
Let k(t) be the third derivative of -5*t**8/168 + 73*t**7/105 - 11*t**6/4 + 107*t**5/30 + 7*t**4/6 - 8*t**3 + 2*t**2 - 206. Suppose k(j) = 0. What is j?
-2/5, 1, 12
Factor 3/4*r**3 + 333/4 + 213/4*r - 117/4*r**2.
3*(r - 37)*(r - 3)*(r + 1)/4
Let j(g) = -2*g**2 - 7*g - 26. Let a be j(-7). Let u be 270/a*4/(-6). Determine s, given that -u*s**2 - 3/5*s**3 - 9/5*s + 0 = 0.
-3, -1, 0
Let t(r) be the first derivative of r**7/3780 - r**6/810 + r**5/540 - 79*r**3/3 - 2. Let p(a) be the third derivative of t(a). Factor p(c).
2*c*(c - 1)**2/9
Let b(z) be the first derivative of z**6/6 - 23*z**5 + 333*z**4/2 - 1316*z**3/3 + 436*z**2 - 1149. Factor b(d).
d*(d - 109)*(d - 2)**3
Let p(h) be the first derivative of -h**4 - 184*h**3/3 - 422*h**2 - 984*h - 1345. Determine o, given that p(o) = 0.
-41, -3, -2
Let c = -2108818 + 2109396. Find k, given that 1666/3*k**4 + 5404/9*k**3 - c*k**5 - 2/9 - 4996/9*k**2 - 202/9*k = 0.
-1, -1/51, 1
Factor -4515625/7 - 1/7*z**2 + 4250/7*z.
-(z - 2125)**2/7
Let u = 147426/5 - 29484. Factor u - 32/5*l + 26/5*l**2.
2*(l - 1)*(13*l - 3)/5
Let j = -3 - -16. Let x = -11 + j. Factor d**3 - 16*d**3 + 18*d + 20*d - 12*d**4 + 21*d**x - 32*d.
-3*d*(d - 1)*(d + 2)*(4*d + 1)
Factor -618*b**2 - 54636350 - 318270*b - 2/5*b**3.
-2*(b + 515)**3/5
Let h = 13 + 8. Suppose -i = -h - 9. Determine o, given that -4*o**5 - 11 + 16*o**4 + 9 - 56*o**2 - 4*o**3 - i + 80*o = 0.
-2, 1, 2
Let j(q) be the first derivative of 4*q**3/3 - 482*q**2 - 968*q - 3233. Factor j(f).
4*(f - 242)*(f + 1)
Let f be (-5)/((-25)/14) + 1/5. Factor 42*b**3 + 145*b**4 - 104*b**2 + 8*b + 99*b**f + 69*b**3 + 755*b**4.
2*b*(2*b + 1)*(15*b - 2)**2
Let u(r) be the first derivative of -334*r**5 + 10015*r**4/4 - 6670*r**3 + 6650*r**2 + 40*r - 1839. Suppose u(s) = 0. Calculate s.
-1/334, 2
Factor 863 + 4713*k + 820*k**2 + 5*k**3 - 1008*k + 4627 - 180*k**2.
5*(k + 3)**2*(k + 122)
Let f(u) = -14*u**3 + 30*u**2 + 66*u + 34. Let d(x) = -x**3 - x**2 - 2*x - 1. Let o(z) = 12*d(z) - f(z). Suppose o(a) = 0. Calculate a.
-1, 23
Suppose 3*d**5 + 31*d**3 + 10*d**4 + 6*d - 26*d - 46*d**3 - 30*d**2 + 2*d**5 - 10*d**2 = 0. What is d?
-2, -1, 0, 2
Let n(k) be the second derivative of 7/48*k**4 - 1/2*k**2 - 1/8*k**3 + 3*k - 36. Factor n(j).
(j - 1)*(7*j + 4)/4
Let o(y) be the third derivative of y**6/240 - 47*y**5/120 - y**4/12 + 47*y**3/3 + 56*y**2 - 19*y. Let o(i) = 0. Calculate i.
-2, 2, 47
Let s(l) = -19*l - 4. Let q be s(-1). Let n be ((-39)/65)/(2 + (-36)/q). Let n*x + 9/4 + 1/4*x**2 = 0. Calculate x.
-3
Suppose -368 = -3423*v + 3239*v. Factor -v*y**2 - 48/7*y - 18/7.
-2*(y + 3)*(7*y + 3)/7
Suppose 0 = -69*l - 2242 + 2380. Factor 0 + 9/7*x**l - 1/7*x**4 + 0*x - 8/7*x**3.
