 = 0.
-2, -1, 1
Find f, given that -6/5*f**3 - 2/5*f**4 + 0*f + 0 + 36/5*f**2 = 0.
-6, 0, 3
Let b(j) be the second derivative of 1/96*j**4 + 1/336*j**7 - 28*j - 1/160*j**5 + 0*j**3 + 0*j**2 + 1 - 1/240*j**6. Suppose b(c) = 0. Calculate c.
-1, 0, 1
Let f = -51119/8 - -173451/40. Let d = 2054 + f. Solve 0 - 6/5*c**2 + d*c**3 + 2/5*c**5 + 6/5*c**4 - 4/5*c = 0 for c.
-2, -1, 0, 1
Let k(i) be the first derivative of i**4/108 + 4*i**3/27 - 39*i + 19. Let u(o) be the first derivative of k(o). Factor u(n).
n*(n + 8)/9
Let b(c) be the third derivative of -53*c**6/30 - 176*c**5/5 - 435*c**4/2 + 100*c**3/3 - 16*c**2 + 15*c. Let b(y) = 0. What is y?
-5, 2/53
Let n(k) = -3*k**2 + 1019*k + 1056. Let q(p) = -p**2 + 339*p + 352. Let d(i) = 6*n(i) - 17*q(i). Solve d(w) = 0.
-1, 352
Let i(n) be the second derivative of 3 - 6/5*n**2 + 1/3*n**3 + 7*n + 1/30*n**4. Factor i(h).
2*(h - 1)*(h + 6)/5
Let n(f) be the third derivative of f**6/360 + 2*f**5/15 - 31*f**4/72 - 25*f**3/3 - 2926*f**2 - f. Solve n(l) = 0 for l.
-25, -2, 3
Suppose -36 = -0*n + 4*n. Let u be n/(-12) + -1 + 106/8. Factor -3 - 6*i**2 + u + 7*i**2 + 15*i + 4*i**2.
5*(i + 1)*(i + 2)
Let h(f) = -f**3 + 12*f**2 - 12*f - 26. Let r be h(10). Suppose 260 = -49*u + r*u. Let -12*p - 4*p + 17*p**2 + 6*p - u*p**2 = 0. Calculate p.
-2/7, 0
Let n(c) = -2*c**4 - 416*c**3 - 21202*c**2 + 44092*c + 8. Let v(k) = k**2 - k + 1. Let a(r) = n(r) - 8*v(r). Solve a(i) = 0.
-105, 0, 2
Let -22/3*l + 20/3*l**2 - 140/3 - 2/3*l**3 = 0. What is l?
-2, 5, 7
Let y(p) be the second derivative of -p**6/2700 + 17*p**5/900 - p**3/3 + 73*p**2/2 - 89*p. Let o(w) be the second derivative of y(w). Find m such that o(m) = 0.
0, 17
Let g be ((-30)/24)/(-1 + 66/96). Let h(p) be the third derivative of -19*p - 8/5*p**3 - 7/20*p**g + 2*p**2 + 0 + 1/50*p**5. Factor h(o).
6*(o - 8)*(o + 1)/5
Let z(k) = -k**2 - 16*k - 37. Suppose t = -5*r + 8, 3*t + 2*t + 2*r = -52. Let y be z(t). Factor 12*f - 1 + 4*f**2 + 14*f**4 - 11*f**4 + 5*f**2 - 12*f**3 - y.
3*(f - 2)**2*(f - 1)*(f + 1)
Let m(r) = 3*r**2 + 40*r + 11. Let u be m(-13). Let q be (-793)/(-244) + u/8*1. What is c in 1/3*c**q + 0 - 2/3*c**2 - c = 0?
-1, 0, 3
Let d(i) be the second derivative of i**7/4095 + i**6/1560 - i**5/780 - 25*i**4/12 - 52*i. Let y(t) be the third derivative of d(t). Factor y(k).
2*(k + 1)*(4*k - 1)/13
Suppose -14 + 37 = -23*x. Let r(v) = 10*v**5 + 10*v**4 - 5*v**3. Let w(t) = t**5 + t**4 + t**2. Let y(d) = x*r(d) + 5*w(d). Factor y(f).
-5*f**2*(f - 1)*(f + 1)**2
Let k(p) = -7*p**3 + 27*p**2 - 85*p + 5. Let o(t) = 3*t**3 - 13*t**2 + 40*t - 2. Let x(j) = 6*k(j) + 15*o(j). Solve x(b) = 0 for b.
0, 5, 6
Let f(o) be the first derivative of 3*o**4/4 - 476*o**3 - 2865*o**2/2 - 1434*o - 2434. Solve f(g) = 0.
-1, 478
Let l be (-460)/(-1725)*((-12)/24)/(2*2/(-24)). What is n in -l*n**2 - 28/5*n - 48/5 = 0?
