z**2 + 68/3*z**3 + s*z**4 = 0.
-1, 2/7
Let m(q) be the third derivative of -q**5/75 - 22*q**4/15 + 6*q**3 + 690*q**2. Factor m(a).
-4*(a - 1)*(a + 45)/5
Let b(x) = -48*x**5 - 129*x**4 + 225*x**3 + 561*x**2 + 336*x. Let y(v) = 7*v**5 + 19*v**4 - 32*v**3 - 80*v**2 - 48*v. Let p(i) = -4*b(i) - 27*y(i). Factor p(k).
3*k*(k - 4)*(k + 1)*(k + 2)**2
Let s(g) = -5*g**2 + 787*g + 765. Let c(x) = -12*x**2 + 1580*x + 1529. Let a(h) = -3*c(h) + 7*s(h). Solve a(y) = 0 for y.
-768, -1
Suppose 2*z - 724 = -2*f, -f = -2*z - 2*z + 1438. Let m be 3 - 7/21 - (-4)/(-6). Let -333*d - 31 + 1 + z*d + 3*d**m = 0. What is d?
-10, 1
Let r(d) be the first derivative of 272/7*d**3 + 53 - 8/7*d**4 + 50/7*d - 201/7*d**2. Suppose r(f) = 0. What is f?
1/4, 25
Let s(r) = -r**3 + 4*r**2 + 9*r - 33. Suppose 378*t = 366*t + 36. Let u be s(t). Factor -32/5*o**u - 48/5*o + 9/5*o**4 + 16/5 + 56/5*o**2 - 1/5*o**5.
-(o - 2)**4*(o - 1)/5
Suppose 0 = -3*h + 3*n - 21, 109*h - 57 = 112*h - 7*n. Factor 16/3 + 8/3*a + 1/3*a**h.
(a + 4)**2/3
Solve -3075/7 - 165*n - 93/7*n**2 + 3/7*n**3 = 0.
-5, 41
Let s = 181 - 187. Let k be 242/220 + s/20*2. Let 1/6*r + k*r**3 + 1 - 5/3*r**2 = 0. What is r?
-2/3, 1, 3
Let r(h) be the first derivative of 8*h**2 - 115 - 84*h + 4/3*h**3. Let r(m) = 0. Calculate m.
-7, 3
Let y(q) be the third derivative of q**8/1344 - q**7/168 + q**6/80 + 4*q**2 + 39. What is s in y(s) = 0?
0, 2, 3
Let q be (-102*(-78)/(-3315))/(8/(-10)). Factor -76/5*z**2 - 24*z - 54/5 - 8/5*z**q + 2/5*z**4.
2*(z - 9)*(z + 1)**2*(z + 3)/5
Let f(b) = 6*b + 38. Let y be -7*1 - (-1 + 0/(-4)). Let s be f(y). Factor 5*d**2 + 4*d**s + 3*d**3 + 0*d**3 - 39*d**2 + 75*d.
3*d*(d - 5)**2
Suppose -30 = -3*x + 3*p, 2*p - 3 + 9 = 0. What is s in 10*s - x*s**4 + 5*s**4 - 7*s**3 - 3*s**4 + 5*s**2 + 5*s**5 - 8*s**3 = 0?
-1, 0, 1, 2
Let y(w) be the third derivative of 2 + 0*w + 0*w**3 + 7/120*w**4 + 13/300*w**5 - 1/1050*w**7 + 1/120*w**6 + 3*w**2. Factor y(m).
-m*(m - 7)*(m + 1)**2/5
Let r(l) be the second derivative of -l**6/90 + 4*l**5/5 - 45*l**4/2 + 300*l**3 - 3375*l**2/2 + 7*l - 42. Determine q, given that r(q) = 0.
3, 15
Let t be 608/112 - 3/7. Suppose -9*m - t = -14*m. Factor 11*o**2 + 32*o - 7*o**2 + 63 + m.
4*(o + 4)**2
Let u be (4 - 156/42) + 96/56. Let b(m) be the first derivative of 0*m - 5 - 2/9*m**3 - 1/15*m**5 + 0*m**u + 1/4*m**4. Factor b(x).
-x**2*(x - 2)*(x - 1)/3
Let v be -2*(-1 - 3 - -3569). Let g be (-2392)/v - (-4)/62. Factor g*k**3 + 0*k + 4/15*k**2 + 0 - 2/15*k**5 + 0*k**4.
-2*k**2*(k - 2)*(k + 1)**2/15
Let t be 11 - (10 + 8 - 12). Let g(h) be the first derivative of 0*h**4 - 3*h + 0*h**2 - 3/5*h**t + 2*h**3 - 28. What is w in g(w) = 0?
