
-2, 0
Let u(f) be the first derivative of f**8/1680 - f**7/168 + f**6/60 + 27*f**3 + 128. Let a(q) be the third derivative of u(q). Solve a(o) = 0 for o.
0, 2, 3
Let c = -29 - -35. Suppose c*f - 10*f = -12. What is a in 0*a + 3*a**3 - a**2 - 2*a + 8*a**2 - 8*a**f = 0?
0, 2/5, 1
Let h(y) = -y**3 + 24*y**2 - 47*y + 60. Let k be h(20). Let n = -5031/7 + k. Find x, given that 0 + n*x**3 + 0*x + 6/7*x**2 + 3/7*x**4 = 0.
-2, -1, 0
Let g(f) be the third derivative of -f**5/90 + 191*f**4/20 + 344*f**3/45 + f**2 - 1511*f. Factor g(u).
-2*(u - 344)*(5*u + 1)/15
Suppose -a - m = -1, -7*m = a - 9*m - 16. Suppose 16*s + 47*s - 21 - 11 - a*s**2 - 11*s = 0. What is s?
2/3, 8
Let g be 119/21 + ((-1664)/78)/4. Factor 4 - g*k**3 + 0*k**2 + 13/3*k.
-(k - 4)*(k + 1)*(k + 3)/3
Let k(b) be the third derivative of 3*b**7/1120 + b**6/120 + b**5/160 - 27*b**3/2 - b**2 - 77*b. Let n(m) be the first derivative of k(m). Factor n(r).
3*r*(r + 1)*(3*r + 1)/4
Let f be (-14 - -3) + 1 - (-17 + 0 + (-18800)/(-2800)). Suppose -f*c**2 + 2/7 + 1/7*c - 1/7*c**3 = 0. Calculate c.
-2, -1, 1
Let r(w) be the first derivative of w**3/21 + 2*w**2/7 + 117. Solve r(t) = 0 for t.
-4, 0
Let s(t) = t**2 + 4*t - 19. Let q be s(-7). Suppose 4*y**3 - 2*y - 5*y**3 + 14*y - y**3 + 10*y**q = 0. Calculate y.
-1, 0, 6
Let p be (-300)/75 - (-6 + 2 + 0). Let n(h) be the third derivative of -1/10*h**3 + 1/100*h**5 - 17*h**2 + 0*h + p*h**4 + 0. Factor n(k).
3*(k - 1)*(k + 1)/5
Let s(h) = -33*h**3 - 120*h**2 + 231*h + 663. Let v(y) = -2*y**3 - y**2 + 7*y + 1. Let q(l) = -s(l) + 15*v(l). What is n in q(n) = 0?
-36, -2, 3
Suppose 1042*f - 905*f - 135 = 139. Let k(q) be the first derivative of 17 - 8/69*q**3 - 3/23*q**f + 36/23*q + 1/46*q**4. Factor k(g).
2*(g - 3)**2*(g + 2)/23
Let z(s) be the third derivative of s**5/240 - 1139*s**4/48 + 1297321*s**3/24 + s**2 + 391*s - 1. Find d, given that z(d) = 0.
1139
Factor -4/7*u**4 - 145152 + 376/7*u**3 - 27072*u - 4804/7*u**2.
-4*(u - 56)**2*(u + 9)**2/7
Let a(t) = 114 - 14*t + 171 - 23*t + 14. Let r be a(8). What is q in q - 1/3 - q**2 + 1/3*q**r = 0?
1
Let u(l) be the third derivative of 1/120*l**5 - 1/420*l**7 + 0*l + 0*l**3 - 21 - 1/48*l**4 + 1/240*l**6 + l**2. Factor u(n).
-n*(n - 1)**2*(n + 1)/2
Factor 3/5*o**2 - 468/5 + 3/5*o.
3*(o - 12)*(o + 13)/5
Let k(q) be the second derivative of 64*q**6/15 - 132*q**5/5 + 1153*q**4/24 - 11*q**3 + q**2 - 4*q + 34. Determine n so that k(n) = 0.
1/16, 2
Let y = 5449732/11 + -496249. Let l = y + 819. Factor 10/11*a**2 + 2/11*a**3 - l*a**4 + 0 + 6/11*a.
-2*a*(a - 3)*(a + 1)**2/11
Let r(f) be the second derivative of -51*f**5/5 - 8*f**4/3 + 1701*f + 2. Factor r(i).
-4*i**2*(51*i + 8)
Let k(a) be the second derivative of 135*a - 1/12*a**4 - 38/3*a**3 - 722*a**2 + 1. Factor k(m).
-(m + 38)**2
Let a = 366 - 174. Let i = 192 - a. Factor 0*g + 0*g**4 + i*g**2 + 1/5*g**3 - 1/5*g**5 + 0.
