- 216. Let o(u) be the third derivative of 1/168*u**4 + 1/280*u**6 + 0*u**3 - 1/1470*u**7 + 0 + 2*u**2 - 1/140*u**5 + z*u. Solve o(p) = 0.
0, 1
Let c(g) be the third derivative of 0*g**4 - 3*g**2 + 0*g**3 + 1/15*g**5 + 0 - 1/30*g**6 + 0*g. Factor c(r).
-4*r**2*(r - 1)
Factor -13/4*t**3 + 33/8*t**2 + 7/4*t + 0 + 3/8*t**4.
t*(t - 7)*(t - 2)*(3*t + 1)/8
Let c = -31571 - -31573. Find q such that 2/7*q**3 + 0*q**c + 0 - 2/7*q = 0.
-1, 0, 1
Suppose 0 = 4*s + 3*i, 0 = -2*i - 12 + 4. Let k(z) be the first derivative of 9*z + 3 - 1 + 7 - 3*z**s + 6*z**2 + 6*z**2. Factor k(q).
-3*(q - 3)*(3*q + 1)
Let t be -8*(-20 + 8)/48. Factor -3/2*j**t + 0*j + 1/2*j**3 + 2.
(j - 2)**2*(j + 1)/2
Let p = -26713/15 + 1781. Factor -2/5*j + 0 + p*j**3 - 4/15*j**2.
2*j*(j - 3)*(j + 1)/15
Let q(i) = -i**3 + i + 1. Let u(x) = 7*x**3 + 10*x**2 - 2*x - 2. Let l(z) = 2*q(z) + u(z). Determine c, given that l(c) = 0.
-2, 0
Let u be -64 + 12/(-4) + 2. Let q = -62 - u. Determine g so that -2/9*g**2 + 2/9*g**4 + 0*g**q + 0 + 0*g = 0.
-1, 0, 1
Let x(l) = l**2 + l. Let r(q) = 11*q**2 + q - 2. Let b be r(2). Let u(d) = 16*d**2 + 12*d - 4. Let i(a) = b*x(a) - 2*u(a). Find h, given that i(h) = 0.
-1, -2/3
Let j be (925/1110)/(5/9). Factor -3*d**2 - j*d**3 + 0*d + 0.
-3*d**2*(d + 2)/2
Let j(a) be the second derivative of a**7/294 + a**6/105 - 3*a**5/140 - a**4/21 + 2*a**3/21 + 129*a + 1. Factor j(t).
t*(t - 1)**2*(t + 2)**2/7
Suppose 0 = 2*p - s - 5, 2*s - 18 = -3*p. Suppose 13 = p*m + 1. Factor 9*x**2 - 5 - 5*x**3 + 5*x - 5*x**m + x**2 - 5*x**4 + 5*x**5.
5*(x - 1)**3*(x + 1)**2
Let r(j) = -j**2 - 11*j - 23. Let m be r(-6). Factor 4 + 13*g**2 - 4 + m*g - 2 - 18*g**3.
-(g - 1)*(2*g + 1)*(9*g - 2)
Let t = -36 + 24. Let w = 14 + t. Factor -3*g**2 + 0*g**3 + g**w - 2*g**3 + 0*g**3.
-2*g**2*(g + 1)
Let x(v) be the first derivative of -v**6/180 + v**5/15 - v**4/4 - 11*v**2/2 + 15. Let y(c) be the second derivative of x(c). Factor y(p).
-2*p*(p - 3)**2/3
Let y(o) be the first derivative of -o**8/288 + 4*o**7/315 - o**6/180 + 3*o**2 + 11. Let q(n) be the second derivative of y(n). Factor q(k).
-k**3*(k - 2)*(7*k - 2)/6
Suppose -39*b - 65 = -38*b. Let u be b/(-15) - 0 - 3 - 1. Factor 1/3 - u*r**2 + 0*r.
-(r - 1)*(r + 1)/3
Let s(o) be the second derivative of -o**8/6720 - o**7/1680 + o**5/240 + o**4/96 + 5*o**3/3 + 8*o. Let w(u) be the second derivative of s(u). Factor w(z).
-(z - 1)*(z + 1)**3/4
Let w = 2363/5 + -472. What is r in 6/5 + 3/5*r - w*r**2 = 0?
-1, 2
Let l(h) = 5*h**5 + 3*h**4 - 10*h**3 - 6*h**2 + 2*h + 6. Let b(r) = -r**4 + 2*r**2 + r - 2. Let z(y) = -3*b(y) - l(y). Let z(j) = 0. What is j?
-1, 0, 1
Let n(v) = -2*v**5 + v**3 - v**2. Let i(d) = 9*d**5 - 4*d**4 + 7*d**3 + 3*d**2 - 11*d + 6. Let x(w) = i(w) + 5*n(w). Solve x(j) = 0.
