3
Let d(u) be the third derivative of 0 + 142*u**2 + 1/4*u**4 - 4/15*u**5 + 1/504*u**8 + 11/90*u**6 - 8/315*u**7 + 0*u + 0*u**3. Determine p so that d(p) = 0.
0, 1, 3
Let p(k) = 11*k**2 - 125*k - 810. Let s(n) = 5*n**2 - 64*n - 405. Let a(g) = -4*p(g) + 9*s(g). Find f such that a(f) = 0.
-5, 81
Find g such that 6/5*g**3 + 6*g + 24/5*g**2 + 12/5 = 0.
-2, -1
Solve 0 + 0*h - 27889/7*h**2 - 1/7*h**4 + 334/7*h**3 = 0 for h.
0, 167
Let g(t) be the first derivative of -t**4/4 + 23*t**3/2 - 33*t**2 - 49*t - 132. Let o(f) be the first derivative of g(f). Determine u so that o(u) = 0.
1, 22
Let y be ((-1)/(-16))/(63/108)*(-4)/(-9). Let z(m) be the first derivative of -3 + y*m**3 - 4/7*m + 3/14*m**2. Factor z(b).
(b - 1)*(b + 4)/7
Let x(c) be the second derivative of 0 - 1/180*c**5 - 1/2*c**2 + 1/6*c**3 + 1/36*c**4 + c. Let n(i) be the first derivative of x(i). Solve n(t) = 0.
-1, 3
Let w(j) be the second derivative of -5*j**4/4 - 475*j**3/3 - 315*j**2/2 - 53*j. Factor w(h).
-5*(h + 63)*(3*h + 1)
Let z be 43/126 + 38/(-133). Let f(g) be the third derivative of -z*g**3 + 5*g**2 + 0 - 1/144*g**4 + 0*g + 1/360*g**5. Find d, given that f(d) = 0.
-1, 2
Let w(b) be the first derivative of -b**5/110 + 37*b**4/22 - 1369*b**3/11 + 21*b**2 + b - 101. Let g(t) be the second derivative of w(t). Factor g(u).
-6*(u - 37)**2/11
Let r = 583 + -6415/11. Let d = r + 15/22. Factor 0*y - 1/2 + d*y**2.
(y - 1)*(y + 1)/2
Suppose -739*p + 1688 = 305*p - 200*p. Let -16/11*l + 32/11 + 2/11*l**p = 0. What is l?
4
Find h, given that 196/11*h + 5/11*h**3 + 63/11*h**2 + 96/11 = 0.
-8, -4, -3/5
Find m, given that -447*m + 1439*m - 232*m**2 - 15763 + 15763 - 4*m**3 = 0.
-62, 0, 4
Let m(a) be the first derivative of 431*a**3 - 48*a - 264*a**3 + 80*a**2 - 58 - 203*a**3 + 5*a**4. Factor m(q).
4*(q - 3)*(q - 2)*(5*q - 2)
Let f be (0 + 6)*(25 - 17 - 119/15). Let x(a) be the second derivative of 0 + 8*a + 6/5*a**5 + 3/4*a**4 - 5/2*a**3 - 3*a**2 - f*a**6. Let x(l) = 0. What is l?
-1/2, 1, 2
Let d(a) be the second derivative of 4/3*a**4 - 13/6*a**3 + 55*a + 0 + 3/2*a**2 - 1/5*a**5. Let d(q) = 0. What is q?
1/2, 3
Let g be (-72)/(-240) + (5586/220)/19. Factor 0*n + 0*n**2 + g*n**5 + 0 + 2/11*n**3 - 12/11*n**4.
2*n**3*(3*n - 1)**2/11
Let b(p) = -p**3 + 151*p**2 - 386*p + 256. Let q(n) = 6*n**3 - 768*n**2 + 1932*n - 1280. Let i(c) = -22*b(c) - 4*q(c). Factor i(j).
-2*(j - 2)*(j - 1)*(j + 128)
Let v = 167 + -167. Let p(n) be the second derivative of 7/24*n**4 + v - 11*n - 3/20*n**5 - 1/6*n**3 + 0*n**2. Determine g so that p(g) = 0.
0, 1/2, 2/3
Let h(v) be the third derivative of v**7/70 - 2979*v**6/20 + 2958147*v**5/5 - 979146657*v**4 + 3527*v**2 - 1. Factor h(x).
3*x*(x - 1986)**3
Suppose -6 = 4*w + 4*f + 2, -3*f = 4*w + 3. Suppose -19*q + 9*q**2 - 44*q**w + 93*q**3 + 7*q - 46*q**3 = 0. What is q?