-1, 1
Let v be (57/36)/(-19)*(-18)/50. Let d(h) be the second derivative of 28*h + 1/10*h**4 - v*h**5 + 0 + 1/2*h**3 - 9/5*h**2. Factor d(s).
-3*(s - 3)*(s - 1)*(s + 2)/5
Let y(u) be the second derivative of -12*u + 1 + 1/18*u**4 + 49/3*u**2 + 14/9*u**3. Solve y(z) = 0.
-7
Let s(j) be the first derivative of -20/7*j - 13/7*j**2 + 132 - 4/21*j**3 + 1/14*j**4. Solve s(i) = 0 for i.
-2, -1, 5
Let l(r) = r**2 + 17766*r + 230792. Let w be l(-13). Factor -16 - 1/4*n**5 - 145/4*n**2 - 19/4*n**w - 44*n + 13/4*n**4.
-(n - 8)**2*(n + 1)**3/4
Let n(d) be the first derivative of 19/2*d - 37/8*d**2 + 123 - 1/12*d**3. Suppose n(x) = 0. What is x?
-38, 1
Let q(h) be the second derivative of -1/70*h**7 + 0 + 0*h**3 + 0*h**5 + 79*h + 1/50*h**6 + 0*h**4 + 0*h**2. Determine o, given that q(o) = 0.
0, 1
Let s(i) be the first derivative of -40*i - 33 + 4/3*i**3 + 6*i**2. Factor s(r).
4*(r - 2)*(r + 5)
Suppose -2*o - 3 = 3*i, 0*i + 2*i = -2*o. Suppose 12 = o*s - 3*v, -5*s - 4*v = -8 - 12. Let -4 + 10*n - 22*n + 8*n**2 - s = 0. Calculate n.
-1/2, 2
Let q = -611 - -624. Factor -2*k**3 + 7*k**3 + 9*k**2 + 15*k - 37 + 21*k**2 - q.
5*(k - 1)*(k + 2)*(k + 5)
Let i(j) be the third derivative of -1/16*j**4 - 270*j**2 + 1/48*j**5 - 1/480*j**6 + 0 + 0*j + 0*j**3. Factor i(r).
-r*(r - 3)*(r - 2)/4
Let a be ((-60)/(-35))/4 - (-1734)/(-518). Let o = 1484/407 + a. Find j, given that 0 - 2/11*j**3 + 0*j**2 + o*j = 0.
-2, 0, 2
Let r be ((-16)/9)/(6704/(-5028)). Factor 10/3*s**2 - 1/3*s**3 - r*s**4 - 1/3*s**5 + 4/3*s - 8/3.
-(s - 1)**2*(s + 2)**3/3
Let w = 42440 + -42438. Let m(n) be the second derivative of -1/210*n**5 - 1/126*n**4 + 0*n**w + 1/63*n**3 - 26*n + 1/315*n**6 + 0. Factor m(h).
2*h*(h - 1)**2*(h + 1)/21
Let z = -761889 + 761891. Factor -7 - 1/6*c**z + 17/6*c.
-(c - 14)*(c - 3)/6
Let k(t) be the first derivative of -122/33*t**3 + 280 + 960/11*t**2 + 1/22*t**4 - 1800/11*t. Factor k(o).
2*(o - 30)**2*(o - 1)/11
Let 54 - 887*q - 3*q**3 + 1032*q - 2*q**3 - 40*q**2 + 846 = 0. What is q?
-9, -4, 5
Let z(w) be the first derivative of 2*w**3/15 + 33*w**2/5 + 36*w - 331. Find i such that z(i) = 0.
-30, -3
Let n(l) = 10681*l - 256344. Let v be n(24). Factor v - 213/4*h - 3/4*h**2.
-3*h*(h + 71)/4
Let q(j) be the second derivative of j**4/42 + 6*j**3/7 + 80*j**2/7 + 1699*j. Factor q(o).
2*(o + 8)*(o + 10)/7
Let c(y) be the third derivative of -1/4*y**5 - 49*y**2 + 5/16*y**4 + 0 + y + 5/3*y**3 - 5/48*y**6. Determine s, given that c(s) = 0.
-1, 4/5
Suppose 7*x + 4219 + 6463 = 0. Let t = x + 1528. Factor -2/3*r**t - 10/3*r + 0.
-2*r*(r + 5)/3
Factor 228 + 3417/5*z + 3411/5*z**2 + 1131/5*z**3 - 3/5*z**4.
-3*(z - 380)*(z + 1)**3/5
Factor 5*o**4 - 68*o**3 - 675*o + 540 - 105115*o**2 + 3*o**3 + 105430*o**2 + 0*o**4.