-g**3*(g - 1)*(g + 1)/5
Determine g so that -4*g**3 + 20*g**2 + 79677*g - 79677*g = 0.
0, 5
Let o(y) be the third derivative of y**8/1008 - 59*y**7/630 + 257*y**6/120 + 3131*y**5/180 - 961*y**4/18 - 9*y**2 - 16. What is j in o(j) = 0?
-4, 0, 1, 31
Suppose 62*s + 399 = 83*s. Let f(h) be the third derivative of -7/6*h**4 + 49/3*h**3 + 0 - s*h**2 + 0*h + 1/30*h**5. Factor f(i).
2*(i - 7)**2
Find c such that 779760*c - 6887*c**3 + 5*c**4 + 405798*c**2 - 411858*c**2 - 388800 + 4*c**4 + 1168137*c**2 + 413*c**3 = 0.
-1, 1/3, 360
Let w(g) be the third derivative of -1/8*g**4 + 0*g - 1/40*g**5 - 1/4*g**3 - 45*g**2 + 0. Factor w(i).
-3*(i + 1)**2/2
Let z = -95725 + 861527/9. Determine q so that 2/9*q - 2/9*q**4 - 4/9*q**3 + 2/9*q**5 + 4/9*q**2 - z = 0.
-1, 1
Let j be (12 - 12 - 7) + 9. Let m(u) be the first derivative of -144/7*u - 4/21*u**3 + 24/7*u**j + 1. Factor m(n).
-4*(n - 6)**2/7
Suppose 67 = -2*x + 63. Let g(o) = 90*o**3 + 156*o**2 - 28*o + 22. Let k(q) = q**3 + 2*q**2 + q + 1. Let i(d) = x*g(d) + 36*k(d). Let i(c) = 0. What is c?
-2, 1/6
Let u(l) be the second derivative of -3*l**5/20 - 51*l**4/2 + 207*l**3/2 - 156*l**2 + 345*l. Factor u(q).
-3*(q - 1)**2*(q + 104)
Let a(z) = -z**2 + 4*z - 186 + 181 + 2*z. Let f be a(4). Factor f*h**2 + 3 - 7 - 3*h**3 + 4.
-3*h**2*(h - 1)
Let q be 340/78 - 464/(-1508). Find o, given that q*o + 32/3 - 1/3*o**2 = 0.
-2, 16
Let h(n) be the third derivative of n**5/24 - 215*n**4/48 + 35*n**3/2 - 1861*n**2. Let h(t) = 0. Calculate t.
1, 42
Suppose -4*l + 5*j = -30, 10*l - 5*l + 2*j - 21 = 0. Let a be (-14)/l*(5/(-12) - 0). Factor -1/3*y**2 + a*y - 1/2.
-(y - 3)*(2*y - 1)/6
Let b = 118247 + -354559/3. Determine g, given that 34/3*g**2 + 2/3*g**3 + 98 + b*g = 0.
-7, -3
Let q(u) = -16*u**3 + 5*u + 5*u**4 + 16*u + 2 - 3*u**4 - 19*u - 10*u**2. Let o(y) = 2*y**4 - y**3 + y**2 + y + 1. Let t(r) = 2*o(r) - q(r). Factor t(x).
2*x**2*(x + 1)*(x + 6)
Let k(s) be the second derivative of -s**4/6 - 2*s**3/3 + 399*s**2 - 1948*s + 2. Factor k(q).
-2*(q - 19)*(q + 21)
Suppose 7*j = -2*p + 2*j - 1, -5*p + 5*j + 15 = 0. Find c, given that 7*c + 6*c + 25*c**p - 28*c - 32*c**3 + 42*c**3 = 0.
-3, 0, 1/2
Let r = 287949 - 287946. Suppose -2/3*d**r + 4/3*d**2 + 14/3*d + 8/3 = 0. Calculate d.
-1, 4
Let q(j) be the first derivative of j**3/3 + 19*j**2/2 - 42*j - 2733. Find v such that q(v) = 0.
-21, 2
Factor 787021103104*p - 2*p**4 - 6*p**4 - 14*p**4 + 18*p**4 - 68474467*p**2 + 58624*p**3 - 253723037*p**2 - 720911330443264.
-4*(p - 3664)**4
Let f(p) = 8*p + 20. Let z be f(0). Factor -40 + z*h**2 + 269*h - 5*h**3 - 194*h - 50.
-5*(h - 6)*(h - 1)*(h + 3)
Let n(c) = c**3 + 14*c**2 - 178*c - 2333. Let d be n(-16). Factor 3/2*m**d + 0*m + 0 - 3*m**2.
