5*m - 2)
Suppose 30*q + 8 + 22 = 0. Let z be 19/114 + q/(-3). Determine s, given that -1/4*s**3 + 0 - z*s**2 + 3/4*s = 0.
-3, 0, 1
Suppose -21*p - 39*p = 9*p + 31*p. Solve 1/6*i**5 + 7/6*i**2 - 1/6*i**3 + p*i - 7/6*i**4 + 0 = 0 for i.
-1, 0, 1, 7
Let y be 1/(-1) - (-16352)/11040. Let v = 22/69 + y. Determine t so that -8/5*t - 7/5*t**3 + v - 19/5*t**2 = 0.
-2, -1, 2/7
Let w(i) be the first derivative of 2/5*i**2 - 1/5*i**3 + 6*i + 1/30*i**4 + 11. Let m(c) be the first derivative of w(c). Suppose m(u) = 0. Calculate u.
1, 2
Let d = -1053 - -1055. Let p(j) = -j**2 + 6*j + 2. Let o be p(6). Solve d*g**3 + 2*g**3 + 37*g**o - 33*g**2 = 0.
-1, 0
Let u = -736216/3 + 245407. Suppose 4 + u*a - 2*a**2 + 1/3*a**3 = 0. Calculate a.
-1, 3, 4
Find h such that -82*h**2 + 41*h**5 + 9*h**5 - 8 + 10*h**3 - 4*h**4 + 12*h**4 + 82*h**4 - 12*h**3 - 48*h = 0.
-1, -2/5, 1
Let p be 572/66 + 14272/84. Let 2/7*v**2 + p + 100/7*v = 0. Calculate v.
-25
Let j(k) be the first derivative of -2*k**5/95 + 213*k**4/38 - 7632*k**3/19 + 11236*k**2/19 - 219. Factor j(m).
-2*m*(m - 106)**2*(m - 1)/19
Suppose 0 = 8*p + 72 - 3424. Factor 7*m**4 + 211*m**5 + 0*m**3 - 13*m + 22*m**2 + 207*m**5 + 3 - p*m**5 - 18*m**3.
-(m - 3)*(m - 1)**4
Let y(p) = 2*p - 29. Let u be (2/2)/(94/(-32) + 3). Let a be y(u). Suppose -3*z**a - 2*z**3 + 5*z**3 - 4*z**3 + 4*z**4 = 0. Calculate z.
0, 1
Let d(z) be the first derivative of z**5/5 - 117*z**4 + 54286*z**3/3 + 54990*z**2 + 55225*z + 1556. Let d(r) = 0. What is r?
-1, 235
Let d(a) = a**3 - 40*a**2 - 3*a - 65. Let h be d(40). Let t be (-10)/6*444/h. Solve -2/17*j**3 + 0 - 2/17*j**t + 8/17*j**2 + 8/17*j = 0.
-2, -1, 0, 2
Let y = 3613 - 3608. Let m(o) be the third derivative of 0 + 0*o - 5/12*o**3 - 1/120*o**y - 1/8*o**4 + 15*o**2. What is z in m(z) = 0?
-5, -1
Factor -v**2 + 1/2*v**5 + v**4 - 2*v**3 + 0 + 3/2*v.
v*(v - 1)**2*(v + 1)*(v + 3)/2
Let c(p) = 25*p**4 + 5*p**3 - 40*p**2 - 35*p. Let b(r) = 2*r**4 - r**3 - 2*r**2 - r - 1. Suppose 10*k - 14*k + 60 = 0. Let s(j) = k*b(j) - c(j). Factor s(t).
5*(t - 3)*(t - 1)**2*(t + 1)
Factor -73167/5*p**3 + 192/5 - 4176/5*p + 30276/5*p**2.
-3*(29*p - 4)**3/5
Let y(f) be the first derivative of -5/8*f**4 - 1/10*f**5 - 39 - 7/4*f**2 - 3/2*f**3 - f. Factor y(m).
-(m + 1)**3*(m + 2)/2
Determine z, given that -194/5*z**2 + 0 + 2/5*z**3 + 76*z = 0.
0, 2, 95
Let z(m) be the first derivative of -4*m**5 + 95*m**4/4 + 65*m**3/3 - 235*m**2 - 120*m + 1474. Let z(w) = 0. Calculate w.
-2, -1/4, 3, 4
Let u be (-3)/6*4/(-1)*(367 - 366). Factor -4/5*a + 0 + 12/5*a**u.
4*a*(3*a - 1)/5
Let v(d) = -903*d - 55986. Let x be v(-62). Factor 6/5*c**3 + x*c**4 - 1/5*c**5 + 8/5*c**2 + 0 + 3/5*c.
