
Let s(g) be the second derivative of -1/110*g**5 + 1/33*g**6 + 2/33*g**3 + 8/11*g**2 - 1/231*g**7 + 208*g - 13/66*g**4 + 0. Find l such that s(l) = 0.
-1, 1, 2, 4
Let m = -679278 + 29886059/44. Let f = 546/11 + m. Suppose f*o**2 - 1/4*o - 1/4 + 1/4*o**3 = 0. Calculate o.
-1, 1
Let v(o) = -9*o - 54. Let w be v(-6). Suppose 0*g = -2*g - 3*j, -2*g - j + 4 = w. Factor 0 - 4*h**g - 20/3*h**2 - 8/3*h.
-4*h*(h + 1)*(3*h + 2)/3
Let t(m) = m + 29. Let o(c) = -c**2 - 40*c - 283. Let w(j) = 5*o(j) - 10*t(j). Factor w(s).
-5*(s + 11)*(s + 31)
Let h(c) be the second derivative of c**7/98 + c**6/10 + 27*c**5/70 + 11*c**4/14 + 13*c**3/14 + 9*c**2/14 - 1717*c. Factor h(r).
3*(r + 1)**4*(r + 3)/7
Let v(h) = -5*h**4 - 19*h**3 - 85*h**2 - 91*h - 36. Let n(g) = 21*g**4 + 72*g**3 + 342*g**2 + 363*g + 144. Let r(u) = -2*n(u) - 9*v(u). Factor r(c).
3*(c + 1)**2*(c + 3)*(c + 4)
Let s = -123 + 113. Let m(p) = -3*p**2 - 30*p. Let z be m(s). Suppose -2/7*o + 2/7*o**3 - 1/7*o**4 + 1/7 + z*o**2 = 0. Calculate o.
-1, 1
Let -144/19*l + 72/19*l**3 - 32/19 + 10/19*l**4 + 94/19*l**2 = 0. What is l?
-4, -1/5, 1
Let m(o) be the first derivative of o**7/126 - o**6/45 - o**5/20 + 54*o + 80. Let r(q) be the first derivative of m(q). Determine u so that r(u) = 0.
-1, 0, 3
Suppose -m - 7 = -7*j + 4*j, 4*m + 1 = 3*j. Let g(i) be the first derivative of 10 - 2/9*i**j + 5/3*i**2 - 8/3*i. Solve g(c) = 0.
1, 4
Let i(q) = q**3 + q**2 - 2. Let j(a) = 5*a**3 - 45*a**2 + 60*a - 20. Suppose 5 = -307*r + 312*r. Let p(n) = r*j(n) - 10*i(n). Factor p(c).
-5*c*(c - 1)*(c + 12)
Let n be 6578/(-2990) + 4874/20. Find k such that -3/2*k**5 - 147/2 - 141*k**3 - 285*k**2 - n*k - 51/2*k**4 = 0.
-7, -1
Let u(x) be the first derivative of -2/9*x**3 + 1/6*x**4 + 0*x + 52 + 0*x**2. Factor u(a).
2*a**2*(a - 1)/3
Suppose 234*l**3 + 240*l**3 - 471*l**3 + 2061 + 399 + 3696*l + 1239*l**2 = 0. Calculate l.
-410, -2, -1
Let t(m) = -15*m - 88. Let n be t(-6). Factor -n*s + 34*s**2 + 2*s**3 - 48*s**2 + 14*s.
2*s*(s - 6)*(s - 1)
Suppose 40*y - 38 = 282. Suppose 3*o + 6 = z, 11*o = -3*z + y*o + 6. Suppose 0 - 1/6*s**4 + 0*s + 0*s**2 + 1/3*s**z = 0. What is s?
0, 2
Let o(t) = 2*t**3 - 4*t**2 + 4*t - 9. Let x be o(4). Let 195*p + p**2 - 237*p + 370 + x = 0. Calculate p.
21
Suppose 195*l - 5 = 196*l, -25 = -2*k + 5*l. Suppose 24/7*o**2 + 0 - 50/7*o**5 + 8/7*o**3 + k*o - 150/7*o**4 = 0. Calculate o.
-3, -2/5, 0, 2/5
Let s(o) = o**2 + 20*o + 24. Let y be s(-19). Let 66*n**4 + 5*n**3 + 25*n**y - 11*n**4 - 15*n**5 + 40*n**5 = 0. What is n?
-1, -1/10, 0
Let p(l) be the first derivative of -l**5/300 + 7*l**4/120 + 4*l**3/15 + 47*l**2 - 76. Let t(q) be the second derivative of p(q). Let t(h) = 0. What is h?
-1, 8
Let g = 1495 + -1777. Let j be g/47*(-1)/3. Determine c so that 5*c**j + 25/3*c + 10/3 - 5/3*c**4 - 5/3*c**3 = 0.
