4*j - 108. Find n, given that o(n) = 0.
-9, -1
Let u(a) be the third derivative of -a**5/12 + 235*a**4/24 - 115*a**3/3 + 15*a**2 + 20*a. Factor u(g).
-5*(g - 46)*(g - 1)
Let u(c) be the second derivative of -c**6/120 + 59*c**5/80 - 43*c**4/2 + 1079*c**3/6 + 676*c**2 + 3789*c. Suppose u(n) = 0. Calculate n.
-1, 8, 26
Let g = 112/27 - 22/27. Let z = -4522/3 + 1508. Factor -g*x**2 - z*x**3 - 2*x + 6.
-2*(x - 1)*(x + 3)**2/3
Let s = -16361/2 + 8181. Factor -1/2*q - 1 + s*q**2.
(q - 2)*(q + 1)/2
Let i(z) be the first derivative of -z**5/40 + 7*z**4/32 + 19*z**3/8 + 45*z**2/16 - 27*z/2 - 1727. Determine d, given that i(d) = 0.
-3, 1, 12
Let y = -69/3019 + 67315/39247. Determine c so that -2/13*c**4 - 20/13 + y*c**2 + 6/13*c - 6/13*c**3 = 0.
-5, -1, 1, 2
Let h(n) be the third derivative of 17/60*n**6 - 4/3*n**3 + 13/30*n**5 - 1/84*n**8 + 0*n - 47 - 2*n**2 - 1/4*n**4 + 1/35*n**7. Solve h(p) = 0.
-1, 1/2, 4
Let s = 7461 - 14913/2. Factor 27/2 - s*o - 12*o**2 + 6*o**3.
3*(o + 1)*(2*o - 3)**2/2
Suppose 0 = -m + 4*u + 39, 3*m - 5*m = -u - 43. What is t in 3*t**3 + 15*t**2 + 9*t + 13*t + m*t - 23*t = 0?
-3, -2, 0
Let m(h) be the third derivative of 0*h**5 - 1/180*h**6 - 9*h**2 + 0*h + h**3 + 0 + 1/3*h**4. Let g(t) be the first derivative of m(t). Factor g(b).
-2*(b - 2)*(b + 2)
Let q be (-1*(405/(-3))/9)/3. Let d(z) be the second derivative of -z**q + 1/6*z**6 - 7*z + 25/12*z**4 + 0*z**2 + 0 - 5/3*z**3. Factor d(m).
5*m*(m - 2)*(m - 1)**2
Let a(i) be the first derivative of 16/11*i + 151 + 2/55*i**5 - 2/11*i**3 + 2/11*i**4 - 10/11*i**2. What is h in a(h) = 0?
-4, -2, 1
Let s(y) = -9*y**2 - 55*y + 4. Let r be s(-5). Suppose 0 = 45*v - r*v + 36. Solve 0*k + 1/5*k**v + 4/5*k**3 + 4/5*k**2 + 0 = 0 for k.
-2, 0
Let f(g) = g**3 + 6*g**2 + g + 50. Let a be f(-7). Let h be (-408)/119 + (0 - a - 2). Factor -1/7 + h*n**2 + 3/7*n.
(n + 1)*(4*n - 1)/7
Let j(u) be the third derivative of -1/12*u**4 + 2*u + 7/24*u**3 + 1/240*u**5 - 17*u**2 + 0. Determine f, given that j(f) = 0.
1, 7
Let o = 619/465 + 1/465. Let z(h) be the third derivative of -h**5 - o*h**4 + 0 + 2*h**3 - 20*h**2 - 2/15*h**6 + 0*h. Factor z(c).
-4*(c + 1)*(c + 3)*(4*c - 1)
Let r = -3983/288 - -251/18. Let o(q) be the third derivative of 1/4*q**3 + 14*q**2 + 1/40*q**5 - 1/480*q**6 - r*q**4 + 0*q + 0. Factor o(j).
-(j - 3)*(j - 2)*(j - 1)/4
Let o(j) be the third derivative of -1/315*j**7 + 0*j - 14/9*j**3 - 1/2*j**5 + 17/180*j**6 + 43/36*j**4 + 0 + 119*j**2. Suppose o(x) = 0. Calculate x.
1, 14
Let s be -6 - (5 - 57281/63). Let m = s - 898. Determine g, given that m*g**2 - 16/3*g + 32 = 0.
12
Suppose 0 = 20*b + 12104 - 12204. Let z(r) be the first derivative of -19 + 2/35*r**b - 12/7*r**2 + 1/7*r**4 - 22/21*r**3 + 72/7*r. Factor z(i).
2*(i - 2)**2*(i + 3)**2/7
Suppose 5*u + 93 = 2*u. Let t = -29 - u. Factor 3*s**4 - 18*s**3 + 12*s**2 - 8*s**t + 11*s**2.
