**3 + 6*s**3 - 24*s**3 + 28 - 165*s**2 + 12.
-5*(s + 1)*(s + 4)*(7*s - 2)
Let z(t) be the third derivative of t**6/840 + 43*t**5/84 + 11663*t**4/168 + 11449*t**3/42 + 949*t**2. Factor z(i).
(i + 1)*(i + 107)**2/7
Solve 0 + 1/4*n**4 + 12*n**2 + 9*n + 13/4*n**3 = 0.
-6, -1, 0
Suppose 10*r = 3*r + 273. Suppose 1 = v - 1. Find b such that -r*b + 7*b - 66 + 4*b**2 + 2 - 8*b**v = 0.
-4
Let a(b) be the third derivative of -b**8/1512 - b**7/135 - b**6/36 - 13*b**5/270 - b**4/27 + 919*b**2. Solve a(g) = 0.
-4, -1, 0
Let j(s) = 2*s + 11. Let g be j(-4). Determine z, given that 0*z**3 - 5*z**3 + 4 + 6*z**3 + g*z**4 - 9*z**2 - z**4 - 4*z = 0.
-2, -1, 1/2, 2
Suppose 0 = -8*l + 7*l - 6. Let u(p) = 4*p**2 - 11*p + 16. Let k(z) = -9*z**2 + 23*z - 32. Let r(d) = l*k(d) - 14*u(d). Suppose r(o) = 0. Calculate o.
4
Let r be 5 - ((-52)/12)/(-1). Suppose 2*c - 3*g = 5 - 1, -8 = -4*c - 3*g. Solve 0 + 2/3*l**c + r*l**3 + 0*l = 0.
-1, 0
Let d(m) = -4*m**2 - 267*m - 196. Let u be d(-66). Factor -8/3*c + 8/3*c**3 - 4/3 + 4/3*c**4 + 0*c**u.
4*(c - 1)*(c + 1)**3/3
Let s = 15181/4 - 3795. Suppose 0 + 2*m**2 + 3/4*m**3 - 1/2*m**4 - s*m**5 + m = 0. Calculate m.
-2, -1, 0, 2
Let u = -51 - -62. Let z = u + -43/4. Find v such that -1/4*v + 1/4*v**2 - z*v**4 + 0 + 1/4*v**3 = 0.
-1, 0, 1
Let i(x) be the second derivative of -54*x**7/7 - 1158*x**6/5 - 2096*x**5 - 4168*x**4 - 2720*x**3 - 800*x**2 - 73*x + 2. Find j such that i(j) = 0.
-10, -1, -2/9
Let b(z) = z**3 - 2*z**2 - 3*z + 3. Suppose 4*r + 9 = 3*v, 5*r - 1 + 16 = 5*v. Let n be b(v). What is p in -p**3 + 2*p**3 - 7*p**n + 3*p**3 = 0?
0
Find w, given that -3/7*w**5 - 423/7*w**3 - 30*w**2 + 0*w + 0 - 216/7*w**4 = 0.
-70, -1, 0
Let s(c) be the third derivative of c**6/450 - c**5/75 + c**4/30 + c**3/6 - 16*c**2. Let v(z) be the first derivative of s(z). Suppose v(l) = 0. What is l?
1
Let d be -2*2/12*2/(-8). Let x(k) be the second derivative of 0 + 1/42*k**7 - 1/20*k**5 + 0*k**3 - k - d*k**4 + 1/30*k**6 + 0*k**2. Solve x(t) = 0 for t.
-1, 0, 1
Determine o, given that 45*o**2 + 0 + 0*o + 5/3*o**3 = 0.
-27, 0
Suppose -5*q + 23 = -2. Suppose -q*k**4 + 17*k**2 - 11*k**2 + 3*k**4 + 2*k**3 - 10*k + 4 = 0. Calculate k.
-2, 1
Let w(u) be the second derivative of 3*u**5/80 + u**4/16 - u**3/2 - 3*u**2/2 - 21*u - 7. Solve w(h) = 0.
-2, -1, 2
Suppose 88/5*o - 12*o**2 - 48/5 + 18/5*o**3 - 2/5*o**4 = 0. What is o?
2, 3
Let s = 30 + -34. Let c(x) = 8*x**3 - 10*x**2 + 8*x - 2. Let u(w) = -15*w**3 + 20*w**2 - 16*w + 4. Let v(g) = s*u(g) - 7*c(g). Factor v(n).
2*(n - 1)**2*(2*n - 1)
Let k = -66 + 261. Factor k*v**3 - 210*v**4 - 84*v**2 + 12*v + 75*v**5 - 26*v**3 + 38*v**3.
3*v*(v - 1)**2*(5*v - 2)**2
Factor 83*w**2 - 2*w - 43*w**2 + 2*w - 44*w**2 + 2*w**4 + 2*w**3.
