h + 8)/9
Let c(q) be the third derivative of -q**5/330 + q**4/44 + 6*q**3/11 + 147*q**2 - 3. Factor c(n).
-2*(n - 6)*(n + 3)/11
Let q(c) = -c**3 - 9*c - 8. Suppose -57 = 9*a - 48. Let z be q(a). Factor -1/4*x + 0 - 1/4*x**z.
-x*(x + 1)/4
Let v(o) be the first derivative of o**6/45 - 892*o**5/75 + 66601*o**4/30 - 1349464*o**3/9 + 6549296*o**2/15 - 6483584*o/15 + 1043. What is c in v(c) = 0?
1, 148
Let b(t) = t**3 - 2*t**2 + t - 5. Let y(d) = 234*d**2 - 386*d - 206. Let s(w) = 28*b(w) - 2*y(w). What is g in s(g) = 0?
-2/7, 2, 17
Let k(p) be the second derivative of -p**5/5 + 31*p**4 + 390*p**3 + 1782*p**2 - 1872*p. Let k(s) = 0. Calculate s.
-3, 99
Let k be ((-21)/2912)/(612/(-13056)). Find o, given that -1248*o - k*o**3 - 24*o**2 - 21632 = 0.
-52
Let j(s) be the first derivative of -s**4/38 - 94*s**3/57 - 731*s**2/19 - 7514*s/19 - 1367. Determine r, given that j(r) = 0.
-17, -13
Let d(b) be the third derivative of 9*b**8/28 - 118*b**7/21 + 1139*b**6/30 - 1777*b**5/15 + 139*b**4 + 48*b**3 - 3339*b**2. Determine l, given that d(l) = 0.
-2/27, 1, 3, 4
Suppose 5*d + 24 = -3*o, 7 = -d + 4*o + 39. Let t(u) be the second derivative of 1/80*u**5 + 3/16*u**4 - 4*u + 9/8*u**3 + 27/8*u**2 + d. Factor t(r).
(r + 3)**3/4
Let t(z) be the second derivative of z**5/300 + 9*z**4/40 - 85*z**2/2 - 105*z. Let y(p) be the first derivative of t(p). Factor y(q).
q*(q + 27)/5
Let v = -1265 + 1267. Let k(r) be the first derivative of -12 + 1/40*r**4 - 1/20*r**v - 3/10*r + 1/10*r**3. Solve k(q) = 0.
-3, -1, 1
Let g be (67 + -68)/((-1)/5). Suppose 5*k - g*d - 25 = 0, 4*k + 7*d = -4*d - 25. Suppose 0 - 1/4*y - 1/4*y**k = 0. What is y?
-1, 0
Let a(u) be the third derivative of u**8/2184 + 86*u**7/1365 + 77*u**6/780 - 346*u**5/195 - 85*u**4/13 - 431*u**2 - 3. Find h such that a(h) = 0.
-85, -2, 0, 3
Let s(a) = 5*a**4 - 106*a**3 - 341*a**2 - 232*a - 2. Let o(y) = y**4 + y**3 + 2*y**2 + y - 1. Let n(b) = -2*o(b) + s(b). Let n(q) = 0. What is q?
-2, -1, 0, 39
Let x(m) = 3*m**2 + 403. Let z(r) = -r**2 - r - 202. Let u(a) = -2*x(a) - 5*z(a). Let u(n) = 0. Calculate n.
-12, 17
Let r(d) = -d**2 + 6*d + 16. Suppose -g - g + 4*q + 14 = 0, 7 = g - 5*q. Let h be r(g). Let h*j + 7*j + 20 - 36*j**2 + 32*j**2 = 0. What is j?
-1, 5
Let b(f) be the third derivative of f**5/105 + 11*f**4/42 + 20*f**3/21 + 142*f**2 - 3*f. Find y, given that b(y) = 0.
-10, -1
Let w(d) be the third derivative of d**6/240 + 67*d**5/120 - 23*d**4/8 - 578*d**2. Factor w(h).
h*(h - 2)*(h + 69)/2
Factor 759/4*n**2 + 3/4*n**3 - 3/4*n - 759/4.
3*(n - 1)*(n + 1)*(n + 253)/4
Let k(p) = 8*p**4 + 36*p**3 + 8*p**2 - 4*p - 12. Let y(c) = c**4 + 5*c**3 - c**2 - c - 3. Let n(t) = -k(t) + 4*y(t). Factor n(l).
