13/6*r**3 + 0*r**5 + 0 + 0*r + 14*r**2. Let i(f) be the first derivative of g(f). Solve i(u) = 0.
0
Suppose 12*i = 14*i - 4. Let f = -69 - -97. Factor -16*n + 3*n**2 - 5*n**4 - 20*n**3 + 6*n - f*n**i.
-5*n*(n + 1)**2*(n + 2)
Let u(s) be the third derivative of -1/300*s**5 + 2*s**2 + 0 + s - 3/10*s**3 + 1/20*s**4. Find p such that u(p) = 0.
3
Factor -c**3 - 6670*c**2 - 1073*c + 323*c + 3*c**3 + 3*c**3 + 6545*c**2.
5*c*(c - 30)*(c + 5)
Let o(i) be the first derivative of i**6/27 - 2*i**5/9 + 2*i**4/9 + 7078. Let o(h) = 0. Calculate h.
0, 1, 4
Let x(z) be the third derivative of 0*z**3 - 17/60*z**6 + 0*z + 1/5*z**5 - 1/42*z**8 + 0*z**4 + 65*z**2 - 9/35*z**7 + 0. Solve x(d) = 0 for d.
-6, -1, 0, 1/4
Let d(s) = -3*s**3 + 1125*s**2 + 47052*s - 265080. Let t(p) = p**3 - 561*p**2 - 23544*p + 132540. Let f(a) = 4*d(a) + 9*t(a). Factor f(k).
-3*(k - 5)*(k + 94)**2
Factor -4*f**5 + 2708*f**2 + 1484*f**3 + 83*f**4 - 145 + 201*f**4 + 2120*f + 445 + 379 - 71.
-4*(f - 76)*(f + 1)**3*(f + 2)
Let q(i) be the third derivative of -3*i**2 + 0*i**3 + 0*i + 1/40*i**5 + 1/6*i**4 + 1 - 1/480*i**6. Factor q(m).
-m*(m - 8)*(m + 2)/4
Factor 47*r**4 + 100*r**2 - 120*r**4 + 49*r**4 + 181*r**5 - 180*r**5 + 75*r**3.
r**2*(r - 20)*(r - 5)*(r + 1)
Let k(d) be the third derivative of -d**7/525 - 136*d**6/75 + 8714*d**2. Factor k(q).
-2*q**3*(q + 544)/5
Let w(b) = 21*b**4 + 94*b**3 + 169*b**2 + 122*b - 58. Let m(v) = 7*v**4 + 31*v**3 + 56*v**2 + 41*v - 21. Let d(f) = -14*m(f) + 5*w(f). Factor d(l).
(l + 1)*(l + 2)**2*(7*l + 1)
Suppose 3*p + 167 = 2*m + 3*m, -57 = p - 2*m. Let g = 66 + p. Let 52*s**3 + 65*s - 119*s**2 + 30 - 11*s**2 - g*s**3 = 0. Calculate s.
-2/7, 1, 3
Suppose -b = -o + 6, -6*b + 18 = -7*b - 2*o. Let n be (630/(-2646))/(b/6). Suppose 0 - 2/7*c - n*c**2 = 0. What is c?
-2, 0
Let g(m) be the third derivative of -m**7/630 + m**6/40 - m**5/6 + 11*m**4/18 - 4*m**3/3 - 10*m**2 - 2*m. Solve g(v) = 0 for v.
2, 3
Suppose -94/11*t**2 + 40/11 - 112/11*t - 14/11*t**3 = 0. What is t?
-5, -2, 2/7
Let c(b) be the first derivative of -2*b**3/3 - b**2/2 + 3*b + 16. Let h(a) = -14*a**2 + 190*a + 64. Let d(f) = 20*c(f) - 4*h(f). Find w such that d(w) = 0.
-1/4, 49
Let b(c) be the third derivative of c**6/160 + 3*c**5/10 + 59*c**4/32 - 21*c**3/2 + c**2 + 1382. Find g, given that b(g) = 0.
-21, -4, 1
Let p(g) be the first derivative of -7/20*g**5 + 1/16*g**4 + 0*g**2 + 7/12*g**3 - 1/24*g**6 + 0*g + 172. What is j in p(j) = 0?
-7, -1, 0, 1
Suppose -9*c**4 - 501*c**3 - 56*c - 856*c**2 + 96 - 152*c - 71*c**4 + 36*c**5 + 374*c**3 - 541*c**3 = 0. Calculate c.
-2, -1, 2/9, 6
Let d(a) be the third derivative of a**6/80 + 22*a**5/5 + 7917*a**4/16 + 7569*a**3/2 - 2*a**2 + 621. Suppose d(n) = 0. What is n?