-4, 0, 1
Let x(r) be the second derivative of -r**4/3 + 17104*r**3/3 - 36568352*r**2 - 6049*r + 1. Determine d, given that x(d) = 0.
4276
Let s = 2202 + -2199. Let b(r) be the second derivative of 1/3*r**2 + 0 + 1/30*r**5 + 5*r - 1/18*r**4 - 1/9*r**s. Factor b(i).
2*(i - 1)**2*(i + 1)/3
Let u(p) = 194*p**2 - 20*p + 21. Let k be u(1). Factor -35*f + 5*f**4 + 8 + k*f - 150*f**2 - 4 - 59 + 40*f**3.
5*(f - 1)**3*(f + 11)
Suppose 11*u - 51 - 103 = 0. Let m(t) be the first derivative of -5*t**3 - 13*t**2 - 12 + u*t**2 - 2*t**2. Suppose m(o) = 0. Calculate o.
-2/15, 0
Determine n, given that -100/3*n - 200 + 4/3*n**2 = 0.
-5, 30
Factor -508*v**2 + 24*v**2 - 2*v**4 + 103*v**3 - 7*v**4 + 269*v**2 + 157*v - 36.
-(v - 9)*(v - 1)**2*(9*v - 4)
Let o(j) be the second derivative of j**6/40 - 633*j**5/40 + 46177*j**4/16 - 43677*j**3 + 257094*j**2 + j - 1817. Factor o(b).
3*(b - 207)**2*(b - 4)**2/4
Suppose 2*t - b - b - 14 = 0, -5*t - 5 = 3*b. Let q be 2890/20230*(0 - -2)*1. Suppose q*v**3 - 8/7 - 6/7*v**4 + t*v**2 + 0*v - 2/7*v**5 = 0. Calculate v.
-2, -1, 1
Let o(g) be the second derivative of -95*g**4/12 - 35*g**3/2 - 5*g**2 + 2*g - 1080. Factor o(x).
-5*(x + 1)*(19*x + 2)
Let h(x) be the first derivative of x**5/20 + 9*x**4/8 + 9*x**3 - 7*x**2 - 2*x - 44. Let f(o) be the second derivative of h(o). Factor f(d).
3*(d + 3)*(d + 6)
Let k(j) = 39*j**3 + 6390*j**2 + 264*j + 33. Let n(w) = 6*w**3 + 983*w**2 + 40*w + 5. Let s(q) = 5*k(q) - 33*n(q). Factor s(a).
-3*a**2*(a + 163)
Let f be 0/72 - (-10)/12. Let c(z) be the second derivative of 1/20*z**5 + 0 - z**2 + 16*z - 1/3*z**4 + f*z**3. Factor c(s).
(s - 2)*(s - 1)**2
Suppose 3*f + 31 + 11 = 0. Let l(r) = -24*r**2 - 314*r - 276. Let u(n) = 5*n**2 + 63*n + 55. Let g(v) = f*u(v) - 3*l(v). Factor g(a).
2*(a + 1)*(a + 29)
Let w(y) be the first derivative of y**6/15 - 38*y**5/25 + 12*y**4 - 168*y**3/5 + 7957. Factor w(b).
2*b**2*(b - 7)*(b - 6)**2/5
Let l(z) be the first derivative of -z**6/24 + 9*z**5/20 + 7*z**4/2 - 16*z**3 - 80*z**2 + 192*z - 2019. Solve l(p) = 0.
-4, 1, 4, 12
Let d(o) = -3*o**2 + 42*o - 30. Let c be ((-22)/66)/((-2)/(-24)). Let b(x) = -x**2 + 21*x - 16. Let r(h) = c*d(h) + 9*b(h). Find p such that r(p) = 0.
-8, 1
Let s(z) be the third derivative of -z**7/1260 + z**6/180 - z**4/9 + 4*z**3/9 + 3*z**2 - 3*z - 16. Solve s(v) = 0.
-2, 2
Let f(g) be the second derivative of -g**5/240 - 17*g**4/96 - 2*g**3/3 - 51*g**2 + 81*g. Let l(c) be the first derivative of f(c). Solve l(w) = 0.
-16, -1
Let r be 21*((-92)/(-28) + -3). Suppose 92 = 4*d + 9*h - 5*h, 3*h + r = 0. Determine j so that -27*j - 3*j**2 - 2*j - d + 7 = 0.
-9, -2/3
Let m = -14/31 + -116/155. Let n = m - -27/10. Factor -9/2 - 15/2*p**2 + n*p**3 + 21/2*p.
3*(p - 3)*(p - 1)**2/2
Factor 7705 + 4097 - 3*z**3 + 4098*z**2 + 4638 + 16428*z.
