 be the second derivative of -z**4/36 + 8*z**3/3 - 152*z. Factor a(t).
-t*(t - 48)/3
Let p(w) be the second derivative of -w**4/42 - 8*w**3/21 - 15*w**2/7 + 94*w. Determine s, given that p(s) = 0.
-5, -3
Let n be 5/(-6) - (-16 - 79/(-6)). Factor 4/7*p**2 - 10/7*p**4 + 12/7*p**3 + 6/7 - n*p + 2/7*p**5.
2*(p - 3)*(p - 1)**3*(p + 1)/7
Let w = 170 - 167. Factor -10 - 4*h**3 + 0*h**3 - 20*h**2 + 0*h**w + 25*h + 9*h**3.
5*(h - 2)*(h - 1)**2
Let b be 256/6*(-12)/(-21) - 0. Let i = b - 68/3. Factor 0 - 8/7*n**4 - 2/7*n**5 - i*n**3 - 8/7*n**2 - 2/7*n.
-2*n*(n + 1)**4/7
Suppose 27*a = 18*a + 27. Let m(t) be the first derivative of -49/18*t**6 - 4/3*t + 73/12*t**4 + 7/5*t**5 - 17/9*t**a - 4*t**2 - 8. Solve m(l) = 0 for l.
-1, -2/7, 1
Let 1/2*o**3 + 0*o + 7/2*o**2 + 0 = 0. Calculate o.
-7, 0
Let i(t) = t**3 - 16*t**2 + 15*t - 9. Let p be i(15). Let h be 8/3 + 6/p. Let -18*w - 12*w - 18*w - 6*w**h + 45*w = 0. Calculate w.
-1/2, 0
Let c(n) be the third derivative of -n**8/1680 + 2*n**7/105 - 4*n**6/15 + 32*n**5/15 - 32*n**4/3 + 512*n**3/15 + 123*n**2. Suppose c(s) = 0. Calculate s.
4
Suppose 0 = -18*v + 17*v + 1. Let h be (-34)/(-72) - v/4. Factor 0 + 4/9*r**3 + 0*r + h*r**4 + 2/9*r**2.
2*r**2*(r + 1)**2/9
Let f(h) be the third derivative of -2*h**7/525 + h**6/75 + 7*h**5/75 + 2*h**4/15 - 76*h**2. Find d, given that f(d) = 0.
-1, 0, 4
Suppose -5*u + 7 + 3 = 0. Let d = 65162 - 65160. Let 1/2*z**3 + d - 3/2*z**u + 0*z = 0. Calculate z.
-1, 2
Let s be 343/28 - (-13 - -24). Let c(q) be the second derivative of -s*q**4 - 6*q**2 + 6*q + 4*q**3 + 3/20*q**5 + 0. Factor c(m).
3*(m - 2)**2*(m - 1)
Let n(u) be the second derivative of 169*u**4/28 - 104*u**3/7 + 96*u**2/7 + 51*u + 2. Factor n(c).
3*(13*c - 8)**2/7
Let k(m) be the third derivative of -m**5/150 + 10*m**4/3 - 2000*m**3/3 - 27*m**2 + 5*m. Find n such that k(n) = 0.
100
Let y(m) be the second derivative of 3/4*m**4 - 9/20*m**5 + 1/10*m**6 + 0 + 0*m**2 - 1/2*m**3 - 15*m. Factor y(p).
3*p*(p - 1)**3
Suppose -16 = -z - z + 4*j, 4*z = -4*j - 4. Suppose -5*n + 5*k + 20 = 0, -2*k + 4*k + 17 = 5*n. Solve t**z + t - t + 0*t**3 + t**n = 0 for t.
-1, 0
Let r = -51 - -55. Suppose -o - 4 = 0, 0 = -r*b + 2*o + 3 + 13. Factor 2/11*y + 2/11 - 4/11*y**b.
-2*(y - 1)*(2*y + 1)/11
Let v(w) be the third derivative of 7*w**6/180 - 5*w**5/3 - 17*w**4/7 - 88*w**3/63 - 101*w**2. Factor v(a).
2*(a - 22)*(7*a + 2)**2/21
Let s be ((-1431)/90)/((-2)/4). Let j = -31 + s. Find a, given that j + 2/5*a**2 - 6/5*a = 0.
1, 2
Factor -5*x**4 + 72*x**3 - 125 + 718*x**2 - 1066*x**2 + 608*x - 67.
-(x - 6)*(x - 4)**2*(5*x - 2)
Suppose 0 = 4*n, 0 = -4*s - s + n + 70. Let k be (-1184)/(-28) - 4/s. Find t such that -t**3 + k - t**4 - 42 = 0.