-6, -1, 1
Let s = -21 + 26. Suppose -s*q + 6 = -4. Factor -533*b**2 + 10*b + 458*b**q - 3*b**3 + 93*b**3.
5*b*(3*b - 2)*(6*b - 1)
Let b(f) be the first derivative of -3*f**5/5 - 3*f**4/2 + 3*f**3 + 12*f**2 + 12*f - 78. Determine x so that b(x) = 0.
-2, -1, 2
Find d, given that -68/3*d**3 + 0 + 2/9*d**4 - 78608/9*d + 2312/3*d**2 = 0.
0, 34
Let t(p) = -6*p**2 + 145*p + 137. Let y(x) = 4*x**2 - 97*x - 91. Let h(i) = 5*t(i) + 7*y(i). Factor h(n).
-2*(n - 24)*(n + 1)
Let x(j) be the first derivative of 3*j**5/20 - j**4/12 - 5*j**3/18 - j**2/6 + 12*j + 20. Let y(u) be the first derivative of x(u). Solve y(h) = 0.
-1/3, 1
Let j(v) be the third derivative of -v**7/630 + v**6/5 - 47*v**5/60 + 35*v**4/36 + 667*v**2. Let j(d) = 0. Calculate d.
0, 1, 70
Suppose -3*j + 8 = -61. Suppose -g + 0*g = -3. Find y, given that 72*y**2 + 0 + j*y**g + 18*y**5 + 3 + 69*y**4 + 79*y**3 + 24*y = 0.
-1, -1/2, -1/3
Let j be (9/(-6))/(3/(-6)). Suppose 7*i - 8 = j*i. Factor -4*f**5 + 17*f**4 + 41*f**3 + 35*f**2 + 1 + 8*f + 8*f**5 - 13*f**i - 13*f**3.
(f + 1)**4*(4*f + 1)
Factor 78/5*c - 6/5*c**2 + 0.
-6*c*(c - 13)/5
Suppose -29*r + 42/5 - 7/5*r**2 = 0. Calculate r.
-21, 2/7
Suppose 48 - 44 = 86*g - 168. Suppose 0 + 4/7*v**g + 0*v - 4/7*v**3 + 4/7*v**5 - 4/7*v**4 = 0. Calculate v.
-1, 0, 1
Let m = -332 + 332. Let q(a) be the third derivative of 1/105*a**7 + 1/30*a**5 + 0*a**3 - a**2 + 0*a**4 + 0*a + m - 1/30*a**6. Factor q(i).
2*i**2*(i - 1)**2
Let u(a) be the second derivative of a**4/4 - 11*a**3/10 + 3*a**2/5 + a + 2. Factor u(f).
3*(f - 2)*(5*f - 1)/5
Let g(z) be the second derivative of -5/2*z**2 - 9*z + 35/6*z**3 + 0 + 9/4*z**5 - 25/4*z**4. Factor g(h).
5*(h - 1)*(3*h - 1)**2
Let b(u) be the first derivative of u**4/8 - 5*u**3/6 + 7*u**2/4 - 3*u/2 + 19. Solve b(w) = 0.
1, 3
Suppose 3*a + 6 = 5*x - 4, -4*a = -3*x + 6. Factor -5*c**4 + 3*c**3 + 0*c**4 + 2*c**2 + a*c**2.
-c**2*(c - 1)*(5*c + 2)
Let r(q) be the first derivative of 20*q**4 + 13 + 4*q**3 - 1 - 18*q**4 + 2*q**2. Factor r(d).
4*d*(d + 1)*(2*d + 1)
Let j(p) = p**2 + 2*p - 1. Let k be j(-3). Suppose g + 5*q - 5 + 0 = 0, -5*g = 5*q - 25. Factor 3*b**3 + g*b - 8*b - 3*b**4 - 4 + 9*b**k - 2.
-3*(b - 2)*(b - 1)*(b + 1)**2
Let t(z) be the second derivative of -2*z**6/15 + 4*z**5/5 - 2*z**4 + 8*z**3/3 - 2*z**2 - 117*z. Determine l so that t(l) = 0.
1
Factor 15*z**4 - 15*z**3 - 2*z**5 + 7*z**5 - 7*z**2 - 845*z - 28*z**2 + 875*z.
5*z*(z - 1)**2*(z + 2)*(z + 3)
Factor 0*t + 0 + 3/2*t**5 + 3*t**2 + 15/2*t**3 + 6*t**4.
3*t**2*(t + 1)**2*(t + 2)/2
Factor 9 + 24*u - 26*u + 0 - u**2 + 26.
-(u - 5)*(u + 7)
Let n(h) be the second derivative of h**4/6 - 61*h**3/3 - 62*h**2 - 456*h. Suppose n(t) = 0. Calculate t.
-1, 62
Let n = -17 + 3. Let c = 16 + n. Let 21*q**3 - 5*q - 3*q + q + 57*q**c - 11*q = 0. What is q?