-87, -2
Let k(h) be the second derivative of h**8/8400 + h**7/1050 + h**6/450 - 23*h**4/6 - h**2 - 17*h + 3. Let r(m) be the third derivative of k(m). Factor r(p).
4*p*(p + 1)*(p + 2)/5
Determine t so that -5/2*t - 75/4 - 1/12*t**2 = 0.
-15
Factor -98/9*q + 2/9*q**2 + 0.
2*q*(q - 49)/9
Suppose 2*h - 132 - 67 = -37. Let n = -28 + 391. Solve -150*u**2 + 72*u**2 - 66*u + n + h*u**2 = 0 for u.
11
Suppose 67*f - 40 = 57*f. Suppose f*y - 5*n - 12 = 21, -2*y = 5*n + 21. Factor -9/4 - 33/4*b**y + 3*b**3 + 15/2*b.
3*(b - 1)**2*(4*b - 3)/4
Let m be 15/(-85) - (-156310)/12495. Solve 1/3*i**5 + 0 - 13/3*i**4 - i**3 + 26/3*i + m*i**2 = 0 for i.
-1, 0, 2, 13
Let b(q) be the first derivative of -q**3/7 + 93*q**2/14 + 60*q + 1812. Let b(f) = 0. Calculate f.
-4, 35
Let v(l) = 319*l**2 - 164*l + 51. Let y(j) = 107*j**2 - 57*j + 18. Let h(n) = 6*v(n) - 17*y(n). Factor h(c).
5*c*(19*c - 3)
Let a be (6 + -4 + 240/(-70))/(5/(-42)). Let f(b) be the first derivative of -a + 1/9*b**3 - 1/15*b**5 + 0*b + 1/6*b**2 - 1/12*b**4. Factor f(d).
-d*(d - 1)*(d + 1)**2/3
Let d = 553 - 458. Find u such that -5*u**3 - 233*u - d*u**2 - 273*u + 500 + 106*u = 0.
-10, 1
Let t(v) = -2*v**2 - 10*v + 1000. Let z be t(20). Let u(m) be the first derivative of z*m + 5/3*m**3 - m**5 - 8 + 0*m**4 + 0*m**2. Factor u(d).
-5*d**2*(d - 1)*(d + 1)
Let i(v) be the second derivative of -v**4/16 + 81*v**3/2 - 5446*v. Find s, given that i(s) = 0.
0, 324
Let n be 2 - (5 + -3) - 99/(-16)*(-32)/(-24). Solve 0 - n*q**2 + 3/4*q**4 - 3*q**3 + 45/2*q = 0.
-3, 0, 2, 5
Let h(y) be the third derivative of 0*y - 85*y**2 - 25/3*y**3 + 1/12*y**5 + 15/8*y**4 + 0. Suppose h(t) = 0. What is t?
-10, 1
Suppose -5*a + 35 = -5*f - 0, 0 = 4*a + f - 3. Suppose -168*z**4 - z + 11*z - 128*z**2 - 2 + 232*z**3 + 44*z**5 + 10 + a*z = 0. What is z?
-2/11, 1
Let h = 119 - 112. Suppose 7*f = -h*f + 42. Suppose -1490*j**2 - 38*j**5 - 690*j**f - 105*j**4 + 118*j**5 - 1305*j - 40*j**5 - 405 - 45*j**5 = 0. Calculate j.
-9, -1
Let w(o) = o**2 - 2*o. Let k(l) = -64 - 68*l - l**2 + 5*l**2 + 116 + 6*l**2. Let f(u) = -k(u) + 6*w(u). What is b in f(b) = 0?
1, 13
Let x(r) = 15*r**3 - 203*r**2 - 365*r - 153. Let g be 2/15 - 1175/375. Let u(p) = 30*p**3 - 407*p**2 - 730*p - 307. Let c(b) = g*u(b) + 7*x(b). Factor c(m).
5*(m - 15)*(m + 1)*(3*m + 2)
Let x = 31701 + -31697. Let c(a) be the first derivative of -1/22*a**x - 10/33*a**3 + 2/55*a**5 - 3/11*a**2 - 19 + 0*a. Determine g, given that c(g) = 0.
-1, 0, 3
Let z(u) be the first derivative of 1/12*u**4 + 1/5*u**3 - 10*u - 11 + 1/10*u**2. Let c(q) be the first derivative of z(q). Factor c(f).
(f + 1)*(5*f + 1)/5
Let l be 0 + 18/36*12/3. Factor 0 - 5*u - 2*u**l - 1/5*u**3.
-u*(u + 5)**2/5
Let b(j) be the third derivative of 0 - 1/60*j**5 + 25*j**2 + 0*j + 5/2*j**3 - 1/12*j**4. Factor b(w).