3*s**2*(s - 5)*(s - 1)
Let f(g) be the first derivative of g**4/2 - 79*g**3/15 - 104*g**2/5 - 4*g - 1151. Factor f(l).
(l - 10)*(l + 2)*(10*l + 1)/5
Let o(g) be the first derivative of g**5/80 - g**4/24 - g**3/24 + g**2/4 + 197*g - 267. Let k(r) be the first derivative of o(r). Factor k(i).
(i - 2)*(i - 1)*(i + 1)/4
Let r(g) be the first derivative of -g**3/3 - 62*g**2 + 512*g + 3087. Factor r(k).
-(k - 4)*(k + 128)
Let j be ((-96)/9)/4*279/(-372). Factor 3 + 45/4*t**j - 21/4*t**3 - 39/4*t + 3/4*t**4.
3*(t - 4)*(t - 1)**3/4
Determine v, given that -95/4*v**2 - 13*v - 33/4*v**3 + 11/4*v**4 + 1/4*v**5 + 0 = 0.
-13, -1, 0, 4
What is j in 0*j + 50/3*j**4 - 116/3*j**3 + 0 + 0*j**2 + 4/3*j**5 = 0?
-29/2, 0, 2
Let x be (0*3/(-6))/((-3)/(-3)). Suppose -5*l + 2*l + 21 = x. Factor 2*y**3 + 7 + 13*y**3 - 10*y**4 - 5*y**5 + 20*y**2 - l - 20*y.
-5*y*(y - 1)**2*(y + 2)**2
Let f = 28118 + -84352/3. Let c(t) be the first derivative of -t**2 + 1/6*t**3 + f*t + 5/24*t**4 - 14. Determine g, given that c(g) = 0.
-2, 2/5, 1
Let s be (243585/(-33))/5 - 1. Let k = 1478 + s. Factor -2/11*y**2 + 8/11*y - k.
-2*(y - 2)**2/11
Factor -365*d**3 + 45*d**4 - 244 - 550*d + 215*d + 274 + 625*d**2.
5*(d - 6)*(d - 1)**2*(9*d - 1)
Factor -3/8*u**2 - 25/8*u - 21/8 + 1/8*u**3.
(u - 7)*(u + 1)*(u + 3)/8
Suppose -32 + 16 = -2*s. Suppose -f = -s*f + 28. Find w, given that 2*w**4 + 2*w**3 - 24*w + f*w**3 - 16 + 1881*w**2 - 1885*w**2 = 0.
-2, -1, 2
Factor -6*s**3 - 44853*s + 312 + 44777*s - 48*s**2 + 10*s**3.
4*(s - 13)*(s - 2)*(s + 3)
Let a(k) = 12*k**2 - 116*k + 1682. Let q(x) = 30*x - 49*x + 2*x**2 + 19*x. Let u(p) = 2*a(p) - 10*q(p). Factor u(o).
4*(o - 29)**2
Let g(y) be the second derivative of -13*y**4/20 - 227*y**3/5 + 21*y**2/2 - 2002*y. Factor g(v).
-3*(v + 35)*(13*v - 1)/5
Let z(p) = -p**2 + 16*p + 62. Let h be z(19). Let j(b) = -207*b**2 + 427*b + 19. Let c(y) = -723*y**2 + 1494*y + 66. Let w(s) = h*c(s) - 18*j(s). Factor w(x).
3*(x - 2)*(37*x + 2)
Let -17*x**2 - 434*x + 264*x + 12*x**2 - 165 = 0. What is x?
-33, -1
Let p(m) be the first derivative of 7*m**4/26 + 170*m**3/39 + 152*m**2/13 + 40*m/13 - 2550. Solve p(f) = 0 for f.
-10, -2, -1/7
Let q(k) be the third derivative of k**7/175 + 53*k**6/200 + 61*k**5/50 + 6*k**4/5 + 2*k**2 - 247*k. What is i in q(i) = 0?
-24, -2, -1/2, 0
Let g = -386 - -390. Factor -14*z**3 + 9*z**2 + 77*z**3 - g*z**4 - 27*z**3 - z**3.
-z**2*(z - 9)*(4*z + 1)
Let y(i) be the second derivative of -3*i**5/100 + 3*i**4/4 + 33*i**3/10 + 51*i**2/10 - 31*i - 10. Solve y(t) = 0 for t.
-1, 17
Let 6/7*g**4 + 0 + 4875/7*g + 360/7*g**3 - 2550/7*g**2 - 3/7*g**5 = 0. Calculate g.
-13, 0, 5
Let o(h) be the first derivative of -h**4/14 - 22*h**3/21 - 18*h**2/7 - 442. Factor o(y).