-1, 2
Suppose 85202 + 4*j**2 + 156503 - 601*j - 1943*j + 162791 = 0. Calculate j.
318
Let o(r) be the second derivative of 5*r**4/22 + 136*r**3/33 - 87*r**2/11 - 2981*r. Factor o(y).
2*(3*y + 29)*(5*y - 3)/11
Suppose -2*b + 3*r = -31, 3071*b + 42 = 3074*b - 4*r. Find f, given that 1/2*f**b + 5 - 11/2*f = 0.
1, 10
Let f = 306 - 301. Factor -7*q**3 - 6*q**3 + q**f + q + 17*q**3 - 6*q**3.
q*(q - 1)**2*(q + 1)**2
Let y(t) = -394*t + 542. Let g be y(5). Let v be 10/2*g/(-1360). Determine b so that -63/2*b + 183/8*b**2 + 3/8*b**4 + 27/2 - v*b**3 = 0.
1, 6
Let g(q) be the third derivative of 0*q + 0*q**4 + 0 - 1/540*q**6 - 17*q**2 + 0*q**5 + 1/945*q**7 + 0*q**3. Determine h so that g(h) = 0.
0, 1
Let n(b) be the second derivative of -b**4/36 - 28*b**3/9 - 104*b**2/3 + 857*b + 1. Determine a, given that n(a) = 0.
-52, -4
Let a be -69*(-24)/736 - ((14/(-8) - 1) + 3). Determine l so that -49/2*l**a - 1/4*l**5 - 71/2*l**3 + 143/4*l - 23/4*l**4 + 121/4 = 0.
-11, -1, 1
Let j(w) be the first derivative of -2*w**3/27 + 61*w**2/3 - 724*w/9 - 3380. Factor j(b).
-2*(b - 181)*(b - 2)/9
Let -66*n - 10*n**4 + 118/3*n**3 + 18*n**2 + 56/3 = 0. Calculate n.
-7/5, 1/3, 1, 4
Suppose 415*j - 409*j = 0. Suppose 9*r + 3*r - 36 = j. Determine k so that 0 + 2/5*k**2 + 1/5*k - 1/5*k**5 + 0*k**r - 2/5*k**4 = 0.
-1, 0, 1
Let v(m) be the first derivative of 7*m**2 + 0*m + 10/3*m**3 + 18 - 5/8*m**4 - 1/12*m**5. Let q(r) be the second derivative of v(r). Find a such that q(a) = 0.
-4, 1
Let m(t) be the second derivative of 2/45*t**4 - 4/45*t**3 - 1/150*t**5 + 0 - 7*t + 0*t**2. Factor m(s).
-2*s*(s - 2)**2/15
Suppose 9*q = -20*q + 87. Factor -15*u**q - 373*u**2 + 188*u**2 + 189*u**2 - 4*u**4.
-u**2*(u + 4)*(4*u - 1)
Suppose -42 = 16*p - 18*p. Suppose 5*l + p = 12*l. Factor 4*s**2 - s**5 + 7*s**3 - s**5 + s**l - 6*s - 7 + 3.
-2*(s - 2)*(s - 1)*(s + 1)**3
Let s(f) be the second derivative of 5*f**7/42 + 361*f**6/3 + 130321*f**5/4 - 60*f + 38. Factor s(r).
5*r**3*(r + 361)**2
Suppose 11*b + 32 = 7*b. Let d be (-63)/(-28) - 0 - (-2)/b. Factor 9*x**d - 128 - 39*x**2 - 10*x**2 + 109*x + 19*x + 4*x**3.
4*(x - 4)**2*(x - 2)
Find w such that 4*w**3 + 39*w**4 + 40*w**4 + 15*w**3 - 78*w**2 + 34*w**4 - 114*w**4 = 0.
0, 6, 13
Let l(w) = 4*w**2 + 36*w - 6. Let c be l(-10). Factor c*z - 4 - 5 - 6*z + 3*z**2 - 7*z**2 - 15.
-4*(z - 6)*(z - 1)
Let o(n) be the third derivative of 7/8*n**4 + 3/35*n**7 - 1/5*n**6 - 3/10*n**5 + 14*n + 0 + 0*n**3 + 6*n**2 + 1/112*n**8. Find z, given that o(z) = 0.
-7, -1, 0, 1
Let x(c) = -7*c**2 - 3060*c - 468180. Let w(v) = -120*v**2 - 52020*v - 7959060. Let r(z) = -2*w(z) + 35*x(z). Factor r(o).
-5*(o + 306)**2
Factor -32/5*q + 112/5 + 1/5*q**2.
