(h) = 0. Calculate h.
8
Let k(l) be the third derivative of -l**6/600 - 2*l**5/25 + 17*l**4/24 + 18*l**3/5 - 1803*l**2. Determine g, given that k(g) = 0.
-27, -1, 4
Let 483148/11*h + 2/11*h**4 + 20352/11*h**2 + 340/11*h**3 + 297754 = 0. What is h?
-53, -11
Let a = -271 + 768. Suppose -2*z**3 + 497 - a + 2*z = 0. What is z?
-1, 0, 1
Let u(x) be the second derivative of 50*x + 0*x**2 + 0 + 5/12*x**4 + 95/3*x**3. Let u(p) = 0. What is p?
-38, 0
Factor 341*q**4 - 500*q + 1 - 150*q**2 + 20*q**3 - 114 - 336*q**4 + 481 + 257.
5*(q - 5)*(q - 1)*(q + 5)**2
Let b = 2/116161 - -8131264/348483. Solve 70/3*l**2 - b - 5/3*l + 5/3*l**3 = 0.
-14, -1, 1
Let a = 120487/1680 - 502/7. Let x(d) be the third derivative of 0*d**3 + 8*d**2 + 0 + 1/48*d**4 + 0*d - 1/480*d**6 + a*d**5. Let x(r) = 0. What is r?
-1, 0, 2
Let a(c) be the first derivative of 5*c**3/3 - 6310*c**2 + 7963220*c + 3235. Factor a(r).
5*(r - 1262)**2
Let s be (11 + -6 + -11)/2. Let u be (s - (-17 + 7)) + 68/(-10). Factor u*h**2 + 0 + 9/5*h.
h*(h + 9)/5
Solve -1/3*a**4 + 0 - 130/3*a**3 + 130/3*a + 1/3*a**2 = 0.
-130, -1, 0, 1
Factor -457*f**3 + f**4 + 3994452 - 110*f**3 - 4755432 - 19816020 + 106590*f**2 - 7726751*f + 1192651*f.
(f - 190)**3*(f + 3)
Let t(o) be the third derivative of 5*o**9/12096 + o**8/672 - 17*o**3/6 - 86*o**2. Let c(u) be the first derivative of t(u). Factor c(z).
5*z**4*(z + 2)/4
Let y(l) = 6*l**2 + 170*l + 366. Let s(a) = 15*a**2 + 426*a + 912. Let z(w) = 5*s(w) - 12*y(w). Solve z(c) = 0.
-28, -2
Let c(m) = -9*m**2 - 55*m + 64. Let d be (0 + 5/(-10))*10. Let v(b) = 8*b**2 + 56*b - 64. Let w(n) = d*v(n) - 4*c(n). Factor w(s).
-4*(s - 1)*(s + 16)
Let g = -33 - -67/2. Let u be 5/(-15) - (-1211)/519. Factor 0 + 1/2*q**4 + 3/2*q**u + 3/2*q**3 + g*q.
q*(q + 1)**3/2
Let k = -19188536/679 - -28260. Let a = 2029/1358 + k. Factor -3/4*x**4 - 21/8*x**3 - a*x**2 + 3/8*x**5 + 0*x + 0.
3*x**2*(x - 4)*(x + 1)**2/8
Find v, given that 0 - 1/8*v**4 - 41/4*v**3 - 161/8*v**2 - 10*v = 0.
-80, -1, 0
Suppose -635*a + 565*a = -140. Factor -1/4*v + 1/4*v**a - 1/2.
(v - 2)*(v + 1)/4
Solve 3/7*p**3 - 172/7 - 137/7*p**2 + 348/7*p = 0 for p.
2/3, 2, 43
Let q = -169 + 194. Factor -162*y + q*y**2 + 338*y - 5 - 156*y.
5*(y + 1)*(5*y - 1)
Let f(j) = 13*j**3 - 724*j**2 - 1501*j - 764. Let i(s) = 3*s**3 - 144*s**2 - 300*s - 153. Let y(u) = 3*f(u) - 14*i(u). Determine g, given that y(g) = 0.
-50, -1
Suppose 0 = -2*b + b + 9. Suppose 23 = q - b. Factor -43 - 4*r**2 - q*r - 21 + 0*r**2.
-4*(r + 4)**2
Let x(l) be the second derivative of l**6/1620 + l**5/180 + l**4/54 - l**3/2 + 23*l. Let r(a) be the second derivative of x(a). What is m in r(m) = 0?
-2, -1
Let g(p) = -2*p**3 - 28*p**2 - 72*p + 348. Let w(b) = -4*b**3 - 51*b**2 - 144*b + 695. Let d(s) = -9*g(s) + 4*w(s). Solve d(h) = 0 for h.