3*m**2*(m - 2)/2
Suppose 4*r + 267 + 385 = 0. Let k = r + 165. Factor 0 - 1/4*n**4 + 1/4*n**k + 0*n + 1/4*n**3 - 1/4*n**5.
-n**2*(n - 1)*(n + 1)**2/4
Suppose -v = -3*v - 20. Let m(u) = -u**2 + 4*u + 2. Let y(k) = 2*k + 10 + 15 - 24 - 3*k. Let z(i) = v*y(i) + 5*m(i). Solve z(w) = 0 for w.
0, 6
Suppose 0 = 4*w - 19 - 1. Suppose -w*c = y - 127, 8*y - 35 = -c + 3*y. Factor 2*t**5 + 5*t**5 + 2*t - 13*t**2 + 27*t**3 + 2*t**4 - c*t**4.
t*(t - 1)**3*(7*t - 2)
Let -4*d**4 + 0 - 69/5*d**3 - 32/5*d - 1/5*d**5 - 82/5*d**2 = 0. Calculate d.
-16, -2, -1, 0
Factor 3201267/8 - 3099/4*a + 3/8*a**2.
3*(a - 1033)**2/8
Let x(c) = 457*c**2 - 2*c + 1. Let o be x(1). Suppose 25*y - 918 + o + 20*y**3 + 472 - 55*y**2 = 0. Calculate y.
-1/4, 1, 2
Let i = 0 + 1. Let l(u) = 3*u**2 - 6*u - 4. Let p(j) be the second derivative of -j**3/6 - 4*j - 40. Let r(f) = i*l(f) - 2*p(f). Suppose r(h) = 0. Calculate h.
-2/3, 2
Let k = 10992/5467 + -186/497. Find b such that 12/11*b - k - 2/11*b**2 = 0.
3
Suppose 3*g - 4 = 2*w - 11, 4*w + 2*g = 6. Suppose -4 = -w*b, -x - 1 = b - 7. Factor 0*n**2 - x*n**3 + 10*n**2 - 3*n**2 - 32*n + 13*n**2 + 16.
-4*(n - 2)**2*(n - 1)
Let r(i) = -i**2 + 1. Let p be (1 + 1)*1*(4 - 3). Let d(z) = -9*z**2 + 2*z**p + 8*z**2 - 40*z + 10*z - 79. Let h(b) = -d(b) - 4*r(b). Factor h(s).
3*(s + 5)**2
Suppose -8547*s**4 + 210*s**2 - 77*s**2 - 516 - 160*s + 8546*s**4 + 40*s**3 = 0. What is s?
-3, -2, 2, 43
Let i(b) = 3*b**2 - 1022*b + 264192. Let y(w) = -4*w**2 + 1019*w - 264190. Let u(s) = 3*i(s) + 2*y(s). Find c such that u(c) = 0.
514
Let j = 2271 + -2269. Solve -1/2*z**3 + 0 - 3*z + 5/2*z**j = 0.
0, 2, 3
Let k(s) = s**2 - 62*s + 745. Let f be k(16). Let w(h) be the first derivative of -f + 0*h**2 + 0*h + 1/3*h**3. Suppose w(i) = 0. What is i?
0
Suppose 14*v - 210 = -63*v + 7*v. Let l(p) be the first derivative of -2/3*p**2 + 14/3*p + 2/63*p**v + 12. Factor l(d).
2*(d - 7)**2/21
Let z(m) be the first derivative of -25*m**6/36 - 17*m**5/6 + 41*m**4 - 1130*m**3/9 + 488*m**2/3 - 96*m - 7168. Determine i, given that z(i) = 0.
-9, 4/5, 2
Let h(s) = 2*s**3 - 91*s**2 + 811*s - 982. Let k be h(34). Suppose 0 + 6*f + 15/2*f**3 - 12*f**2 - 3/2*f**k = 0. What is f?
0, 1, 2
Let o(b) = b**2 - 18*b + 47. Let m be o(15). Let p(q) be the second derivative of 1/12*q**3 - 1/40*q**5 - 1/8*q**4 + 3/4*q**m + 11*q + 0. Factor p(c).
-(c - 1)*(c + 1)*(c + 3)/2
Suppose 42*v + 3/8*v**2 - 339/8 = 0. Calculate v.
-113, 1
Determine l so that 0 - 230/3*l**2 + 0*l + 2/9*l**3 = 0.
0, 345
Let a = 174 - 179. Let f(z) = 5*z**2 + 86*z + 1847. Let c(j) = 12*j**2 + 172*j + 3693. Let g(b) = a*f(b) + 2*c(b). Factor g(l).
-(l + 43)**2
Let g(s) = 309*s**3 +