-1, 0
Suppose 13*y = -37*y. Let p(f) be the second derivative of 0*f**2 - 1/15*f**6 + 1/3*f**4 - 1/10*f**5 + y + 0*f**3 - 3*f. Factor p(s).
-2*s**2*(s - 1)*(s + 2)
Let y(v) be the first derivative of 3*v**5/20 - 15*v**4/16 - 2*v**3 + 9*v**2/2 - 418. Suppose y(z) = 0. Calculate z.
-2, 0, 1, 6
Let b(a) = -2*a - 15. Let y be b(-8). Let w be -6*(-1 - y/(-2)). Let -3*s**2 + 3*s**4 - 9*s**4 + 0*s**4 + 3*s**4 + 6*s**w = 0. What is s?
0, 1
Let d = -53/20 + 17/5. Let r(h) be the first derivative of 12/5*h**3 + 5 + 0*h - d*h**4 - 6/5*h**2. Factor r(o).
-3*o*(o - 2)*(5*o - 2)/5
Factor -2*v**4 + 8*v**3 - 4*v**4 + v**5 - 11560 + 11560.
v**3*(v - 4)*(v - 2)
Let m be -1 + 63/18*6/12. Factor m*s**5 + 0 + 243/4*s - 9*s**4 - 81*s**2 + 81/2*s**3.
3*s*(s - 3)**4/4
Let z(x) be the second derivative of x**5/60 + x**4/8 - 2*x**3/3 + 10*x**2 + 8*x + 3. Let n(t) be the first derivative of z(t). Solve n(r) = 0 for r.
-4, 1
Let f(n) be the third derivative of n**9/635040 + n**8/105840 + n**5/20 + 16*n**2. Let u(j) be the third derivative of f(j). Let u(h) = 0. Calculate h.
-2, 0
Let i(l) be the second derivative of l**7/840 - l**6/72 + 7*l**5/120 - l**4/8 - 11*l**3/6 - 17*l. Let n(w) be the second derivative of i(w). Factor n(z).
(z - 3)*(z - 1)**2
Let i be 3/18 - (-1346)/4740. Let q = i - 4/79. Solve 6/5*k**3 - 4/5*k**2 + 0 - q*k**5 + 0*k + 0*k**4 = 0 for k.
-2, 0, 1
Let g = 2085 - 125099/60. Let y(r) be the third derivative of 1/315*r**7 + 0*r + 1/12*r**4 - 2/9*r**3 - g*r**6 + 0 + 1/90*r**5 - 7*r**2. Factor y(n).
2*(n - 2)*(n - 1)**2*(n + 1)/3
Let c(l) be the second derivative of l**8/3920 - l**7/1960 - l**6/168 - 3*l**5/280 - l**3/2 - 19*l. Let n(w) be the second derivative of c(w). Factor n(v).
3*v*(v - 3)*(v + 1)**2/7
Suppose -2*z + 6 = f - z, f - 10 = -2*z. Suppose -6*x = f*x - 9*x. Factor 3/5*y**2 + x + 3/5*y.
3*y*(y + 1)/5
Suppose -9*k - 5 = 13. Let y(z) = 2 + 2*z**2 - 3*z**2 - 1. Let t(n) = -2*n**2 + 2*n + 4. Let a(l) = k*t(l) + 6*y(l). Let a(x) = 0. Calculate x.
-1
Let c(b) = 2 + 12*b + 5 - 8 - 2*b**2. Let x be c(5). Solve x - 3*m**2 + 0*m**2 - 6*m + 0*m**2 = 0 for m.
-3, 1
What is a in -263*a**2 + 607*a**2 + 1338*a**2 - 42*a + 1 + 7 + 274*a = 0?
-2/29
Let u(p) be the first derivative of p**8/1120 + p**7/140 + p**6/80 - 23*p**3/3 - 41. Let i(a) be the third derivative of u(a). Determine b so that i(b) = 0.
-3, -1, 0
Suppose 0 = -9*t + 7*t. Suppose t = -0*z + 5*z - 10. Suppose 10*f**3 - 4*f - 10*f**3 - z*f**3 - 3*f**2 - 3*f**2 = 0. What is f?
-2, -1, 0
Let q be 222/42 - 2/7. Suppose q*z - 14 = 3*w, 4 + 1 = 2*z - w. Let -1 + 6*f**2 - 3*f**5 + 9*f**3 + z + 0*f**5 = 0. What is f?
-1, 0, 2
Suppose -80 = -t + 59. Let h = t - 137. Find l such that 5/6*l + 1/6 + 2/3*l**h = 0.
-1, -1/4
Let f = -13 - -19. Factor -36*d**4 + 34*d**4 + f*d**3 - 4*d**3.