-22, -4, 2
Let m(j) be the first derivative of -j**4/32 - j**3/2 - 40*j - 21. Let p(b) be the first derivative of m(b). Suppose p(o) = 0. What is o?
-8, 0
Let a(f) be the second derivative of -f**4/66 - 2*f**3/3 + 48*f**2/11 - 1860*f. Factor a(h).
-2*(h - 2)*(h + 24)/11
Suppose 25 = 6*j - 53. Let f(o) = 149*o - 189*o**2 + 12 + 15 + j. Let c(a) = 47*a**2 - 37*a - 10. Let v(z) = 9*c(z) + 2*f(z). Factor v(l).
5*(l - 1)*(9*l + 2)
Suppose 12*a + 50 = 110. Let o(p) be the second derivative of -1/20*p**2 + 0 - 1/200*p**a + 1/120*p**4 + 1/60*p**3 + 7*p. Solve o(k) = 0 for k.
-1, 1
Let d be ((-4)/(-6))/(27360/(-6480))*-19. Factor -20/7*o**d + 4*o**2 - 12/7 + 4/7*o.
-4*(o - 1)**2*(5*o + 3)/7
Let s = -4 - -10. Suppose -14 - s = -4*a. Factor m**4 + 4*m**5 + 2 + 9*m**4 + 20*m**2 - 20*m**3 + 5*m**a - 10*m - 11*m**5.
-2*(m - 1)**5
Let z(c) be the second derivative of c**4/42 - 458*c**3/21 + 52441*c**2/7 - 569*c. Suppose z(d) = 0. Calculate d.
229
Let t be (66062/87)/67 + 10/(-12). Factor -3/2*d**2 + 0 + t*d.
-3*d*(d - 7)/2
Suppose n + 271 - 273 = 0. Suppose -4*k = -k + 3*z - 12, -n*z = 0. Factor 3/5*r**k - 48/5*r - 48/5 + 12/5*r**3 + 0*r**2.
3*(r - 2)*(r + 2)**3/5
Let m(v) = 2*v**5 + 14*v**4 + 5*v**3 - 5*v - 5. Let y = -386 - -380. Let t(f) = -f**5 - 7*f**4 - 2*f**3 + 2*f + 2. Let b(z) = y*m(z) - 15*t(z). Factor b(c).
3*c**4*(c + 7)
Let u(z) = 3*z**2 + 83*z + 436. Let l be u(-7). Factor 2/7*s**5 - 4/7*s + 2/7*s**4 - 6/7*s**3 - 10/7*s**l + 0.
2*s*(s - 2)*(s + 1)**3/7
Suppose 35 = -25*r + 30*r + k, r - 83 = -4*k. Solve -8/3*x**r + 7/3*x**2 + 1/3*x**4 + 0 + 0*x = 0 for x.
0, 1, 7
Suppose -102 = 19*o - 31*o - 30. Let n(k) be the second derivative of 4*k + 0*k**2 + 0*k**3 + 0 + 2/3*k**o - 4/3*k**4 + 8/5*k**5. Factor n(b).
4*b**2*(b + 2)*(5*b - 2)
Let b(s) be the first derivative of s**7/2940 + s**6/126 + 5*s**5/84 + 2*s**3 - 2*s**2 + 23. Let g(v) be the third derivative of b(v). Factor g(n).
2*n*(n + 5)**2/7
Let k be -1 + 209/187 - (-23)/((-24633)/(-180)). Factor 2*r - k*r**2 + 0.
-2*r*(r - 7)/7
Let x(u) be the third derivative of 1/840*u**7 + 35*u**2 - 1 - 1/480*u**6 - 1/12*u**3 + 5/96*u**4 - 1/80*u**5 + 0*u. Solve x(w) = 0 for w.
-2, 1
Find t, given that -112*t**2 + t**4 + 25*t**3 - 3656*t - 3821*t + 7593*t = 0.
-29, 0, 2
Let j = 558231 + -5024063/9. Factor 0 + 8/9*w**2 + j*w - 7/9*w**3 + 1/9*w**4.
w*(w - 4)**2*(w + 1)/9
Let u be ((-2)/(-10))/((-9)/(-20430)). Let l = -452 + u. Determine c, given that 18/7*c**l - 30/7*c - 2/7*c**3 - 50/7 = 0.
-1, 5
Suppose 15*r + 33 = 13 + 65. Factor 1/2*p**3 - 5/2*p**2 - r*p + 0.
p*(p - 6)*(p + 1)/2
Let i = 2/7 + 8/21. Let t be -3 + ((-4)/2 - 26/((-754)/261)). Solve 2*j**2 + 4/3 - 10/3*j + 2/3*j**3 - i*j**t = 0 for j.
