*z**4 - 85/4*z**3 + i + 10*z + 35/2*z**2 = 0.
-4, -2/5, 0, 1
Let f be (3 - -11)*516/37926. Let r(z) be the first derivative of 0*z + 1/14*z**4 + 1/7*z**2 + f*z**3 - 22. Factor r(x).
2*x*(x + 1)**2/7
Factor 5*y**3 + 2952*y - 132*y**2 - 330 + 3399*y - 5474*y.
(y - 15)*(y - 11)*(5*y - 2)
Factor 358 + 8 + 65*b**2 - b**3 + 1810*b - 492*b**2 + 61 - 1809*b.
-(b - 1)*(b + 1)*(b + 427)
Suppose -4*o = -204 - 16. Let x = o + -60. Let b(s) = -s**3 + s**2. Let y(p) = 8*p**3 - 4*p**2 + 2*p. Let g(d) = x*y(d) - 35*b(d). What is m in g(m) = 0?
-2, -1, 0
Let h(c) be the first derivative of 0*c**2 + 0*c + 4*c**3 + 1/1260*c**6 - 1/21*c**4 + 1 + 1/140*c**5. Let v(w) be the third derivative of h(w). Factor v(o).
2*(o - 1)*(o + 4)/7
Let w(x) be the second derivative of 0 - 253*x - 1/30*x**3 + 1/100*x**5 + 1/10*x**4 - 3/5*x**2. Let w(b) = 0. Calculate b.
-6, -1, 1
Let m = 326 + -794. Let a = -4208/9 - m. Let 0 - 2/9*r**2 + 2/9*r**3 - a*r = 0. What is r?
-1, 0, 2
Suppose 0 - 6/7*y**4 + 6/7*y**3 + 222/7*y**2 + 30*y = 0. What is y?
-5, -1, 0, 7
Let o(a) be the second derivative of -1664/3*a**3 - 118*a**4 + 2*a - 7*a**5 - 1024*a**2 - 2/15*a**6 + 11. Factor o(r).
-4*(r + 1)*(r + 2)*(r + 16)**2
Let n(h) = -4*h + 40. Let b be n(9). Suppose 0*r - 3*r - 4*d = 7, -4*d = 4*r + b. Factor -3*j + 3*j**2 - j**r - 96 + 0*j + 97.
-(j - 1)**3
Let i(r) be the second derivative of 99*r**4/20 + 148*r**3/5 - 9*r**2/10 - 2257*r. Factor i(k).
3*(k + 3)*(99*k - 1)/5
Let 32*q - 7*q - 49 - 18*q + 2*q**2 = 0. Calculate q.
-7, 7/2
Let o(y) = -16*y + 67. Let v be o(3). Factor -30*f**3 - 1059*f - v*f**3 + 675*f**2 + 124 + 872*f**2 + 187*f.
-(f - 31)*(7*f - 2)**2
Let c(n) = 1812*n - 97846. Let w be c(54). Suppose -72 - 1/2*j**w + 12*j = 0. What is j?
12
Let a(b) be the first derivative of 5*b**4/12 + 65*b**3/6 + 100*b**2 + 14*b + 192. Let m(c) be the first derivative of a(c). Solve m(d) = 0.
-8, -5
Find w such that 627/8*w**2 - 939/4*w - 9/8 = 0.
-1/209, 3
Let w = 113 + -61. Let p(l) = l**3 + 9*l**2 - 9*l + 12. Let q be p(-10). Suppose -53*c**2 - 7*c**3 + w*c**q + 12*c**3 = 0. What is c?
0, 1/5
Let f be (28/(-84))/((0 - 0) + -4 + (-25984)/(-6699)). Solve -3/2*x**4 + 0*x + 1/4*x**5 + f*x**3 + 0 - 3/2*x**2 = 0 for x.
0, 1, 2, 3
Factor 1587/2*k + 0 + 657*k**3 + 3/2*k**5 - 66*k**4 + 1518*k**2.
3*k*(k - 23)**2*(k + 1)**2/2
Let s = 12834 - 12832. Let f(d) be the first derivative of 14 - 2/5*d**5 + 0*d + 0*d**4 + 0*d**s + 2/3*d**3. Factor f(i).
-2*i**2*(i - 1)*(i + 1)
Suppose 5*z = 827*r - 828*r + 112, 5*z = -5*r + 580. Let k be (-20)/(-6) - (-2)/3. Let k*n**3 - 213*n**2 + r*n**2 - 4*n**5 + 104*n**2 - 8*n**4 = 0. Wha