7*n**4/4 + 23763*n**3/2 - 2114907*n**2/2 - 419*n. Factor k(m).
3*(m - 89)**3
Let -9*d**3 - 162*d**2 - 11*d**3 + 3*d**4 - 25*d**3 = 0. Calculate d.
-3, 0, 18
Factor -3/7*p**2 + 120/7 + 117/7*p.
-3*(p - 40)*(p + 1)/7
Let m be -2 - (186/18)/(-31)*(1 + 14). Let 0 - 15/7*t**m + 3/7*t**2 + 3/7*t + 9/7*t**4 = 0. What is t?
-1/3, 0, 1
Suppose 0 = -29*f + 37*f - 144. Let o be (-3 - 184/(-36)) + (-2)/f. Determine a, given that 8/3*a**2 + 0 - 8/9*a - o*a**3 = 0.
0, 2/3
Let c(n) = n**3 + 4*n**2. Let p be c(-3). Let u(z) = z - 6. Let d be u(p). Suppose 15*w**4 + 3*w**2 - 3 + 4*w**d - 5 - 8*w - 17*w**4 + 3*w**2 = 0. Calculate w.
-1, 2
Let j(c) be the first derivative of c**8/672 + c**7/420 - c**6/240 - c**5/120 - 5*c**2/2 - 13. Let u(n) be the second derivative of j(n). Factor u(q).
q**2*(q - 1)*(q + 1)**2/2
Let l = 23672 + -165701/7. Let v be (-3)/(-2)*(-2)/(-7). Factor -3/7*m**3 + l*m**2 + v*m - 3/7.
-3*(m - 1)**2*(m + 1)/7
Let v(b) be the first derivative of 2*b**5/25 - 2*b**4/5 + 2*b**3/5 + 31. Factor v(z).
2*z**2*(z - 3)*(z - 1)/5
Let v(m) be the second derivative of 3*m**6/160 - m**5/15 + 5*m**4/96 + m**3/12 + 33*m**2/2 + 32*m. Let a(l) be the first derivative of v(l). Factor a(o).
(o - 1)**2*(9*o + 2)/4
Let o(c) = -c**2 - 8*c + 11. Let z be o(-8). Let u be (29/z)/(-1) - (-27)/9. Suppose -2/11*h**2 + 0 + u*h = 0. Calculate h.
0, 2
Let x(n) be the first derivative of -39/2*n**2 + 12 - 51*n**3 - 57/5*n**5 - 165/4*n**4 + 6*n. Let x(q) = 0. Calculate q.
-1, 2/19
Let q(j) be the first derivative of -15*j**4/4 + 102*j**3 - 810*j**2 + 600*j + 468. Factor q(t).
-3*(t - 10)**2*(5*t - 2)
Factor 32/3*m + 1/3*m**3 + 10/3*m**2 + 32/3.
(m + 2)*(m + 4)**2/3
Let i(c) = 31*c**2 + 3*c + 2. Let v be i(-1). Let q be 171/(-156) + v/24. Determine w, given that 4/13 - 2/13*w - q*w**2 = 0.
-2, 1
Suppose 0 = 2*r - 3*q - 5, -38*r + 33*r - 5*q = -25. Find d, given that 1/7 + 1/7*d**5 + 1/7*d**r + 1/7*d - 2/7*d**2 - 2/7*d**3 = 0.
-1, 1
Factor -3/4*k**3 - 441*k + 2058 + 63/2*k**2.
-3*(k - 14)**3/4
Let u(m) be the third derivative of 3*m**2 - 4/3*m**3 - 1/2*m**4 + 0 + 0*m + 1/10*m**6 + 1/15*m**5 + 2/105*m**7. Determine i, given that u(i) = 0.
-2, -1, 1
Factor 87/2*f**2 - 117/2*f + 3/2*f**4 - 27/2*f**3 + 27.
3*(f - 3)**2*(f - 2)*(f - 1)/2
Suppose -v + 3*n - 1 = -9, 0 = -4*v + 6*n + 20. Factor 0 + 4/3*t**v + 0*t + 2/3*t**4 + 2*t**3.
2*t**2*(t + 1)*(t + 2)/3
Let q(h) = h**2 - 12*h - 22. Let j be q(14). Let f be (-2)/(((-18)/15)/j). Find k, given that 5 - 9*k + f - 10*k**2 - 16*k = 0.
-3, 1/2
Let -576/11 - 38*n**3 + 2252/11*n**2 + 192*n + 18/11*n**4 = 0. Calculate n.
-1, 2/9, 12
Let w(v) be the second derivative of 0*v**2 - 24*v - 2/9*v**4 + 1/15*v**6 + 0 + 0*v**3 + 1/63*v**7 + 0*v**5. Solve w(l) = 0.
