derivative of b**5/60 + 227*b**4/6 + 103058*b**3/3 + 46788332*b**2/3 + 1227*b. Suppose g(s) = 0. Calculate s.
-454
Let v(a) be the third derivative of 17/140*a**7 + 16*a**3 + 0 - 11/20*a**6 + 0*a + 1/56*a**8 - 7/2*a**5 + 14*a**4 + 61*a**2. Find o such that v(o) = 0.
-4, -1/4, 2
Let p(m) be the first derivative of -413/4*m**2 - 9/8*m**4 + 49*m + 101 - 62/3*m**3. Solve p(j) = 0 for j.
-7, 2/9
Let f(j) be the third derivative of j**8/3 + 46*j**7/105 - 284*j**6/15 + 97*j**5/15 + 10*j**4 + 3*j**2 + j + 40. What is c in f(c) = 0?
-5, -1/4, 0, 3/7, 4
Let b(c) = 2*c**5 + 8*c**4 + 22*c**3 + 8*c**2 + 12*c. Let t(a) be the first derivative of a**4/4 + a**2/2 - 21. Let f(g) = -2*b(g) + 20*t(g). Factor f(o).
-4*o*(o + 1)**4
Let q(i) = i**4 + 22*i**3 + 122*i**2 + 95*i + 3. Let c(m) = 2*m**4 + 43*m**3 + 245*m**2 + 190*m + 7. Let s(z) = 3*c(z) - 7*q(z). Factor s(x).
-x*(x + 1)*(x + 5)*(x + 19)
Suppose 0 = 535*x - 3809 - 1006. Let u(q) be the second derivative of -1/225*q**6 + 0*q**2 + 0 - 1/30*q**5 - 2/45*q**4 - x*q + 0*q**3. Factor u(f).
-2*f**2*(f + 1)*(f + 4)/15
Let a = 325/14 + -267/14. Let z = a - 4. Factor -2/7*o**2 + 0*o + 0*o**3 + 1/7 + z*o**4.
(o - 1)**2*(o + 1)**2/7
Let d(x) be the second derivative of -1/50*x**5 - 256/5*x**3 + 0 - 4096/5*x**2 - 8/5*x**4 + 70*x. Suppose d(f) = 0. Calculate f.
-16
Let z(a) be the third derivative of -a**8/448 + 99*a**7/70 - 39203*a**6/160 - 99*a**5/20 + 9801*a**4/8 - a**2 + 1605*a. What is h in z(h) = 0?
-1, 0, 1, 198
Let s be (-10873)/(-13100) - (4 + 98/(-25)). Factor -1/2 - 5/2*n**2 - 9/4*n - s*n**3.
-(n + 1)*(n + 2)*(3*n + 1)/4
Let l = -159498 + 1435484/9. Suppose l*s**4 - 2/9*s**2 - 8/9*s + 8/9*s**3 + 0 = 0. Calculate s.
-4, -1, 0, 1
Let z be (-1 + (-2)/(-3))/(181/(-4344)). Factor 8*x**3 + 28*x + 6 - z + 5 + 28*x**2 + 5.
4*(x + 1)*(x + 2)*(2*x + 1)
Let q(z) be the third derivative of z**6/40 - 19*z**5/10 + 131*z**4/8 + 85*z**3 - 568*z**2. Factor q(x).
3*(x - 34)*(x - 5)*(x + 1)
Let h(o) be the second derivative of 4*o**4/27 + 110*o**3/27 + 34*o**2/3 - 1920*o. What is c in h(c) = 0?
-51/4, -1
Let t be 3/((-25)/10 + 4). Let u = -43 - -46. Determine l so that -10*l**t - u*l**3 - 8*l**3 + 12*l + 13*l**3 = 0.
0, 2, 3
Let d be 562/(-2380) + (-9)/54. Let o = -1/357 - d. Factor o*n**2 + 4*n + 10.
2*(n + 5)**2/5
Factor -42*j**2 - 480*j - 79 - 340*j**3 - 346*j**3 + 685*j**3 - 721.
-(j + 2)*(j + 20)**2
Factor 66*s**2 + 32400 - 25*s**2 - 19*s**2 - 18*s**2 - 720*s.
4*(s - 90)**2
What is h in -2196*h + 3*h**4 + 757*h**2 - 288*h**3 + 1133 + 632*h**2 - 41 = 0?
1, 2, 91
Let a = 604945/9 + -67213. Factor 2/9*u - 8/9 + a*u**2 + 2*u**3.
2*(u + 1)**2*(9*u - 4)/9
Find v such that 1713981 + 250796 - 27336*v + 48*v**2 + 1927186 = 0.