-(w - 3)*(w + 5)
Let g(u) be the second derivative of 2*u**6/75 - 1509*u**5/25 + 7*u - 4. Factor g(y).
4*y**3*(y - 1509)/5
Factor -2/11*t**2 + 384/11 + 382/11*t.
-2*(t - 192)*(t + 1)/11
Let n(w) be the first derivative of 780448/7*w + 232/7*w**3 - 30 - 1/7*w**4 - 20184/7*w**2. Determine o so that n(o) = 0.
58
Suppose 0 = 15*g - 2741 + 2711. Let q(v) be the first derivative of -2/57*v**3 - 4/19*v + 3/19*v**g - 4. Find z such that q(z) = 0.
1, 2
Let o = 86 - 87. Let y(p) = 9*p**2 - p - 1. Let k be y(o). Find q such that -k*q**2 - 2*q**2 + 11*q**2 + 16*q + 2*q**2 = 0.
-8, 0
Let g(z) = 4*z**3 - 248*z**2 + 2492*z - 7060. Let m(q) = 4*q**3 - 247*q**2 + 2493*q - 7059. Let i(p) = -3*g(p) + 4*m(p). Determine d so that i(d) = 0.
6, 49
What is n in -34*n**2 + 0 + 0*n - 1/5*n**4 + 87/5*n**3 = 0?
0, 2, 85
Let t(q) = -4*q**4 - 3*q**3 + 3*q**2 - q - 10. Let k(j) = -12*j**4 - 12*j**3 + 12*j**2 - 4*j - 32. Let z(r) = 5*k(r) - 16*t(r). Suppose z(n) = 0. What is n?
0, 1
Let x be (9 - 14)*(-1 - (3 + -3)). Let n be (-5)/10*x*216/(-105). Factor 16/7*q**2 + 8/7 + n*q.
4*(q + 2)*(4*q + 1)/7
Factor 16*r - 5*r**4 + 203*r - 240*r**3 + 7464*r + 5911*r + 75000 - 1344*r - 2505*r**2.
-5*(r - 6)*(r + 4)*(r + 25)**2
Let i(o) be the first derivative of 1/9*o**6 + 14/15*o**5 - 64 + 0*o + 3/2*o**4 - 14/9*o**3 - 10/3*o**2. Determine n so that i(n) = 0.
-5, -2, -1, 0, 1
Suppose 5*v = -4 + 29. Suppose 0 = 5*h + 4*q - 11, v*h - 2*q - 14 = -3*q. Factor 0*l**2 - h*l + 5*l**2 - 9*l + 180 - 48*l.
5*(l - 6)**2
Let l(t) be the first derivative of -2 + 0*t**2 + 0*t - 1/4*t**3 + 9/32*t**4 + 0*t**5 - 1/16*t**6. Suppose l(d) = 0. What is d?
-2, 0, 1
Find s, given that -135*s**3 + 1772 + 148*s**2 + 5*s**5 - 5*s**4 - 2372 + 57*s**2 + 530*s = 0.
-5, -2, 1, 3, 4
Suppose -225/2*r + 3/2*r**2 - 351 = 0. Calculate r.
-3, 78
Let f = 20176 - 20143. Let c(v) be the first derivative of -2/7*v - 1/7*v**3 - 5/14*v**2 - f. Factor c(r).
-(r + 1)*(3*r + 2)/7
Factor -63*j**2 + 151*j + 32*j**2 + 40*j**2 + 289*j - 11*j**2 + 442.
-2*(j - 221)*(j + 1)
Let k = 204620/3 - 68206. Factor 0 - k*a**2 - 1/3*a - 1/3*a**3.
-a*(a + 1)**2/3
Let f be 0*1/1*(-1)/(-3). Suppose f = 3*c - 46 - 38. Factor -9*i**5 + 7*i**5 + 8*i**2 - 10*i**5 + 32*i**4 - c*i**3.
-4*i**2*(i - 1)**2*(3*i - 2)
Let i(g) = -40935*g - 450275. Let q be i(-11). Determine k, given that 0 + 25/3*k - q*k**3 + 20/3*k**4 - 20/3*k**2 + 5/3*k**5 = 0.
-5, -1, 0, 1
Let c(j) = 8*j**2 - 972*j + 14. Let n(z) = -3*z**2 + 324*z - 5. Let x(m) = 5*c(m) + 14*n(m). Find s, given that x(s) = 0.
-162, 0
Let w(i) = 28*i**3 + 6*i**2 - 52*i + 187. Let u be w(4). Let y = u - 1864. Solve 12/7*c**y + 2/7*c + 2/7*c**5 + 0 - 8/7*c**4 - 8/7*c**2 = 0 for c.
0, 1
Suppose 113*k**2 + 39*k**3 - 11