2*w**2*(w - 1)*(w + 2)
Let w = -932/1105 - 15366236/7735. Let b = 1992 + w. Factor -b + 16/7*v - 2/7*v**2.
-2*(v - 4)**2/7
Solve -10/11*n**2 - 2/11*n**3 + 0 - 12/11*n = 0.
-3, -2, 0
Let i(c) be the second derivative of 3/40*c**5 - 3/2*c**2 + 5*c + 0 - 9/8*c**4 - 9/4*c**3 + 3/20*c**6. Suppose i(x) = 0. What is x?
-1, -1/3, 2
Let l(x) be the first derivative of -3*x**5/10 - 9*x**4/8 - x**3 - 76. Suppose l(a) = 0. Calculate a.
-2, -1, 0
Let p = 324 - 1295/4. Suppose 1/4*x + 1/4*x**2 - p - 1/4*x**3 = 0. What is x?
-1, 1
Let 1/8*s**4 + 0 + 15/8*s**3 + 17/8*s - 33/8*s**2 = 0. What is s?
-17, 0, 1
Let l(w) = 4*w**4 - 10*w**3 - 8*w**2 + 54*w + 36. Let k be 4/10 - (-56)/(-40). Let s(j) = -j**3 - j. Let z(m) = k*l(m) - 6*s(m). Determine o so that z(o) = 0.
-1, 3
Let d(o) be the third derivative of 0*o + 0 + 0*o**3 - 3*o**2 + 0*o**5 + 1/210*o**6 - 1/42*o**4. Factor d(b).
4*b*(b - 1)*(b + 1)/7
Let m(r) be the third derivative of r**5/60 + r**4/24 - r**3/6 + 19*r**2. Let p(c) = -c**3 + 7*c**2 + 7*c - 7. Let j(s) = -35*m(s) + 5*p(s). Factor j(a).
-5*a**3
Suppose -o + 7 = 2*y + 1, -3*o = -4*y + 2. Factor 1 + 7*s**2 + 6*s**2 - 16*s + 3 - s**o.
4*(s - 1)*(3*s - 1)
Let p(u) = u - 2. Let f be p(10). Let g be (27/24)/(12/f). Suppose -g - 1/2*r + 1/4*r**2 = 0. What is r?
-1, 3
Let p(j) be the first derivative of j**6/120 + j**5/20 + j**4/8 - 4*j**3/3 - 12. Let h(q) be the third derivative of p(q). Factor h(z).
3*(z + 1)**2
Suppose 5*y + 10 = 45. Let i(w) be the second derivative of 1/15*w**6 + 4/3*w**3 - 4*w**2 + 0 - 2/5*w**5 + 1/2*w**4 + y*w. Factor i(c).
2*(c - 2)**2*(c - 1)*(c + 1)
Determine b so that -13/6*b**2 - 2*b + 0 - 1/6*b**3 = 0.
-12, -1, 0
Let c(y) = 3*y**3 + 2*y**2 - 3*y. Let x(z) = 7*z**3 + 5*z**2 - 6*z + 1. Let l(s) = -10*c(s) + 4*x(s). Factor l(o).
-2*(o - 2)*(o + 1)**2
Let v(b) be the second derivative of 2*b**2 + 0 - b**3 + 28*b + 1/6*b**4. What is h in v(h) = 0?
1, 2
Let n(h) be the second derivative of -h**7/21 - 14*h**6/15 - 16*h**5/5 + 64*h**4/3 + 7*h + 6. Factor n(y).
-2*y**2*(y - 2)*(y + 8)**2
Determine x so that 2/5*x**3 + 3/5*x**2 - 18/5*x - 1/10*x**4 + 27/10 = 0.
-3, 1, 3
Let y(f) = -3*f**2 - 10*f + 1. Let w be (-66)/48 + 3/8. Let a(z) = -z + 1. Let o(p) = w*y(p) + a(p). Determine g, given that o(g) = 0.
-3, 0
Suppose 0 = 5*q - 2*q - 15. Let h(i) = 12*i**2 - 22*i - 12. Let n(y) = -11*y**2 + 21*y + 11. Let j(l) = q*h(l) + 6*n(l). Factor j(d).
-2*(d - 3)*(3*d + 1)
Let u = -1092 + 3278/3. Let x(q) be the first derivative of 5/3*q**2 - 4/3*q - u*q**3 - 1. Suppose x(h) = 0. Calculate h.
2/3, 1
Let g(s) = -s**2 + 26*s - 163. Let l be g(11). Factor -6/5 + 3/5*c**l + 3/5*c.
3*(c - 1)*(c + 2)/5
Let q(a) be the first derivative of 0*a**4 + 13 + 0*a**2 - 1/15*a**5 + 0*a + 0*a**3. Let q(f) = 0. What is f?