-4, -3
Factor 1058/13 + 2/13*d**2 + 92/13*d.
2*(d + 23)**2/13
Let c(m) be the third derivative of -7*m**5/30 + 5*m**4/3 - 23*m**3/2 - 5*m**2 + 2*m. Let n(q) = 22*q**2 - 60*q + 104. Let r(z) = -8*c(z) - 5*n(z). Factor r(j).
2*(j - 8)*(j - 2)
Let k(t) = 13*t**2 - 41*t + 28. Let z(a) = 135*a**2 - 414*a + 279. Let d(q) = 21*k(q) - 2*z(q). Factor d(b).
3*(b - 10)*(b - 1)
Let u(x) be the first derivative of -23 - 2/5*x**5 + 0*x + 1/3*x**6 + 2/3*x**3 + 0*x**2 - 1/2*x**4. Determine t so that u(t) = 0.
-1, 0, 1
Let c(t) be the second derivative of 5 + 3/100*t**5 + 6/5*t**2 - 3/20*t**4 - 2*t + 0*t**3. Factor c(j).
3*(j - 2)**2*(j + 1)/5
Factor 55/2 - 109/4*m - 1/4*m**2.
-(m - 1)*(m + 110)/4
Let l(t) be the third derivative of 1/140*t**7 - 6*t**2 - 1/16*t**6 + 0 - 3/2*t**3 + 1/8*t**5 + t + 5/16*t**4. Let l(o) = 0. Calculate o.
-1, 1, 2, 3
Let c(n) be the second derivative of -9*n**5/20 - 31*n**4/2 + 23*n**3/2 + 63*n**2 - 49*n - 3. Let c(w) = 0. Calculate w.
-21, -2/3, 1
Factor -812/5*u + 804/5*u**2 + 272/5 - 52*u**3 - 4/5*u**4.
-4*(u - 1)**3*(u + 68)/5
Let k = 631 - 612. Suppose 0 = -y + k*y. Factor 0 + 3/7*b**3 + y*b + 2/7*b**2 + 1/7*b**4.
b**2*(b + 1)*(b + 2)/7
Let k(y) = 11*y**3 - 24*y**2 + 55*y - 36. Let s be (-10)/2 + -3 + 8/4. Let b(d) = 23*d**3 - 47*d**2 + 110*d - 73. Let r(i) = s*b(i) + 13*k(i). Factor r(w).
5*(w - 3)*(w - 2)*(w - 1)
Solve -2*q**5 + q**5 - 3*q**5 - 12*q**3 - 37*q**2 + 13*q**4 - 3*q**2 + 11*q**4 = 0 for q.
-1, 0, 2, 5
Let f be -379 + 5 + 2 - 8. Let p be (f/(-475))/((-44)/(-10)). Solve -4/11 - 2/11*n + p*n**2 = 0.
-1, 2
Let d(i) be the second derivative of 3/5*i**6 - 69/10*i**5 + 0 + 1/14*i**7 - 75/2*i**3 + 33*i**2 + 23*i**4 - 86*i. What is j in d(j) = 0?
-11, 1, 2
Let m(i) = i**3 - 24*i**2 + 2*i - 19. Let w be m(24). Let f be (w/(-174))/(2/(-64)). Factor -64/3*c + 5/3*c**4 + 24*c**2 - 32/3*c**3 + f.
(c - 2)**3*(5*c - 2)/3
Let n(y) be the first derivative of -10*y**3/27 - 118*y**2/9 - 46*y/3 - 488. Factor n(j).
-2*(j + 23)*(5*j + 3)/9
Let t(d) be the third derivative of -d**8/112 + 6*d**7/35 - 9*d**6/8 + 29*d**5/10 - 3*d**4 + 400*d**2 + 2*d. Determine h, given that t(h) = 0.
0, 1, 4, 6
Let o(u) be the second derivative of u**6/225 - 4*u**5/75 + 8*u**4/45 - 2766*u. Find d, given that o(d) = 0.
0, 4
Factor -8*h**3 + 12 + 1/2*h**4 - 31*h + 53/2*h**2.
(h - 12)*(h - 2)*(h - 1)**2/2
Let x = 29 - 31. Let u(j) = -2*j**3 - 4*j**2 - 4*j - 4. Let i be u(x). Factor i*l**4 + 6*l**2 - 1 - 7 - 4*l**3 - 6*l**4 + 8*l.
-2*(l - 1)**2*(l + 2)**2
Factor -2*n**2 + 11956*n - 5*n**3 - 11526*n + 207*n**2.