-2*y*(y + 2)*(y + 9)/7
Let h be 12/(-30)*360/18. Let m be (-4 - -1) + (-27)/(72/h). Factor m*k + 1/5*k**3 + 0 + 1/5*k**2.
k**2*(k + 1)/5
Let r be (-4716)/(-1548) - ((-196)/301)/(-14). Suppose -10/13*o - 6/13 - 2/13*o**2 + 2/13*o**r = 0. What is o?
-1, 3
Let n(g) be the third derivative of 0*g**6 + 0*g**3 + 1/30*g**4 - 1/50*g**5 + 1/525*g**7 + 62*g**2 + 0*g + 0. Determine j so that n(j) = 0.
-2, 0, 1
Let t(v) = -9*v**2 + 1998*v - 994041. Let w(m) = 2*m**2 - m + 8. Let o(s) = -5*t(s) - 20*w(s). Solve o(h) = 0.
997
Let n(q) be the first derivative of 2*q**5/25 - 73*q**4/10 + 542*q**3/15 + 69*q**2 + 7760. Factor n(o).
2*o*(o - 69)*(o - 5)*(o + 1)/5
Factor -1125/4*f + 0 - 3*f**2.
-3*f*(4*f + 375)/4
Let v be 6/63*(-168)/(-32). Let t = 6/23 + 11/46. Factor 3/2*d**2 - t*d - 1/2*d**4 + v*d**3 - 1.
-(d - 2)*(d - 1)*(d + 1)**2/2
Let p(x) be the third derivative of x**5/20 + 29*x**4/4 + 441*x**3/2 + 505*x**2 - 4. Factor p(a).
3*(a + 9)*(a + 49)
Let s be (-1)/12*(-3654)/3045. Factor -s*v**3 + 0 - 11/10*v - 6/5*v**2.
-v*(v + 1)*(v + 11)/10
Let x(w) = -w**2 + 2*w - 1. Let v(k) be the third derivative of -2*k**5/15 + 2*k**4/3 + 2*k**3 - 8*k**2 + 3. Let t(f) = -v(f) + 3*x(f). Factor t(j).
5*(j - 3)*(j + 1)
Let w(m) = -685*m**2 - 2 + 0*m + 2*m**3 + m + 686*m**2. Let s(k) = 15*k**3 - 2*k**2 + 6*k - 5. Let g(z) = 5*s(z) - 35*w(z). Let g(j) = 0. Calculate j.
-1, 1, 9
Let u(s) = -s**2 + 11*s - 7. Let l be u(10). Let k = -264 - -266. Determine h, given that 20*h**3 + 7*h + 14*h + 9 + 18*h**2 - 17*h**l - 3*h**k = 0.
-3, -1
Solve 193*z - 208*z + z**2 + z**4 + 8*z**2 + 2*z**4 - 12 + 15*z**3 = 0 for z.
-4, -1, 1
Let b(l) be the second derivative of -4/35*l**5 + 3/14*l**4 + 27/7*l**2 + 2*l + 19 + 27/14*l**3 - 4/105*l**6 - 1/294*l**7. Factor b(p).
-(p - 2)*(p + 1)*(p + 3)**3/7
Let g(t) be the third derivative of -5/27*t**3 - 1/27*t**4 - 80*t**2 + 1/270*t**5 + 0 + 0*t. Factor g(z).
2*(z - 5)*(z + 1)/9
Let u = 1084 + -1084. Let w(v) be the third derivative of 1/420*v**7 + 10*v**2 + 0*v + u*v**4 + 1/672*v**8 - 1/120*v**5 + 0 - 1/240*v**6 + 0*v**3. Factor w(h).
h**2*(h - 1)*(h + 1)**2/2
Let j be -38 + 64 + -15 + -8. Factor 1/4*l**5 + 0 + 25/4*l**2 + 0*l + 11/4*l**4 + 35/4*l**j.
l**2*(l + 1)*(l + 5)**2/4
Let l = -18438 + 18442. Let u(h) be the second derivative of 1/66*h**l + 2/11*h**2 - 1/11*h**3 + 21*h + 0. Let u(d) = 0. What is d?
1, 2
Suppose -435*m + 420*m + 30 = 0. Let r be 28*(-35)/(-60) - m/(-3). Let 106/5*d**2 + r*d + 13/5*d**4 + 58/5*d**3 + 5 + 1/5*d**5 = 0. Calculate d.
-5, -1
Factor 1/4*l**2 - 230 - 229/2*l.
(l - 460)*(l + 2)/4
Let x = 9749/7620 + -56/1905. Factor g**2 + 1/4*g**5 + x*g**4 + 0 + 2*g**3 + 0*g.
g**2*(g 