-2, 1
Let h = 15890 - 15885. Let y(l) be the second derivative of 19/4*l**4 - 6*l**2 - 36*l + 21/20*l**h + 0 + 4*l**3. Suppose y(r) = 0. Calculate r.
-2, -1, 2/7
Let r be 126/(-36)*(-8)/7. Suppose -3*p - r*f = -2*f + 1, -2*f = 5*p - 5. Let -6/17*l - 4/17 + 2/17*l**p + 0*l**2 = 0. What is l?
-1, 2
Let f be (-60 - (33 - 57))/(-42). Determine l so that 6/7*l**4 + 0 - 2/7*l**5 + 0*l + 2/7*l**2 - f*l**3 = 0.
0, 1
Let u = 40 - 36. Let u*m**4 + 358 + 1280*m - 9*m**2 + 1242 + 105*m**2 - 64*m**3 = 0. What is m?
-2, 10
Let m = -2095354 - -2095356. Solve 46/7*z**m + 2/7*z**3 + 26*z - 1014/7 = 0 for z.
-13, 3
Let m(b) be the first derivative of -2/9*b**3 - 57 - 12*b**2 - 216*b. Factor m(f).
-2*(f + 18)**2/3
Let s = 107/11 - 2225/231. Let u(k) be the third derivative of 0 + 2/735*k**7 + 4*k**2 + 0*k**6 + s*k**3 - 2/105*k**5 + 0*k + 0*k**4. Factor u(f).
4*(f - 1)**2*(f + 1)**2/7
Let w(j) be the third derivative of 0 - 5/28*j**4 + 1/210*j**5 + 144*j**2 + 0*j - 16/21*j**3. Factor w(r).
2*(r - 16)*(r + 1)/7
Let k = 491507/819180 - -1/819180. Factor 3/5*m + 6/5 - 6/5*m**2 - k*m**3.
-3*(m - 1)*(m + 1)*(m + 2)/5
Let c(o) be the first derivative of -2*o**3/9 - 16*o**2/3 + 38*o + 115. Factor c(m).
-2*(m - 3)*(m + 19)/3
Let m(o) be the first derivative of -o**6/18 - 8*o**5/15 - 5*o**4/4 + 4*o**3/9 + 10*o**2/3 - 1644. Suppose m(x) = 0. What is x?
-5, -2, 0, 1
Suppose 16*m = -177 + 209. Let y be (m - 0) + 22/(-44). Solve 3/4*q**2 + y - 9/4*q = 0 for q.
1, 2
Let f = 342510 - 1027492/3. Solve -2*m**4 - f*m**3 + 0 - 14*m**2 - 10/3*m = 0.
-5, -1, -1/3, 0
Suppose 5*r = 2*f + 4, f - 13 = -6*r + r. Let q be 12/32*r + 1705/372. Let -q*v + 32/3*v**2 - 4*v**3 + 0 = 0. Calculate v.
0, 2/3, 2
Let o be (0 - (-3)/5) + 6740/100. Suppose 2*q**5 + 176*q - o + 91 + 26*q**4 + 110*q**3 + 33 + 206*q**2 = 0. What is q?
-7, -2, -1
Find r such that -122657188/3 - 123245002/3*r - 196251*r**2 - 1/6*r**4 - 1879/6*r**3 = 0.
-626, -1
Let d be (6854 - 6845) + ((-4)/6 - (-416)/(-60)). Let 0 - 1/5*m**4 + 9/5*m + d*m**3 - 3*m**2 = 0. What is m?
0, 1, 3
Let u = -20900 - -20900. Let d(l) be the second derivative of -2*l + 1/105*l**6 + 0 + 3/70*l**5 + 0*l**2 + u*l**3 + 1/21*l**4. Factor d(r).
2*r**2*(r + 1)*(r + 2)/7
Let x(b) be the third derivative of 0 - 2/5*b**3 + 0*b + 19/60*b**4 - 4/75*b**5 + 14*b**2. Factor x(i).
-2*(i - 2)*(8*i - 3)/5
Find z, given that 7/3*z**4 + 2056/3*z + 188 + 191/3*z**2 - 334/3*z**3 = 0.
-2, -2/7, 3, 47
Let i = 353/6 - 5437/102. Let r = -103/34 + i. Find s such that 3*s - 1/2*s**2 - r = 0.
1, 5
Let i(d) be the third derivative of d**7/1470 + d**6/120 - d**5/14 + d**4/42 + 20*d**3/21 + 13*d**2 - 2. Factor i(q).
(q - 2)**2*(q + 1)*(q + 10)/7
Let n = -204915 + 409831/2. Factor 0*l**2 + n*l**3 - 3/2*l + 1.
(l - 1)**2*(l + 2)/2