0
Let o(v) be the first derivative of -7*v**3/6 - 15*v**2/2 - 4*v - 104. Suppose o(u) = 0. Calculate u.
-4, -2/7
Let p(k) = -k**2 + 9*k - 6. Let n be p(1). Factor 888*v - 2*v**3 - 888*v + 0*v**3 + v**n.
-v**2*(2*v - 1)
Factor 119*p**2 - 4*p**3 - 4232 + 268*p - 796*p + 57*p**2 - 1220*p.
-4*(p - 23)**2*(p + 2)
Let t(m) = 4*m**3 - 35*m**2 + 137*m + 5. Let l be t(5). Determine k, given that 12 - 102*k + 375/2*k**4 + l*k**2 - 825/2*k**3 = 0.
2/5, 1
Let z(i) = -2*i**3 + 84*i**2 + 177*i - 44. Let y be z(44). Let -6/7*o**2 - 4/7*o**3 + 2/7 + y*o = 0. Calculate o.
-1, 1/2
Suppose -t = 3 - 6. Suppose -a = -2*m + a, t*m - 2*a = 3. Determine g, given that -3*g**m - 5*g**2 + 3*g**3 + g**3 + g + 3*g**3 = 0.
0, 1/4, 1
Let i(h) = 34*h - 12. Let y(n) = n**2 + 2*n. Let w(j) = 2*i(j) + 18*y(j). Determine k, given that w(k) = 0.
-6, 2/9
Let b = 55786/5 - 11053. Let j = 106 - b. Factor 3/5*p + 1/5*p**3 + j - p**2.
(p - 3)**2*(p + 1)/5
Let r be (-1)/28*-2*(4 + -2). Find q such that 12/7*q - r*q**2 - 36/7 = 0.
6
Let x = 22 - 13. Find i, given that -10*i - 64 - 11*i**3 + i**4 - x*i + i + 2*i + 36*i**2 = 0.
-1, 4
Let k(q) be the second derivative of -q**5/20 - 61*q**4/12 + 125*q**3/6 - 63*q**2/2 + 7*q + 14. Factor k(d).
-(d - 1)**2*(d + 63)
Factor -24*z - 6*z - 2*z**3 + 21*z**2 + 12 - 5*z**2 + 4*z.
-2*(z - 6)*(z - 1)**2
Let h(f) be the second derivative of f**7/56 + 3*f**6/20 + 3*f**5/10 - f**4/8 - 9*f**3/8 - 3*f**2/2 - 48*f - 2. Find a, given that h(a) = 0.
-4, -1, 1
Let c(w) = 498*w**2 - 273*w - 159. Let a(k) = -31*k**2 + 17*k + 10. Let n(b) = 33*a(b) + 2*c(b). Factor n(l).
-3*(l - 1)*(9*l + 4)
Let u(x) be the third derivative of 1/48*x**6 - 10*x**2 + 0 - 5/48*x**4 + 0*x - 5/336*x**7 + 7/160*x**5 + 1/12*x**3. Suppose u(y) = 0. Calculate y.
-1, 2/5, 1
Factor 388*b**2 - 391*b**2 - 467 - 167*b - 187 - 133*b + 66.
-3*(b + 2)*(b + 98)
Factor -11*n + 5*n**2 - 3*n**2 + n**2 - n - 44 + 29.
3*(n - 5)*(n + 1)
Let q(r) be the first derivative of -2/25*r**5 + 0*r**4 + 0*r**2 + 0*r**3 - 1/15*r**6 + 0*r - 2. Solve q(v) = 0.
-1, 0
Suppose 4*w + w - 137 = -4*r, -2*w = -4*r + 102. Suppose -r = 3*a - 7*a. Factor 3*t**4 - a*t**4 - 5*t**4 + 6*t**3 + 14*t**5 - 11*t**5.
3*t**3*(t - 2)*(t - 1)
Let d(p) be the second derivative of -p**4/54 + 5*p**3/9 + 16*p**2/9 + p + 133. Determine y so that d(y) = 0.
-1, 16
Let p = 21 + -6. Factor p*a + 7*a - 6*a + 29*a**2 - 25*a**2.
4*a*(a + 4)
Let n(y) be the third derivative of -7*y**6/120 + 11*y**5/60 + 7*y**4/24 - 11*y**3/6 - 4*y**2 - 2*y. Factor n(i).
-(i - 1)*(i + 1)*(7*i - 11)
Let f(k) be the second derivative of -k**4/6 + 2*k**3 + 3*k + 6. Suppose f(y) = 0. Calculate y.
0, 6
Factor -24*h**4 - 3*h**5 - 280*h**3 + 0*h**5 + 259*h**3.
-3*h**3*(h + 1)*(h + 7)
Let z(t) be the second derivative