-4*l**2*(l + 1)*(l + 3)
Let f(l) = -35*l + 37. Let h be f(-13). Suppose -8 = -h*g + 490*g. Find w, given that -4*w**3 + 33/5*w**2 - 4*w + 4/5 + 4/5*w**g = 0.
1/2, 2
Let a(l) be the third derivative of -l**7/525 + 16*l**6/75 - 92*l**5/75 - 448*l**4 - 11760*l**3 - 5805*l**2. Factor a(u).
-2*(u - 42)**2*(u + 10)**2/5
Find j such that 2/7*j**4 + 2/7*j**2 - 10/7*j**3 + 6*j - 36/7 = 0.
-2, 1, 3
Let m(w) be the first derivative of w**4/4 + 3*w**3/2 - 129*w + 60. Let b(h) be the first derivative of m(h). Factor b(q).
3*q*(q + 3)
Let i(b) be the second derivative of b**4/3 + 796*b**3/3 - 798*b**2 - 338*b. Suppose i(t) = 0. Calculate t.
-399, 1
Let -3200*a - 56/3*a**3 - 2/3*a**4 + 0 + 1720/3*a**2 = 0. Calculate a.
-48, 0, 10
Let y be (-10)/(((-165)/88)/(26/104)). Factor 5/6*q**2 + 2/3 - y*q - 1/6*q**3.
-(q - 2)**2*(q - 1)/6
Let l = 0 + 3. Suppose l*w - 20 = -14. Let -4*h**w + 141*h + h**2 - 6 - 15*h**3 - 126*h + 9*h**4 = 0. Calculate h.
-1, 2/3, 1
Let k = -6854003557/367990 + 4565824/245. Let p = k + -2/3755. Suppose 15/2 - 33/2*t + p*t**2 - 3/2*t**3 = 0. What is t?
1, 5
Let p(j) = -71*j**2 - 109*j + 549. Let l(o) = -13*o**2 - 22*o + 110. Let d(q) = 11*l(q) - 2*p(q). Factor d(v).
-(v - 4)*(v + 28)
Let f be (((-1140)/304)/(15/(-19872)))/(-2 + 9). Suppose 272/7*a**3 + 5/7*a**4 + 11664/7 + f*a**2 + 31104/7*a = 0. What is a?
-18, -2/5
Let k be 0 - 6/(-21) - 128256/(-189). Let i = 680 - k. Factor 0*j + i*j**4 + 0 - 4/9*j**2 - 2/3*j**3.
2*j**2*(j - 1)*(5*j + 2)/9
Let o(b) be the second derivative of -b**6/90 - 2*b**5/5 - 16*b**4/3 - 256*b**3/9 - 5865*b. Determine r, given that o(r) = 0.
-8, 0
Suppose 0 = h - 5*z - 2, 18*h - 36 = -22*z + 17*z. Factor 6561/2 + 1/2*p**4 - 1458*p + 243*p**h - 18*p**3.
(p - 9)**4/2
Let g(x) = 8*x - 86. Let m be g(14). Let a = -232/9 + m. Let 2/9*i**2 - 4/9*i + 0 + 2/3*i**3 - a*i**5 - 2/9*i**4 = 0. Calculate i.
-2, -1, 0, 1
Let y(j) be the third derivative of -j**5/60 - 43*j**4/24 + 78*j**3 - 187*j**2 - 2*j + 3. Let y(v) = 0. What is v?
-52, 9
Suppose 3*g + 3870 = 5*i - 1883, 5*i - g = 5761. Let 2817 - 1299 - i + 360*v - 5*v**2 = 0. Calculate v.
-1, 73
Let m(y) be the first derivative of y**7/1680 + y**6/80 - 17*y**5/120 + y**4/2 + 161*y**3/3 - 92. Let o(b) be the third derivative of m(b). Factor o(a).
(a - 2)*(a - 1)*(a + 12)/2
Let h(v) be the third derivative of -7*v**6/540 - 43*v**5/180 - v**4/6 + 197*v**3/6 - 109*v**2. Let i(j) be the first derivative of h(j). Factor i(w).
-2*(w + 6)*(7*w + 1)/3
What is d in 120 + 35*d + 5/4*d**2 = 0?
-24, -4
Let h = 238 + -235. Find a, given that -37*a**4 - 20*a**5 + 261*a + 267*a + 144 - 35*a**3 - 92*a**4 + 412*a**2 - 25*a**h + 21*a**4 = 0.
-3, -1, -2/5, 2
Let b(k) be the third derivative of k**6/180 - k**5/12 - 7*k**4/6 - 23*k**3/2 + 42*k**2. Let h(i) be the first derivative of b(i). Factor h(z).