-2, 0, 1
Let l(w) be the first derivative of 5*w**3/3 + 55*w**2/2 + 150*w + 198. Suppose l(v) = 0. What is v?
-6, -5
Let q be (64/(-40))/(2*6/(-15)). Find s such that 3/4*s**5 - 1/2*s**q - 3/2*s**3 + 3/4*s + 1/4 + 1/4*s**4 = 0.
-1, -1/3, 1
Let u(l) be the first derivative of l**7/7560 - l**5/270 + 17*l**3/3 - 18. Let y(x) be the third derivative of u(x). Determine n so that y(n) = 0.
-2, 0, 2
Let p = 42 - 27. Suppose 3*c - 6*c = -5*y + p, 0 = -y - c + 3. Suppose 35 + 0*x + 3*x**3 + y*x**2 - 38 - 3*x = 0. Calculate x.
-1, 1
Let h(j) be the first derivative of -j**4/8 - 23*j**3/6 - 143*j**2/4 - 121*j/2 - 124. Factor h(r).
-(r + 1)*(r + 11)**2/2
Let m(a) be the second derivative of a**5/5 + 2*a**4 - 32*a**3/3 - 80*a. Factor m(w).
4*w*(w - 2)*(w + 8)
Let w(a) be the first derivative of a**5/50 + a**4/30 - a**3/15 - a**2/5 - 13*a + 6. Let g(n) be the first derivative of w(n). Factor g(v).
2*(v - 1)*(v + 1)**2/5
Let d = 286 + -283. Let i(b) be the third derivative of -1/20*b**5 + 0*b**d + 0*b - 7*b**2 + 1/40*b**6 - 1/8*b**4 + 0 + 1/70*b**7. Solve i(n) = 0 for n.
-1, 0, 1
Let p(h) be the first derivative of 0*h**2 + 1/2*h**6 + 3/5*h**5 - 24 + 0*h - h**3 - 3/4*h**4. Factor p(w).
3*w**2*(w - 1)*(w + 1)**2
Let y(q) be the first derivative of -q**7/1155 + q**5/330 + 5*q**2 - 19. Let w(v) be the second derivative of y(v). Factor w(f).
-2*f**2*(f - 1)*(f + 1)/11
Suppose 0 = -104*f + 289 - 81. Factor -1 + 1/3*y**f + 2/3*y.
(y - 1)*(y + 3)/3
Let u(y) be the second derivative of 3*y**5/20 + 150*y**4 + 60000*y**3 + 12000000*y**2 + 230*y. What is n in u(n) = 0?
-200
Let s = -256 + 204. Let c be (-1)/((-1)/(-5)) - s/10. Factor -q + 4/5*q**2 + 2/5 - c*q**3.
-(q - 2)*(q - 1)**2/5
Suppose 2*t + 3*v - 14 = 16, -4*t + 5*v + 38 = 0. Let l = t - 12. Determine i so that 2*i**2 + 8*i**3 - 6*i**2 + 8*i - 2 - 8*i**2 - 2*i**4 + l*i = 0.
1
Let j be 4 + (19 - 2 - 4). Suppose -5*o - 3*h + 17 = 0, -5*o + 2*o + j = -5*h. Determine n, given that 0 - 4/3*n**o - 12*n**2 + 8*n**3 + 0*n = 0.
0, 3
Factor 16/7*z + 40/7*z**2 + 33/7*z**3 + 1/7*z**5 + 10/7*z**4 + 0.
z*(z + 1)**2*(z + 4)**2/7
Factor 40*i**2 + 14*i + 16*i**3 + 2*i**4 + 19*i - 18*i + 17*i.
2*i*(i + 2)**2*(i + 4)
Let f(c) be the second derivative of -1/32*c**4 + 0 - 1/8*c**3 + 3/80*c**5 + 0*c**2 - 28*c + 1/80*c**6. Factor f(s).
3*s*(s - 1)*(s + 1)*(s + 2)/8
Let y be (14/6)/((-105)/(-20)). Factor -1/9*v**2 - y + 4/9*v.
-(v - 2)**2/9
Let w(g) = 4*g**2 - 5*g + 7. Let v(p) = 36*p**2 - 44*p + 64. Let a be -1 - 2*(-12)/(-8)*9. Let j(r) = a*w(r) + 3*v(r). Determine u so that j(u) = 0.
1
Let j be (4/10)/((-66)/(-1375)). Factor -j - 10/3*f - 1/3*f**2.
-(f + 5)**2/3
Let j(w) be the third derivative of -w**8/2240 + w**7/840 + 5*w**4/12 - 47*w**2. Let i(p) be the second derivative of j(p). Factor i(o).