-c*(c - 3)*(c + 1)**3/5
Let x(k) be the third derivative of -k**8/2856 + 23*k**7/1785 - 11*k**6/68 + 99*k**5/170 + 81*k**4/34 + 261*k**2. Find f, given that x(f) = 0.
-1, 0, 6, 9
Let z be ((6 + 605/(-100))*-20)/(-1 - (-10)/4). Let -z - 1/3*u**2 + u = 0. Calculate u.
1, 2
Let c be (-567)/(-49) + -12 - (-24)/7. Factor 48*u - 6*u**3 + 4*u**c + 461*u**2 - 449*u**2 + 64 + 3*u**3.
(u + 4)**3
Let z(q) be the third derivative of -q**6/216 - q**5/72 + 7*q**3/3 + 20*q**2 - 2. Let t(i) be the first derivative of z(i). Solve t(n) = 0 for n.
-1, 0
Let f(r) be the second derivative of -r**4/3 + 3772*r**3 - 16006482*r**2 + r + 86. Let f(v) = 0. Calculate v.
2829
Let y = -2211 - -2214. Let b be 96/(-18)*((-525)/(-182) - y). Determine i, given that b*i**4 + 10/13*i**3 + 4/13*i**2 + 0 + 2/13*i**5 + 0*i = 0.
-2, -1, 0
Let o be ((-2)/48)/(384/(-576)). Let f(a) be the second derivative of -1/112*a**7 + 0 + 0*a**2 + o*a**4 + 21*a + 0*a**6 + 0*a**3 + 9/160*a**5. Factor f(u).
-3*u**2*(u - 2)*(u + 1)**2/8
Determine j so that 5*j**4 + 5473*j - 10765*j + 210 - 35*j**3 + 5507*j - 35*j**2 = 0.
-2, -1, 3, 7
Let b(c) = -3*c**3 - 123*c**2 + 398*c - 264. Let d(u) = -2*u**3 - 126*u**2 + 398*u - 264. Let k(g) = 3*b(g) - 4*d(g). Factor k(t).
-(t - 132)*(t - 2)*(t - 1)
Let n(s) be the first derivative of s**6/2 - 53*s**5/15 + 83*s**4/12 + 17*s**3/9 - 58*s**2/3 + 20*s + 7623. Suppose n(u) = 0. What is u?
-10/9, 1, 2, 3
Let u(i) be the third derivative of i**4/4 - 31*i**3/6 - 4*i**2. Let k be u(7). Factor 2*z**2 + 3*z + k + 3*z - 13 - 4*z - 2*z**3.
-2*(z - 1)**2*(z + 1)
Let d(r) be the second derivative of -16*r**4/3 - 336*r**3 - 7938*r**2 + 97*r + 9. Find n, given that d(n) = 0.
-63/4
Suppose 2051*m = 2043*m + 16. Let n(f) be the second derivative of -3*f + 0 + 5/2*f**3 + 5/12*f**4 + 5*f**m. Determine c, given that n(c) = 0.
-2, -1
Suppose 57 = 113*v - 76*v - 17. Factor -t**2 + 0*t**4 + 3/2*t + 1/2*t**5 - v*t**3 + 1.
(t - 2)*(t - 1)*(t + 1)**3/2
Factor -280 + 260*v - 3036*v**3 + 1817*v**3 + 1214*v**3 - 50*v**2.
-5*(v - 2)**2*(v + 14)
Suppose 6*g + 87 = 3*g - 3*j, 3*j = -g - 31. Let p be g/(-35)*(-35)/(-182). Find z, given that -2/13*z**2 - p*z + 0 = 0.
-1, 0
Let w = 616 - 568. Suppose -w*l + 72 = -24*l. What is x in 0*x + 0 - 3/7*x**4 - 6/7*x**l - 3/7*x**2 = 0?
-1, 0
Let t(s) = 24*s**4 + 288*s**3 + 384*s**2 - 1868*s - 552. Let h(z) = z**4 + z**2 - z - 2. Let p(n) = -4*h(n) - t(n). Find c such that p(c) = 0.
-7, -5, -2/7, 2
Suppose 1438*x**2 - 2868*x**2 - 699*x - 336 + 1043*x**2 + 3*x**4 - 17*x**3 - 4*x**3 = 0. What is x?
-7, -1, 16
Let s(l) be the second derivative of l**5/20 + 15*l**4/4 + 7*l**3 - 44*l**2 + 10528*l. Factor s(t).
(t - 1)*(t + 2)*(t + 44)
Let b be (-4752)/2079 + (-927)/(-35). Solve 22/5*d + 1/5*d**2 + b = 0 for d.