1139/4
Let g(k) be the third derivative of k**6/180 + 74*k**5/45 + 2*k**2 - 2*k + 33. Suppose g(q) = 0. What is q?
-148, 0
Let f = 6595 + -6595. Let s(m) be the second derivative of 0 - 2/25*m**5 + 3*m + 2/75*m**6 + f*m**2 + 1/15*m**4 + 0*m**3. Factor s(w).
4*w**2*(w - 1)**2/5
Let x(p) be the second derivative of -5*p**4/12 + 925*p**3/6 - 460*p**2 + 8*p - 65. Determine v so that x(v) = 0.
1, 184
Let d = 273 - 259. Let q be (d/(-70))/(0 + -1)*1. Determine c so that -q*c**2 - 1/5*c**3 + 0 + 0*c = 0.
-1, 0
Let -2*o + 153/4 - 1/4*o**2 = 0. Calculate o.
-17, 9
Let t(l) be the third derivative of -l**7/70 - l**6/24 + l**5/30 + 703*l**2. Determine j so that t(j) = 0.
-2, 0, 1/3
Factor 10372*t**4 + 20*t**3 + t**2 - 10367*t**4 - 30*t - 2*t**2 + 6*t**2.
5*t*(t - 1)*(t + 2)*(t + 3)
Let z(v) = 3144*v + 276675. Let d be z(-88). Factor 2/3 + o + 1/3*o**5 + 0*o**4 - 2/3*o**2 - 4/3*o**d.
(o - 2)*(o - 1)*(o + 1)**3/3
Let 336 + 1665*i**2 + 1504*i - 81/2*i**3 = 0. What is i?
-4/9, 42
Solve 49/3*m**3 + 134/3*m**2 - 184/3*m + 1/3*m**4 + 0 = 0.
-46, -4, 0, 1
Solve -284/5*p**2 - 4/5*p**4 - 144/5 + 2/5*p**5 - 344/5*p - 18*p**3 = 0 for p.
-2, -1, 9
Let a = -1390463/6 - -231744. Factor a*r**4 + 0*r**2 + 0 - 2/3*r + 1/2*r**3.
r*(r - 1)*(r + 2)**2/6
Let m(g) be the first derivative of g**4/2 - 2*g**3 - 952. Factor m(o).
2*o**2*(o - 3)
Let z(w) be the second derivative of -56 + 6*w**2 + 1/4*w**4 - 5/2*w**3 + w. Factor z(i).
3*(i - 4)*(i - 1)
Let a = -17881 - -125171/7. Factor -a - 12/7*u**2 - 26/7*u.
-2*(u + 2)*(6*u + 1)/7
Suppose -7*g + 10 = -2*g. Suppose -32*p = 12*p - 88. Factor -14/3*q + 16/3*q**g + 4/3 - p*q**3.
-2*(q - 1)**2*(3*q - 2)/3
Let f be ((-2)/(-6))/(11/66). Suppose f*r = -4*k + 80, 4*r + 2*k + 0*k = 184. Factor -s**3 - 6*s - 2 + 42*s**2 - r*s**2 - s**3.
-2*(s + 1)**3
Let h be ((-47)/(-3) - 3)/((-32)/(-48)). Let g = 22 - h. Factor -g - 1/3*j**2 - 2*j.
-(j + 3)**2/3
Suppose 0*r - 12 = -4*r. Suppose r*d = -4 + 10. Find x, given that 4*x**d + 4*x + 2*x - 6*x = 0.
0
Let o(g) = -65*g**2 + 5135*g - 5170. Let d(z) = 4*z**2 - 302*z + 304. Let x(v) = -50*d(v) - 3*o(v). What is r in x(r) = 0?
-62, 1
Factor 651/4*y**2 + 10218313/4 - 141267/4*y - 1/4*y**3.
-(y - 217)**3/4
Let o be 1 + 10/(-8) - 33/12. Let k(s) = 2*s**2 + 11*s + 23. Let v be k(o). What is b in -8 - 14 - 2*b**2 - v - 22*b + 10 = 0?
-10, -1
Let j(i) be the second derivative of -1/6*i**3 + 1/20*i**5 + 0 - i**2 - 79*i + 1/6*i**4. Let j(t) = 0. What is t?
-2, -1, 1
Let w be 158 + -1 - (-7 + 54/9). Suppose 15*x - 60*x**2 + 4 - w*x**3 + 1 + 193*x**3 + 5 = 0. What is x?
-2/7, 1
Determine a, given that -69*a**5 - 2742*a**2 - 32*a**5 - 1389*a**3 - 2028*a - 456 + 116*a**5 - 204*a**4 = 0.
-2, -1, -2/5, 19
Let t(g) be the second derivative of -54/5*g**2 + 1/25*g**5 + 18/5*g**3 + 0 - 127*g - 3/5*g**4. Find j, given that t(j) = 0.