-3*o**2*(o - 1)
Let s(k) be the second derivative of -k**7/1680 - k**6/80 - k**5/16 - 7*k**4/48 + 10*k**3/3 + 20*k. Let z(c) be the second derivative of s(c). Factor z(g).
-(g + 1)**2*(g + 7)/2
Let u = 2097/527 - 66/17. Let m = u + 239/93. Solve 5/3*w**5 + 2/3 - 4/3*w**3 + m*w**4 - 1/3*w - 10/3*w**2 = 0.
-1, 2/5, 1
Let n(k) = 6*k**2 + k - 3. Let o be n(1). Let z(c) be the third derivative of -1/300*c**6 + 0 - 1/60*c**o + 1/75*c**5 + 0*c + 0*c**3 + 13*c**2. Factor z(q).
-2*q*(q - 1)**2/5
Factor -38*l**2 + 50*l + 55*l**2 - 44*l**2 - 28*l**2 + 5*l**3.
5*l*(l - 10)*(l - 1)
Let s(f) = -4*f + 0*f - 12 + 6 + 6*f. Let q be s(5). Determine v, given that -4*v**2 - v**q + v**4 + 2*v**4 - 2*v**3 = 0.
-1, 0, 2
Let q(x) be the second derivative of x**6/60 - 7*x**5/40 - 5*x**4/3 - 11*x**3/3 + 179*x. Let q(d) = 0. Calculate d.
-2, 0, 11
Let 0*b - 1/6*b**5 + 0 + 1/2*b**4 - 9/2*b**2 + 3/2*b**3 = 0. Calculate b.
-3, 0, 3
Solve 30*d + 16*d**3 - 9*d**3 - 9*d**3 + 25*d**2 + 7*d**3 = 0 for d.
-3, -2, 0
Suppose 816*b**2 - 1991 + 288*b + 248*b**3 + 1991 + 20*b**4 = 0. Calculate b.
-6, -2/5, 0
Let b(l) = 4*l**2 - 52*l + 16. Let n(z) = -12*z - 1 + 4*z + 7*z + 0*z. Let q(o) = -b(o) + 24*n(o). Solve q(d) = 0.
2, 5
Let a(u) be the third derivative of -u**6/540 - u**5/45 - u**4/9 - u**3/3 - 11*u**2. Let z(o) be the first derivative of a(o). Determine l so that z(l) = 0.
-2
Suppose -228 + 204 = -6*c. Find w such that -3/2*w**3 + 3/2*w**2 + 0 - 1/2*w + 1/2*w**c = 0.
0, 1
Let h(l) be the third derivative of l**6/540 - l**5/45 + l**4/12 - 8*l**3/3 + 11*l**2. Let s(z) be the first derivative of h(z). Solve s(d) = 0 for d.
1, 3
Solve -4*q**5 - 132*q**4 + 124*q**4 + 24*q**3 - 8 - 12*q + 16*q**2 - 4*q**5 - 4*q**5 = 0 for q.
-1, -2/3, 1
Let n(d) = d + 8. Let t be n(-4). Factor -8*k**3 - 33*k**2 + 11*k**4 - 12*k**t - 24*k + 11*k**2 - 9.
-(k + 1)**2*(k + 3)**2
Let s(x) be the third derivative of -x**7/210 - x**6/240 + 13*x**5/24 + 11*x**4/6 - 5*x**3 + 3*x**2 + 41. Solve s(q) = 0 for q.
-5, -2, 1/2, 6
Let z be 1*0*11/88. Suppose -8*h + 4*h = 0. Determine j so that -2/15*j**5 - 2/15*j + 4/15*j**3 + z*j**2 + h*j**4 + 0 = 0.
-1, 0, 1
Let m = 5771 - 28827/5. Factor -m*q + 8/5 + 4*q**2.
4*(q - 1)*(5*q - 2)/5
Let j(i) be the second derivative of i**4/54 - 64*i**3/27 + 1024*i**2/9 - 67*i. Solve j(b) = 0.
32
Let s(y) be the third derivative of y**7/2520 + y**6/80 + y**4/8 + 39*y**2. Let d(p) be the second derivative of s(p). Find z such that d(z) = 0.
-9, 0
Suppose 2*b - 24 = -18. Suppose 2 + 13*t**2 + t**4 - 4*t**2 + 254*t + 5*t**b - 247*t = 0. What is t?
-2, -1
Let h(d) be the first derivative of -1 + 0*d - 1/16*d**4 - 1/8*d**2 - 1/6*d**3. Factor h(b).
-b*(b + 1)**2/4
Let s be (26/(-65))/((-1)/295). Let y = -115 + s. Let -2/7*