-2*d**3*(d - 1)
Let i = 251 - 248. Suppose 4 = -4*h, 0 = 3*u - u + h + 1. Factor u*r**2 + 2/5*r**i + 0 - 2/5*r.
2*r*(r - 1)*(r + 1)/5
Let y(g) = 6*g**2 - 2 + 10*g - g**3 - 2*g + 3 - 6. Let z be y(7). Factor -4/7 - 6/7*u - 2/7*u**z.
-2*(u + 1)*(u + 2)/7
Let s be (-3)/6*6 + -4. Let t(r) = r**3 + 8*r**2 + 6*r - 1. Let v be t(s). Factor -5*w + w**3 - 2*w + v*w - w**2 + 0*w**3 + w**4.
w*(w - 1)*(w + 1)**2
Let l(y) be the first derivative of -16*y**4 - 160*y**3/3 - 66*y**2 - 36*y - 574. Determine h, given that l(h) = 0.
-1, -3/4
Let z(b) be the first derivative of 2*b**3/3 - 22*b**2 + 433. Factor z(i).
2*i*(i - 22)
Suppose -2*m - 20 = 5*k, -2*m = 3*k + 3*m + 31. Let q be (-2 + 6)*(-1)/k. Factor -4*f + 4/3*f**q + 8/3.
4*(f - 2)*(f - 1)/3
Determine c, given that 71*c**2 - 37*c**2 + 80 - 17*c - 23*c - 29*c**2 = 0.
4
Let q(x) be the second derivative of -17*x**7/3780 + 19*x**6/1080 - x**5/90 + x**4/6 + 3*x. Let s(w) be the third derivative of q(w). Factor s(l).
-2*(l - 1)*(17*l - 2)/3
Let v(z) be the third derivative of z**7/420 + z**6/60 - 7*z**5/120 - 11*z**4/24 + 2*z**3 + 3*z**2 - 41. Find b, given that v(b) = 0.
-4, -3, 1, 2
Let j = -9484/3 + 3164. Solve -8/3*x**2 + 2/3*x**3 + 0 + j*x = 0 for x.
0, 2
Suppose -5*w - 5*c = -205 + 165, 0 = -w + c - 4. Solve 0 - 5/2*i**3 + 5/2*i + i**w - i**4 = 0 for i.
-5/2, -1, 0, 1
Let q = -2/55 + 71/440. Let p(b) be the third derivative of -q*b**4 - 4*b**2 - 1/280*b**7 - 1/8*b**3 + 0 + 0*b - 3/40*b**5 - 1/40*b**6. Solve p(l) = 0.
-1
Factor -1/2*p**3 + 1/2*p**5 - 7/2*p**2 + 7/2*p**4 + 0*p + 0.
p**2*(p - 1)*(p + 1)*(p + 7)/2
Let z = -2/133579 - -1736543/1068632. What is p in -z*p**2 + 1/2 - 1/4*p**3 + p + 3/8*p**4 = 0?
-2, -1/3, 1, 2
Let w(c) be the third derivative of c**6/420 - 4*c**5/35 - 27*c**4/28 + 2*c**2 + 88*c. Let w(j) = 0. What is j?
-3, 0, 27
Suppose 0 = -z - 4*z. Factor z + 16*o**2 + 5*o**5 - 10*o**4 + 0 - 5*o - 6*o**2.
5*o*(o - 1)**3*(o + 1)
Let 0*y - 58/7*y**3 + 0 - 32/7*y**4 - 2/7*y**5 - 4*y**2 = 0. Calculate y.
-14, -1, 0
Let x = 325/9 - 322/9. Suppose 0*f + 0 - f**2 + x*f**3 = 0. Calculate f.
0, 3
Let q(r) be the third derivative of 5*r**6/12 + r**5/15 - r**2 - 44. Factor q(y).
2*y**2*(25*y + 2)
Suppose -2*f + 6 = f. Suppose -2*j + 14 = 2*t, -j - f = 3*t - 13. Factor -1 - 3*m**2 - t*m**2 + m**2 - 2*m + 3*m**2.
-(m + 1)**2
Suppose 2/3*k**2 + 16 + 20/3*k = 0. What is k?
-6, -4
Let r(x) be the first derivative of -x**4/10 - 8*x**3/15 - x**2 - 4*x/5 - 37. Factor r(y).
-2*(y + 1)**2*(y + 2)/5
Let h = -76 + 81. Let q be (h/(-25)*0)/1. Factor 1/4*p**2 - 1/4*p + q.
p*(p - 1)/4
Suppose -2003*s + 2009*s = 24. Factor 6*t**2 - 18/7*t - 30/7*t**3 + 0 + 6/7*t**s.
6*t*(t - 3)*(t - 1)**2/7
Let y(z) be the first derivative of z**8/840 - z**7/105 - z**6/60 + 3*z**