2*(z - 7)*(z + 2)
Let z(k) be the third derivative of -k**7/588 - k**6/70 - k**5/35 + 2*k**4/21 + 21*k**3 + 3*k**2. Let q(t) be the first derivative of z(t). Factor q(c).
-2*(c + 2)**2*(5*c - 2)/7
Let m(y) be the first derivative of -2*y**3/39 + 49*y**2/13 - 96*y/13 + 2055. Determine k, given that m(k) = 0.
1, 48
Let g(l) be the first derivative of -l**6/210 + l**5/14 - 3*l**4/7 + 9*l**3/7 - 27*l**2/14 - 70*l + 43. Let f(z) be the first derivative of g(z). Factor f(n).
-(n - 3)**3*(n - 1)/7
Let z(m) be the third derivative of m**6/480 - 9*m**5/80 - 5*m**4/4 - 31*m**3/6 - 1242*m**2. Factor z(b).
(b - 31)*(b + 2)**2/4
Let i(q) be the third derivative of -q**6/80 + 13*q**5/40 - 11*q**4/4 + 8*q**3 - 752*q**2. Find k such that i(k) = 0.
1, 4, 8
Let v = -1/117012 - -234035/1287132. Factor 20/11*c**2 + 64/11*c + 64/11 + v*c**3.
2*(c + 2)*(c + 4)**2/11
Let q(r) = -283*r**2 - 260*r + 179. Let a(t) = -141*t**2 - 125*t + 88. Let n(z) = 13*a(z) - 6*q(z). Factor n(d).
-5*(d + 1)*(27*d - 14)
Suppose -298/21*h**3 + 196/3 - 770/3*h + 2/3*h**4 + 102*h**2 = 0. Calculate h.
2/7, 7
Let t(z) be the first derivative of -7*z**4/10 - 986*z**3/15 - 42*z**2 - 8130. Factor t(j).
-2*j*(j + 70)*(7*j + 3)/5
Let z(b) be the first derivative of 9*b**3 + 345*b**2/2 - 78*b - 1493. Let z(o) = 0. Calculate o.
-13, 2/9
Let k = 94 - 90. What is b in -5*b**3 - 6*b**k + 2*b**5 - 51*b**3 + 270*b**2 + 2*b**3 - 324*b = 0?
-6, 0, 3
Let s be (-2773)/(-58233) - (-118)/168. Factor -s*q**2 + 0 + 12*q.
-3*q*(q - 16)/4
Factor -11 + 405*k**2 - 13 + 30*k**3 + 1 - 30*k - 385*k**2 - 2 + 5*k**4.
5*(k - 1)*(k + 1)**2*(k + 5)
Let n(x) be the first derivative of -2 + 1/12*x**4 + 0*x**3 + 0*x**2 - 4*x - 1/20*x**5. Let s(u) be the first derivative of n(u). Find i, given that s(i) = 0.
0, 1
Let i be 14/(-21) - (-442)/357. Factor -i*f**3 - 150/7 - 46/7*f**2 - 160/7*f.
-2*(f + 5)**2*(2*f + 3)/7
Let l(s) = 4*s**4 - s**2 - 2*s + 2. Let b(t) = 21*t**4 - 104*t**3 + 98*t**2 - 10*t + 10. Let d(k) = -b(k) + 5*l(k). Factor d(g).
-g**2*(g - 103)*(g - 1)
Let j be (1 - 6682/230)/(-14 + -28). Let a = j + -1/805. Factor 16/9 + a*c**2 - 28/9*c.
2*(c - 4)*(3*c - 2)/9
Let -1/3 - 255*i**2 + 766/3*i = 0. What is i?
1/765, 1
Factor -168 + 1/4*s**2 + 41*s.
(s - 4)*(s + 168)/4
Let x(a) be the third derivative of -6*a**3 + 0 + 11/12*a**4 + 0*a - 11/60*a**6 - 112*a**2 + 1/105*a**7 + 17/30*a**5. Suppose x(m) = 0. What is m?
-1, 1, 2, 9
Let k be (645/90)/43*(-1 + 3). Factor -1 - 1/3*r + r**2 + k*r**3.
(r - 1)*(r + 1)*(r + 3)/3
Let d(b) be the second derivative of 4*b**7/21 - 13*b**6/3 - 66*b**5/5 + 101*b**4/6 + 128*b**3/3 - 36*b**2 - 1599*b. Find l such that d(l) = 0.
-2, -1, 1/4, 1, 18
Let o(r) be the first derivative of 17*r**4 - 347 - 2/3*r**6 - 212/3*r**