-x**2*(x - 1)*(x + 9)/7
Let g(v) = -42*v + 467. Let o be g(11). Let y(x) be the first derivative of 0*x + 5 - 2/3*x**3 + 5/2*x**4 - x**2 - 6/5*x**o. Factor y(u).
-2*u*(u - 1)**2*(3*u + 1)
Let d = -2/7235 + 1158/1447. Let v be (164/40 + -4)/(3/6). Let 1/5*c**4 + v + d*c + 4/5*c**3 + 6/5*c**2 = 0. What is c?
-1
What is d in -2413094436*d - 5354*d**3 - 522006250000 + 21546*d**4 - 43405564*d - 10774*d**4 - 4335000*d**2 + 1954*d**3 - 10773*d**4 = 0?
-850
Let w be (-14)/(-12)*(-44 - (-14976)/336). Factor 0*d - w + 2/3*d**2.
2*(d - 1)*(d + 1)/3
Suppose 4*v - 23 = 5*k, k + 9 = -2*k. What is g in 60*g**5 - 25*g**v - 55*g**5 + 0*g + 20*g - g**4 + 20 - 25*g**3 + 6*g**4 = 0?
-2, -1, 1, 2
Suppose 275*g - 101*g**3 - 373*g + 2834*g**4 + 267*g**2 - g**5 + 288 + 47*g**2 - 2818*g**4 - 382*g = 0. Calculate g.
2, 3, 4
Let r = -125873/2004 + -296/167. Let a = -187/3 - r. Find t, given that 3/4*t**3 + 0 + a*t**2 + 3/2*t = 0.
-2, -1, 0
Let f(c) be the first derivative of -c**7/168 + 13*c**6/72 + c**5/24 - 65*c**4/24 + 47*c**3/3 - 60. Let u(x) be the third derivative of f(x). Factor u(t).
-5*(t - 13)*(t - 1)*(t + 1)
Find f such that 47*f**3 - 92 - 98*f**3 - 179*f**2 + 50*f**3 + 362*f + 92 = 0.
-181, 0, 2
Let k(z) be the third derivative of 0 + 1/12*z**4 - 315*z**2 + 0*z + 11/30*z**3 - 1/300*z**5. Suppose k(x) = 0. Calculate x.
-1, 11
Let g(o) = -40*o**3 - 1860*o**2 - 12065*o - 18625. Let h(n) = -5*n**3 - 233*n**2 - 1508*n - 2328. Let z(d) = 12*g(d) - 95*h(d). Factor z(x).
-5*(x + 2)*(x + 9)*(x + 26)
Let c = -3259 - -5621. Suppose -2364*q + c*q + 4 = 0. What is j in 9/2*j - 1 + j**q - 9/2*j**3 = 0?
-1, 2/9, 1
Let n(g) be the first derivative of 2*g**6 - 96*g**5 + 6555*g**4/4 - 10855*g**3 + 27885*g**2/2 - 6591*g + 182. Factor n(o).
3*(o - 13)**3*(2*o - 1)**2
Let l be ((-10 - (-5 - 12)) + -16)/(42/(-16)). Let j(i) be the first derivative of 2*i**2 - 1/7*i**4 + l*i + 0*i**3 + 19. Find c, given that j(c) = 0.
-2, -1, 3
Let r = -321870 + 321873. Factor 1/2*p**r + 11/4*p**2 - 1/4*p**4 - 9 - 3*p.
-(p - 3)**2*(p + 2)**2/4
Factor -1156/13*v - 2/13*v**4 - 714/13*v**2 - 72/13*v**3 + 0.
-2*v*(v + 2)*(v + 17)**2/13
Let p = 552 + -551. Let r = 3 + p. What is b in 0 + 5/2*b**3 - b**2 + 0*b + b**r - 5/2*b**5 = 0?
-1, 0, 2/5, 1
Let p(x) = 8*x + 67. Let q be p(-8). Find m such that 3*m**4 + 4*m**2 + 10*m - 129*m**5 + 4 - 8*m**q - 11*m**4 + 127*m**5 = 0.
-2, -1, 1
Suppose 2*d = -2*d + 8. Let c be 8/3*((-6)/440)/(181/(-2715)). Determine b, given that 4/11*b**d + 0*b - c*b**4 - 6/11*b**3 + 4/11*b**5 + 0 = 0.
-1, 0, 1/2, 2
Let x be 73/438*3/2. Let n(w) be the third derivative of -4/15*w**3 - 7/300*w**5 + 0 + x*w**4 + 0*w - 17*w**2. Factor n(l).
-(l - 4)*(7*l - 2)/5
Factor 10/11*u**2 + 1484/11*u + 592/11.
2*(u + 148)*(5*u + 2)/11
Let r(j) be the second derivative of 1/42*j**4 + 72*j + 529/7*j**2 + 0 - 46/21*j**3. Factor r(v).