-11
Let t = -3548/11 - -4541429/14080. Let o = 23057/21760 + t. Suppose o*l + 4/17 - 10/17*l**2 = 0. What is l?
-1/5, 2
Let p(o) be the third derivative of o**6/140 - 94*o**5/105 + 307*o**4/84 - 122*o**3/21 - 2215*o**2 + 3. Factor p(q).
2*(q - 61)*(q - 1)*(3*q - 2)/7
Let w be 233276/(-174) - (-1*4 + 0). Let c = w + 1337. Solve 2 + 1/3*g - c*g**2 = 0 for g.
-2, 3
Suppose 1984*v - 1979*v - 7 = j, 3*v - j = 3. Determine o, given that 100/13 + 270/13*o**3 + 486/13*o**v + 54/13*o**4 + 370/13*o = 0.
-5/3, -1, -2/3
Determine a, given that -118/15*a**2 + 0 - 46/5*a**3 + 4/3*a = 0.
-1, 0, 10/69
Find n, given that 70/3*n + 145/3*n**2 - 70/3*n**3 - 1/3*n**4 - 48 = 0.
-72, -1, 1, 2
Let r(t) be the third derivative of t**6/1800 - t**4/120 + 77*t**3/3 + 95*t**2. Let p(n) be the first derivative of r(n). Let p(s) = 0. Calculate s.
-1, 1
Let u(a) be the second derivative of -43/54*a**4 - 1/45*a**5 + 31*a + 1/18*a**6 - 5/3*a**3 - 25/18*a**2 - 1/189*a**7 + 0. Determine g so that u(g) = 0.
-1, -1/2, 5
Let w = 169 - 44. Solve 53 + 63 - 471*v**3 + 15*v**2 + w*v + 466*v**3 - 11 = 0.
-3, -1, 7
Let g = 6395 - 6389. Let n(m) be the second derivative of 0*m**3 + 0*m**2 + 2/15*m**g - 24*m + 0*m**5 + 0 + 0*m**4. Factor n(o).
4*o**4
Let f = 348 - 337. Suppose 10*m = f + 9. Factor 0*u**m - 2/9*u**3 + 0*u - 2/9*u**5 + 0 + 4/9*u**4.
-2*u**3*(u - 1)**2/9
Let g be (-7 - -3) + (1513/(-20))/(-17). Let m(n) be the second derivative of -g*n**5 + 0 + 3/2*n**2 - 5/2*n**3 + 21*n + 7/4*n**4. Factor m(f).
-3*(f - 1)**2*(3*f - 1)
Let m(f) be the first derivative of -2*f**3/3 + 10*f**2 + 750*f - 645. Let m(q) = 0. Calculate q.
-15, 25
Suppose 7*u - 179 + 144 = 0. Suppose u = -2*r + 5*q, -3*q - 2*q = -3*r - 5. Factor 0*z**2 + r*z + 0 - 2/9*z**4 + 2/9*z**3.
-2*z**3*(z - 1)/9
Let r(a) be the third derivative of 7*a**7/240 - 7*a**6/160 - 1391*a**5/480 + 25*a**4/8 + 625*a**3/3 + 1916*a**2. Factor r(c).
(c - 4)**2*(7*c + 25)**2/8
Let g = 304617/2 + -152296. Factor -1/2*f**2 - 12*f + g.
-(f - 1)*(f + 25)/2
Let o(f) be the first derivative of 7*f**4/10 - 32*f**3/15 - 17*f**2/5 + 12*f/5 + 831. Suppose o(d) = 0. Calculate d.
-1, 2/7, 3
Suppose -2*s = 2*a - 2270, 79*s = -4*a + 76*s + 4538. Let l = 1133 - a. Factor l + 1/3*t**2 - 1/3*t**4 + t - t**3.
-t*(t - 1)*(t + 1)*(t + 3)/3
Factor 98/15*s + 2/15*s**2 + 92/5.
2*(s + 3)*(s + 46)/15
Let r(s) be the first derivative of -67*s**2 + 122 + 0*s + 2/3*s**3. Find f such that r(f) = 0.
0, 67
Let n(q) be the second derivative of q**4/54 + 28*q**3/27 - 245*q**2/9 + 811*q. Factor n(b).
2*(b - 7)*(b + 35)/9
Let m(r) = -r**3 + 4860*r + 12*r**4 - 4860*r + 37*r**3 - 33*r**2. Let t(v) = -v**4 - v**3 + v. Let z(i) = m(i) + 15*t(i). Factor z(y).
-3*y*(y - 5)*(y - 1)**2
Let k(b) = 7*b**2 - 262*b + 819. Let z be k(34). Determine p so that 1/7*p**4 - 8/7*p**2 + 0 + 0*p - p**z = 0