(q - 28)*(q - 4)/5
Let f(o) = 3*o**2 - 118*o + 268. Let v be f(37). Suppose m + 6 = 2*t, v*m = 4*m - 10. Factor -u**3 + 1/3*u + 0 - 2/3*u**t.
-u*(u + 1)*(3*u - 1)/3
Let h(o) be the third derivative of -o**6/24 + 16*o**5 + 965*o**4/24 + 17*o**2 - 106*o. Factor h(z).
-5*z*(z - 193)*(z + 1)
Solve 67 - 133/4*o**2 - 34*o + 1/4*o**3 = 0 for o.
-2, 1, 134
Let k(v) be the third derivative of -1/70*v**7 + 0*v**3 + v**2 + 0*v**4 + 1/20*v**5 - 12*v + 1/112*v**8 - 1/40*v**6 + 0. Factor k(x).
3*x**2*(x - 1)**2*(x + 1)
Let o(f) = 7*f**2 - 23*f - 12. Let u = 75 - 152. Let l = u - -68. Let r(b) = -3*b**2 + 11*b + 6. Let a(h) = l*r(h) - 4*o(h). Solve a(s) = 0 for s.
-6, -1
Let p(x) be the second derivative of 5*x**7/147 - 2*x**6/35 - 3*x**5/7 + 38*x**4/21 - 3*x**3 + 18*x**2/7 - 1886*x. Determine r so that p(r) = 0.
-3, 1, 6/5
Suppose w + 1 = 44. Factor 3 - 2*u**3 - w - 2*u**3 + 63*u + 69*u**2 + 2 + 72*u.
-(u - 19)*(u + 2)*(4*u - 1)
Let j(o) be the second derivative of o**4/72 + 11*o**3/9 + 65*o**2/4 - 2338*o. Find m such that j(m) = 0.
-39, -5
Let m(d) be the second derivative of -d**7/21 - d**6/15 + 3*d**5/2 + 5*d**4/6 - 34*d**3/3 - 24*d**2 - 11648*d. Solve m(n) = 0.
-4, -1, 2, 3
Suppose -3*d - 11 + 27 = -w, -3*d - 3*w = 0. Factor 3*i + 9*i - 2*i**2 - d*i**2 + 8*i + 4*i**2.
-2*i*(i - 10)
Suppose -43*p + 22 = -64. Let h(q) be the first derivative of 5*q**3 + 15 - 1/4*q**4 + 125*q - 75/2*q**p. Factor h(u).
-(u - 5)**3
Suppose 0*c = 2*i - 3*c + 4, -4*c = 3*i - 11. Let q be (i/(-3))/((-12)/18). Factor -1 - q*k + 1/2*k**2.
(k - 2)*(k + 1)/2
Suppose -4*c = 727 - 739. Suppose 4*o - 4 = 16. Factor 25*m**4 + 9*m**2 - 8*m**4 - 3*m**2 + 5*m**2 + 2*m + 21*m**c + o*m**5.
m*(m + 1)**3*(5*m + 2)
Let t(j) be the third derivative of j**5/210 + 44*j**4/21 - 179*j**3/7 + 16*j**2 - 28*j. Factor t(x).
2*(x - 3)*(x + 179)/7
Suppose -8*u + 675 = 107. Let t = u - 69. Find q such that 8*q**t + 21*q + 15*q**4 - 3*q**5 + 9 - 30*q**4 - 18*q**3 - 2*q**2 = 0.
-3, -1, 1
Let b be 4 - (0 + 8) - (-40)/7. Let o(n) = -n**2 - 3*n + 12. Let q be o(-5). Factor -4/7*r**q - b - 16/7*r.
-4*(r + 1)*(r + 3)/7
Suppose 12 = 4*b - 3*j + 6, -2*b - 30 = 15*j. Factor -1/4*u**2 - 11/2*u + b.
-u*(u + 22)/4
Let m = -1119 - -1137. Suppose 0 = 105*b - 111*b + m. Find t, given that 6/5 + 27/5*t + 18/5*t**4 + 48/5*t**2 + 3/5*t**5 + 42/5*t**b = 0.
-2, -1
Let x(k) be the second derivative of k**7/84 - k**6/5 + 57*k**5/40 - 67*k**4/12 + 13*k**3 - 18*k**2 - 68*k + 20. What is u in x(u) = 0?
2, 3
Suppose 0 = -42*z - 1189 + 2530 - 1089. Determine r so that -18 - z*r**3 + 9/2*r**2 + 24*r = 0.
-2, 3/4, 2
Let i(c) be the first derivative of 30 + 3/8*c**2 - 1/16*c**4 + 0*c**3 + 1/2*c. Factor i(f).
-(f - 2)*(f + 1)**2/4
Let l(j) be the first derivative of j**8/7560 - 