3
Let u = -51 + 54. Suppose 2*i - 2*f = 6, -3*f - 4 = -3*i - 5*f. Find s, given that i*s**2 - 2*s**u + s**3 - 4*s**3 + 3*s**2 = 0.
0, 1
Let y(j) be the first derivative of 175*j**6/2 - 278*j**5 - 11955*j**4/4 + 8260*j**3/3 + 390*j**2 - 720*j - 7586. Suppose y(u) = 0. What is u?
-4, -2/7, 1/3, 3/5, 6
Factor -14*w**3 - 97*w**2 + 2*w**4 + 438*w + 489*w - 967*w + 41*w**2.
2*w*(w - 10)*(w + 1)*(w + 2)
Let t(r) = r**5 - 42*r**4 + 444*r**3 - 1722*r**2 - 12. Let d(h) = -h**4 + 2*h**3 + h**2 - 2. Let l = 175 + -174. Let j(k) = l*t(k) - 6*d(k). Factor j(a).
a**2*(a - 12)**3
Suppose 1091 = 602*k - 699 - 16. Let -1/3*r - 1/9*r**k + 0 - 4/9*r**2 = 0. What is r?
-3, -1, 0
Let z(s) be the second derivative of -s**9/75600 - s**8/33600 + s**7/6300 - s**4/12 - s**2/2 + 2*s - 13. Let n(h) be the third derivative of z(h). Factor n(m).
-m**2*(m - 1)*(m + 2)/5
Let v(z) be the third derivative of -z**7/70 - 3*z**6/2 - 957*z**5/20 - 2299*z**4/4 - 1088*z**2 + 2. Factor v(w).
-3*w*(w + 11)**2*(w + 38)
Solve 352*d**2 - 4/3*d**3 + 726*d + 2/3*d**5 + 0 - 32/3*d**4 = 0.
-3, 0, 11
Let p(i) be the first derivative of -i**4 - 52*i**3/3 - 20*i**2 + 96*i - 761. Let p(g) = 0. What is g?
-12, -2, 1
Let m = -23 - -25. Factor 930*v**2 - 5*v**4 + 580*v + 75*v**3 - 160 - 1260*v**m - 200.
-5*(v - 9)*(v - 2)**3
Let t(k) = -282*k**3 - 1744*k**2 + 64*k + 16. Let y(s) = -88*s**3 - 581*s**2 + 20*s + 5. Let i(u) = -5*t(u) + 16*y(u). Suppose i(q) = 0. What is q?
0, 288
Let v(z) be the first derivative of z**3/21 - 5*z**2/14 - 2187. Find w, given that v(w) = 0.
0, 5
Suppose -9 = 4*f - 3*p - 3, -3*f = -3*p + 3. Let r be (-24)/(-64) - f/(-8). Factor -4/3 + 13*l**2 + r*l - 35/3*l**3.
-(l - 1)*(5*l - 2)*(7*l + 2)/3
Let k(i) be the second derivative of -i**5/10 - 41*i**4/6 + 130*i**3/3 - 88*i**2 + 2493*i. Factor k(g).
-2*(g - 2)*(g - 1)*(g + 44)
Let k(h) be the first derivative of -6*h**4 - 2*h**2 + 0*h - 16/3*h**3 - 16/5*h**5 - 2/3*h**6 + 14. Factor k(s).
-4*s*(s + 1)**4
Let v = 3/563308 - 16031182423/9576236. Let w = v - -1677. Factor -18/17*y + 10/17*y**3 - 42/17*y**2 + w*y**4 + 0.
2*y*(y - 1)*(5*y + 3)**2/17
Let 4377/2*l + 6386043/4 + 3/4*l**2 = 0. Calculate l.
-1459
Let j = 5207/3507 + -240/167. Let q(t) be the first derivative of -j*t**6 - 8/7*t - 17/7*t**2 - 16/35*t**5 - 7 - 11/7*t**4 - 8/3*t**3. Solve q(c) = 0.
-4, -1
Let c(z) = -z**2 + 2*z + 4. Let i be 6/4 - (-2 - (-12)/8). Let h be c(i). Find n, given that 8*n**4 - n**h - 16*n + 4*n**4 + 12*n**3 - 7*n**4 = 0.
-2, 0, 1
Let f(v) be the first derivative of v**4/24 + 271*v**3/18 + 6165*v**2/4 + 6075*v/2 - 1485. Determine u, given that f(u) = 0.
-135, -1
Let k(s) = -s**3 - 575*s**2 + 621*s + 10. Let i(d) = d**3 + 287*d**2 - 315*d - 6. Let c(v) = 10*i