5*(o - 4)*(o - 3)**3
Let z(b) be the second derivative of 27*b + 12/55*b**5 - 83/33*b**4 - 11*b**2 + 2 - 1/165*b**6 + 8*b**3. Factor z(x).
-2*(x - 11)**2*(x - 1)**2/11
Find o such that -20655*o**4 + 20667*o**4 - 69*o**3 - 34*o + 42*o**2 + 49*o = 0.
-1/4, 0, 1, 5
Let h(o) be the first derivative of -o**5/390 + 9*o**4/52 + 28*o**3/39 + 2*o**2 + o + 127. Let x(s) be the second derivative of h(s). Solve x(d) = 0.
-1, 28
Suppose 5285*w = 5281*w + 8. Let s(u) be the first derivative of 1/9*u**4 - 12 - 2/27*u**3 + 0*u + 0*u**w - 2/45*u**5. What is z in s(z) = 0?
0, 1
Let i(r) be the third derivative of 29*r**2 + 2*r + 6*r**3 + 1/210*r**7 + 19/6*r**4 + 7/60*r**6 + 53/60*r**5 + 0. What is p in i(p) = 0?
-9, -2, -1
Factor 219/2*r**2 - 2235/8*r - 87/8*r**3 + 75/4.
-3*(r - 5)**2*(29*r - 2)/8
Let k(z) be the first derivative of z**4/66 + 5*z**3/33 - 162*z + 242. Let p(l) be the first derivative of k(l). Factor p(h).
2*h*(h + 5)/11
Let x be (24/(-9))/(12/(-18)). Suppose 196*l**2 - l - 3*l + 8 - 204*l**2 + x*l**3 = 0. Calculate l.
-1, 1, 2
Let f(q) = 2*q + 30. Let i be f(-15). Let o be 6 + (-1 - -2)*-3 + i. Find s, given that -50*s**3 + 29*s**o + 24*s**3 - 3*s**5 = 0.
-1, 0, 1
Let o(f) be the third derivative of -5*f**8/336 + 11*f**7/14 - 169*f**6/24 + 61*f**5/4 + 425*f**4/12 - 180*f**3 + 2252*f**2. Suppose o(p) = 0. What is p?
-1, 1, 2, 4, 27
Let p be (2/4)/((-46)/(-460)) - 5. Let t(s) be the third derivative of 15*s**2 + p + 1/330*s**5 + 0*s + 0*s**4 + 0*s**3. Let t(f) = 0. Calculate f.
0
Let f(u) = 9*u**2 - 108*u + 336. Let r(h) = -21*h**2 + 222*h - 672. Let t(y) = -5*f(y) - 2*r(y). Factor t(a).
-3*(a - 28)*(a - 4)
Let n(v) be the second derivative of -v**7/5 + 41*v**6/75 + v**5/25 - 7*v**4/5 + 19*v**3/15 + v**2/5 - 2218*v. What is l in n(l) = 0?
-1, -1/21, 1
Let w(d) = 12306*d**2 + 29568*d + 17390. Let l(s) = -1540*s**2 - 3696*s - 2174. Let f(t) = 17*l(t) + 2*w(t). Factor f(m).
-2*(28*m + 33)**2
Suppose 12*x = 68 + 76. Factor 7*c - x*c**2 + c + 10*c**2.
-2*c*(c - 4)
Let k = -273455/2 - -136728. Factor -1/3*i**2 + k*i + 1/3.
-(i - 2)*(2*i + 1)/6
Factor 26/9*h**2 - 2/3 + 32/9*h - 4/3*h**3.
-2*(h - 3)*(h + 1)*(6*h - 1)/9
Let x = 1053/184 + -225/184. Find z such that 56*z - x*z**5 + 15*z**4 - 16 + 4*z**3 - 56*z**2 = 0.
-2, 2/3, 2
Factor -86/7*l**2 - 80/7*l + 2/7*l**4 + 0 - 4/7*l**3.
2*l*(l - 8)*(l + 1)*(l + 5)/7
Let o(c) = -c**3 - 18*c**2 + 248*c - 40. Let n be o(9). Find a such that 3920/3*a**2 - 2176/3*a + 108*a**n - 804*a**4 + 3616/3*a**3 + 256/3 = 0.
-1, 2/9, 4
Let s(l) be the first derivative of 51/4*l**2 + 71 + 1/2*l**3 + 45*l. What is w in s(w) = 0?
-15, -2
Suppose -11625 = -72*h + 2631. Let w = 599/3 - h. Suppose 0 + 10/3*v**3 + 20/3*v**5 + 35/3*v**4 - w*v**2 + 0*v = 0. Calculate v.
-1, 0, 1/4
Let v(j) be the first derivative of j**7/210 + j**6/9 + 5*j**5/6 - 28*j**3/3 + 67. Let y(r) be t