-3, 0, 2/7
Let y(r) be the first derivative of 21/25*r**5 - 13/20*r**4 + 2/5*r**2 - 4/5*r**3 + 0*r + 7. Let y(z) = 0. Calculate z.
-2/3, 0, 2/7, 1
Let n(j) be the first derivative of -j**4/4 - 2*j**3/3 - 4*j + 5. Let i be n(-3). Solve 2*u + i*u + 2 - 5*u**2 - 4*u**2 = 0.
-2/9, 1
Suppose 0 = z - 4*g - 53, 0*g + 5*g - 365 = -5*z. Let d = 69 - z. Determine n so that 1/3*n**4 + 0 - 1/3*n**3 + d*n + 0*n**2 = 0.
0, 1
Let h(m) = -8*m + 1. Let l be h(0). Let y be (2 - (-27)/(-6)) + 3/l. Let 1 - 1/2*w**2 - y*w**4 - 3/2*w + 3/2*w**3 = 0. Calculate w.
-1, 1, 2
Let d(j) = j**3 - j**2 + 2*j - 22. Let k be d(0). Let g = k + 68/3. Factor -g*z**3 + 0*z**2 + 0 + 2/3*z.
-2*z*(z - 1)*(z + 1)/3
Suppose 0 = 5*v - 4 - 31. Let q(r) = -2*r - 59. Let l be q(-31). Factor -v - h**2 - h**2 + 2*h + l + 4*h**2.
2*(h - 1)*(h + 2)
Let w(s) = 2*s**2 + 6*s + 2. Let f be w(-4). Factor y**3 + y**3 - 3*y + f*y**2 - 9 - y**2 + y**3.
3*(y - 1)*(y + 1)*(y + 3)
Let k(q) be the third derivative of 0*q + 0 - 5/24*q**5 - 5/3*q**3 - 5/6*q**4 - 1/48*q**6 + 13*q**2. Determine l so that k(l) = 0.
-2, -1
Let b be 2/(104/33 + (-64)/(-352)). Factor b*m**3 + 0*m**2 + 0 + 0*m.
3*m**3/5
Let r(x) be the second derivative of x**4/30 + 11*x**3/5 + 18*x**2 - 408*x + 1. Factor r(v).
2*(v + 3)*(v + 30)/5
Factor -4*k**3 - 10*k + 3*k**3 + 9*k**3 - 7*k**3 - 4*k**2 - 2*k.
k*(k - 6)*(k + 2)
Let y(z) be the first derivative of -8*z**3 + 36*z**2 - 16 + 1/2*z**4 + 0*z. Factor y(q).
2*q*(q - 6)**2
Suppose 1 = c - 4. Let j be (3 - 0)*28/126. Factor 0*a**2 - j*a**c + 2/3*a**3 + 0*a + 0 + 0*a**4.
-2*a**3*(a - 1)*(a + 1)/3
Let h(g) be the third derivative of g**6/480 + g**5/240 - g**4/48 - 15*g**2 - 3*g. Factor h(d).
d*(d - 1)*(d + 2)/4
Suppose -5*f - 2*r = -7*r - 70, 0 = 2*f + 5*r - 35. Suppose -f = -4*x + x - t, 4*x + 5*t - 31 = 0. Factor 0 - 55/3*v**3 + 4/3*v**2 - 100/3*v**x + 4/3*v.
-v*(4*v - 1)*(5*v + 2)**2/3
Suppose -31 + 11 = -10*u. Find h such that 0 - 2 - 14*h**3 + h**5 - 9*h - 18*h**2 + 2*h**u - 6*h**4 - 2*h**5 = 0.
-2, -1
Suppose 0 = 4*k + 16 + 16. Let g be 1 + 3/(-1) - k. Find x, given that -6*x - 6*x - g + 3*x - 3*x**2 = 0.
-2, -1
Factor 46/3*w - 1/3*w**2 - 529/3.
-(w - 23)**2/3
Let u(i) be the second derivative of i**4/48 + i**3/4 + 5*i**2/8 - 6*i - 24. Determine j, given that u(j) = 0.
-5, -1
Factor 127 + 33*j**3 - 207 + 104 + 43*j**2 + 95*j**2 + 156*j.
3*(j + 2)**2*(11*j + 2)
Let f = 204 - 201. Let p(q) be the second derivative of -1/2*q**f + 0*q**6 + 0*q**4 - 4*q + 0*q**2 + 3/10*q**5 - 1/14*q**7 + 0. Factor p(w).
-3*w*(w - 1)**2*(w + 1)**2
Let i(v) be the third derivative of 0 + 0*v**4 + 1/1008*v**8 + 1/180*v**5 + 0*v + 1/120*v**6 + 1/210*v**7 + 0*v**3 + 2*v**2. Factor i(s).
s**2*(s + 1)