-5*n*(n - 43)*(n + 2)
Let b(g) = g**2 + 8*g + 20. Let s be b(-8). Let 10*u**4 + 0*u**3 + 16*u**5 - 4*u - s*u**2 + 10*u**4 - 11*u**3 - u**3 = 0. Calculate u.
-1, -1/4, 0, 1
Let p = 2836 - 2832. Let g(f) be the second derivative of 7/4*f**p + 4*f - 7/20*f**5 + 2*f**2 - 1/6*f**6 + 0 - 8/3*f**3 + 1/14*f**7. Factor g(v).
(v - 1)**3*(v + 2)*(3*v - 2)
Suppose 1106*o - d - 26 = 1100*o, 2*o + 5*d - 30 = 0. Factor -1/2*p**3 - 12 - 14*p - o*p**2.
-(p + 2)**2*(p + 6)/2
Let c(d) = 127*d**3 - 189*d**2 + 708*d - 548. Let z(m) = 18*m**3 - m**2 - m - 2. Let r(g) = 3*c(g) - 21*z(g). Determine t, given that r(t) = 0.
1, 3, 178
Let z(a) = -52*a - 53. Let s be z(-4). Let f be -2 - (-6)/(150/s). Let 0 + 0*d + f*d**5 - 69/5*d**4 + 12*d**3 - 12/5*d**2 = 0. What is d?
0, 2/7, 1, 2
Let t(g) be the third derivative of g**6/40 - g**5/40 - g**4/4 + 3*g**3 + 57*g**2. Let x(c) be the first derivative of t(c). Factor x(a).
3*(a - 1)*(3*a + 2)
Suppose 10 = 2*i - 3*i - 5*r, 0 = 2*i + 3*r - 1. Suppose -5*t + 170 = -i*w, 2*t - 70 = w - 1. Factor -2 + c - 29*c**2 + 3*c + t*c**2.
2*(c + 1)*(3*c - 1)
Let b be 177/(-413)*((-4)/(-12) + -5). Factor -14/3 - 22/3*a + 2*a**3 - 2/3*a**b.
2*(a + 1)**2*(3*a - 7)/3
Let o be (-77840)/(-34815) + (-6)/11. Let n = o - 5/211. Factor -n*c**2 - 40/3*c - 80/3.
-5*(c + 4)**2/3
Determine n so that -29*n + 13*n**2 + 8*n**3 + 52*n**3 - 20*n - 3*n**4 - 11*n - 10*n**2 = 0.
-1, 0, 1, 20
Let w be (-1470)/44835 + (-508)/(-610). Let t = 5196/1855 + -2/1855. Let -w*p**2 + 8/5 + t*p = 0. What is p?
-1/2, 4
Let s(b) = b**3 + 20*b**2 + 306*b + 4338. Let p be s(-17). Factor 0 + 10/19*q**p + 14/19*q**2 + 4/19*q.
2*q*(q + 1)*(5*q + 2)/19
Let m(q) be the first derivative of 4/7*q + 189 + 106/21*q**3 - 55/7*q**2. Factor m(p).
2*(p - 1)*(53*p - 2)/7
Let k = -47253 + 47255. Factor 144/5*y + 3/5*y**3 + 36/5*y**k + 192/5.
3*(y + 4)**3/5
Let m(c) be the second derivative of c**7/2520 - c**6/120 + 28*c**4/3 - 6*c - 10. Let t(u) be the third derivative of m(u). What is r in t(r) = 0?
0, 6
Let q(h) be the third derivative of -1/24*h**6 + 23*h**2 + 0 + 3/2*h**5 - 45/2*h**4 + 0*h + 180*h**3. Find r, given that q(r) = 0.
6
Factor -937 + 2*a**2 + 237 - 230*a - 24*a**2 + 14*a**2 + 2*a**3.
2*(a - 14)*(a + 5)**2
Factor 16206*t**2 + 1556068 - 810008*t + 1/4*t**4 - 110*t**3.
(t - 146)**3*(t - 2)/4
Let t(n) be the second derivative of -5*n**4/12 + 3565*n**3/6 - 3555*n**2 + 2358*n. Solve t(d) = 0.
2, 711
Let w = -633 + 628. Let j be (-9)/w*((-30)/(-9) - 2). Factor j*k - 4/5*k**2 - 8/5.
-4*(k - 2)*(k - 1)/5
Let k(t) be the second derivative of 35*t**4/12 - 1370*t**3/3 + 390*t**2 + 2878*t. Factor k(f).
5*(f - 78)*(7*f - 2)
Let g(s) be the first derivative of -60/7*s**3 - 23/7*s**4 - 81/7*s**2 - 54/7*s - 1/21*s**6 - 147 - 22/35*s**5. Let g(f) = 0. Calculate f.
-3, -1
Let u(n) be the second derivative of -1/8*n**4 - 9/4*n**2 - 39*n