-3*(z - 1370)*(z + 2)**2
Let x be -4*(16 + (-5551)/260) + -21. Let v = 2130 - 53242/25. Factor v*q**4 + x*q**3 + 0 + 4/25*q**2 + 2/25*q**5 + 0*q.
2*q**2*(q + 1)**2*(q + 2)/25
Let f(i) be the second derivative of -2*i**7/21 + 22*i**6/15 - 29*i**5/5 - 11*i**4/3 + 20*i**3 + 2*i - 929. Suppose f(l) = 0. Calculate l.
-1, 0, 1, 5, 6
Suppose 0 = 5*j + 5*w - 55, 2*w - 6*w = 5*j - 52. Find m, given that 5*m - 15*m**2 - 11*m**2 + j*m**2 + 45*m**3 - 12*m**2 = 0.
0, 1/3
Suppose 0 = -15*k + 18*k - 6. Factor -36*z + 58*z**3 - 4*z**4 - 2*z**5 + 2*z - 6*z - 92*z**k + 95 + 17.
-2*(z - 2)**3*(z + 1)*(z + 7)
Suppose 5*x = -4*h - 6, -2*x + x - h = 2. Let g(u) = -u**2 - 13*u - 24. Let j be g(-10). Suppose -r**3 + j*r**3 + 5*r**x - r**3 + r = 0. Calculate r.
-1, -1/4, 0
Suppose -9*u + 8 = -10. Find d such that 0*d + 18 - 5*d - 9*d + 3*d**u - d = 0.
2, 3
Let d = 881555/7 + -125936. Find j such that 6/7 - 6/7*j**2 + d*j - 3/7*j**3 = 0.
-2, -1, 1
Determine l, given that 175*l**3 + 4200 + 4422*l**2 + 29*l**3 - 424*l + 159*l**3 - 408*l - 8108*l = 0.
-14, 10/11
Let p(r) be the second derivative of -r**4/3 + 239*r**3/2 + 721*r**2/2 + 14*r - 161. Let p(x) = 0. Calculate x.
-1, 721/4
Let k(w) be the first derivative of -5*w**4/8 + 215*w**3/6 + 1485*w**2/2 + 1526. Solve k(s) = 0 for s.
-11, 0, 54
Let w(g) be the second derivative of 3/4*g**4 + 0 - 1/30*g**6 + 0*g**2 - 1/20*g**5 + 10*g + 3/2*g**3. Factor w(p).
-p*(p - 3)*(p + 1)*(p + 3)
Let b(r) be the first derivative of -1/24*r**3 + 15/8*r**2 - 29/8*r - 109. Factor b(u).
-(u - 29)*(u - 1)/8
Let y(d) = 27*d**3 - 121*d**2 + 9*d + 172. Let m be y(4). Solve 3*s**2 - 3/4*s**5 - 3/4*s - 9/2*s**3 + 3*s**4 + m = 0.
0, 1
Let o = 193 - 188. Determine h so that 5*h**2 - 10*h**2 - 5*h + 10*h**2 - o*h**3 + 5*h**2 = 0.
0, 1
Let t(n) be the third derivative of n**6/40 + 23*n**5/10 + 89*n**4/8 + 22*n**3 + 7453*n**2. Factor t(b).
3*(b + 1)**2*(b + 44)
Let t be -10 + (-32)/(-60)*33. Solve 28/5*n**2 + 12/5 + t*n = 0.
-6/7, -1/2
Factor 26*k**3 - 50 + 17*k**3 - 253*k + 230*k**2 - 7*k**3 + 19*k**3 + 18*k.
5*(k - 1)*(k + 5)*(11*k + 2)
Let q be ((-8554)/(-243789))/(2/418). Let 92/9*d**2 - 32/9 + q*d - 2/3*d**3 = 0. What is d?
-1, 1/3, 16
Determine u so that -36/5 + 27/5*u**3 + 93/5*u - 81/5*u**2 - 3/5*u**4 = 0.
1, 3, 4
Let n = 418/3 - 8359/60. Let y(j) be the third derivative of 0 + n*j**5 + 0*j + 0*j**4 - 1/6*j**3 + 18*j**2. Determine p so that y(p) = 0.
-1, 1
Let w(g) be the first derivative of 4/3*g**3 + 83 + 576*g - 48*g**2. Factor w(v).
4*(v - 12)**2
Factor 266256/7 + 1032/7*r + 1/7*r**2.
(r + 516)**2/7
Let r be 42*(4/(-5) - 110/(-75)). Factor 35*w + 57*w - 27*w**2 