2*(v - 23)**2/7
Let d be 243/21 - (-6)/14. Suppose 0*p + 5*p - 3*v - 902 = 0, -3*p - 2*v + 526 = 0. Factor 4*y**5 + 4*y**4 - p*y - 24*y**3 + 134*y + 9*y**2 - d - 65*y**2.
4*(y - 3)*(y + 1)**4
Let r(n) be the second derivative of -n**7/700 + n**6/180 - n**5/150 + n**3/6 + 5*n**2 + 51*n. Let l(t) be the second derivative of r(t). Factor l(w).
-2*w*(w - 1)*(3*w - 2)/5
Let 7/2 + 1/4*p - 15/4*p**2 = 0. Calculate p.
-14/15, 1
Suppose 17*c - 24*c = -42. Factor -39*s**2 - c + 18*s**3 - 3*s**5 + 3*s**4 - 3 - 3*s**2 + 33*s.
-3*(s - 1)**4*(s + 3)
Let r(p) be the first derivative of p**7/4200 - 143*p**3/3 + 25. Let k(b) be the third derivative of r(b). Solve k(f) = 0 for f.
0
Let t(h) be the first derivative of 47/20*h**5 - 11/2*h**2 - 25 - h**3 + 1/8*h**4 + 0*h + 11/10*h**6. Let j(l) be the second derivative of t(l). Factor j(v).
3*(v + 1)*(4*v + 1)*(11*v - 2)
Let c(w) be the second derivative of w**6/10 - 9*w**5/5 - 63*w**4/4 - 11*w**3 + 144*w**2 + w - 1050. Solve c(i) = 0.
-3, -2, 1, 16
Suppose -47*q**3 + 62*q - q + 4*q - 18*q**3 + 19*q**2 - 15 - 4*q**2 = 0. What is q?
-1, 3/13, 1
Let j(t) be the third derivative of 0*t**3 + 1/6*t**6 + 23*t + 2/105*t**7 + 0 + 2*t**2 + 0*t**4 + 4/15*t**5. Factor j(u).
4*u**2*(u + 1)*(u + 4)
Suppose -763821*o**2 - 15138*o**5 - 1622384*o**3 + 22443*o - 1728 - 271788*o**4 - 10605*o + 137634*o - 2430963*o**2 = 0. Calculate o.
-6, 2/87
Let b(m) be the third derivative of -4*m**7/35 + m**6/3 + 23*m**5/90 + m**4/18 - 707*m**2. What is h in b(h) = 0?
-1/6, 0, 2
Suppose -122*t - 1284 = -15*t. Let u(x) = -5*x - 58. Let h be u(t). Factor -4/3 + 14/9*r - 2/9*r**3 + 0*r**h.
-2*(r - 2)*(r - 1)*(r + 3)/9
Let j = 160/231 - 2/77. Let h be (23 - (-65)/(-175)*65)/((-12)/21). Let -2/3*p + 4/3 - j*p**h = 0. What is p?
-2, 1
Let j(c) be the second derivative of -c**5/5 + 883*c**4/3 - 130242*c**3 + 388962*c**2 + 4992*c. Factor j(w).
-4*(w - 441)**2*(w - 1)
Let v be (-7878)/(-143) - 1/11. Find m such that 175*m**5 - 651*m**3 + 96 - 36 - v*m**2 + 186*m - 84*m**3 + 295*m**4 + 74*m = 0.
-3, -2/5, -2/7, 1
Let v be 2 + -6 + (-16)/(-2). Suppose 4*t + v = 5*u, -15*u + 3*t + 3 = -11*u. Find c, given that 1/4*c - 1/8*c**3 + 1/8*c**2 + u = 0.
-1, 0, 2
Let u(y) = 6*y**4 + 52*y**3 - 312*y**2 + 420*y - 166. Let v(d) = d**4 - 3*d**2 - d + 3. Let b(x) = -u(x) + 8*v(x). Suppose b(g) = 0. What is g?
1, 5, 19
Suppose -2/9*b + 2/3*b**5 - 4/9*b**3 + 4/3*b**2 - 2/9 - 10/9*b**4 = 0. Calculate b.
-1, -1/3, 1
Suppose -12*q - 2*q = -28. Let w(d) = 6 + 13 - 21 - 3*d**2 + 2*d**q. Let o(g) = -4*g**2 - g - 8. Let s(i) = -6*o(i) + 22*w(i). Factor s(x).
2*(x + 1)*(x + 2)
Suppose -4*b + 2*b - 5*a + 23 = 0, 0 = -4*a + 12. Let i(o) be the second derivative of 1/84*o**b + 0 + 0*