Let g = -73/6 + 619/51. Let o = 8/17 - g. Factor o*h**2 - 3/2*h - 2.
(h - 4)*(h + 1)/2
Suppose 110 + 58 = 84*g. Let q(p) be the first derivative of 3/2*p - 13 + 1/4*p**3 + 9/8*p**g. Factor q(x).
3*(x + 1)*(x + 2)/4
Let 2504/7*z + 10/7*z**3 + 152*z**2 + 832/7 = 0. Calculate z.
-104, -2, -2/5
Let v be (24*42/(-4032))/(10/(-8)). Factor m**2 - v*m**3 - 4/5*m + 0.
-m*(m - 4)*(m - 1)/5
Determine f, given that 134/19*f + 140/19*f**4 - 132/19*f**3 + 276/19 - 416/19*f**2 - 2/19*f**5 = 0.
-1, 1, 2, 69
Let p(o) be the first derivative of -3 + 8*o**2 + 0*o + 4*o**3 + 1/2*o**4. Factor p(w).
2*w*(w + 2)*(w + 4)
Suppose 334*h - 1117 - 7567 = 0. Let x(g) be the first derivative of 1/2*g**2 - 1/2*g - h - 1/6*g**3. Factor x(d).
-(d - 1)**2/2
Let l = -105891/260440 - 24/1915. Let f = -3/68 - l. Solve -f*b**2 - 3/4*b + 0 = 0 for b.
-2, 0
Suppose 3*q - 50 = -22*q. Find h, given that -114*h + h**q + 82 - 50 + 6*h**2 = 0.
2/7, 16
Suppose -421*n**2 + 147*n**2 + 582 - 285*n + 271*n**2 = 0. What is n?
-97, 2
Let u = 113405/7 - 16199. Solve -4*s + u + 22/7*s**3 - 5/7*s**4 - 13/7*s**2 = 0.
-1, 2/5, 2, 3
Let k be 8 + (-261)/58*(-2)/3. Suppose 28*c - 11 = -k. Suppose -4/3*o**3 + c*o + o**2 + 0 + 1/3*o**4 = 0. Calculate o.
0, 1, 3
Let o(w) = w**3 + 5*w**2 - 4*w + 17. Let t be o(-6). Let 11*z**4 - 5*z**t + 124977*z**2 - z**4 - 124987*z**2 + 5*z**3 = 0. Calculate z.
-1, 0, 1, 2
Let c(g) be the third derivative of 0*g + 1/6*g**4 + 1/9*g**5 + 0*g**3 + 1 - 1/210*g**7 + 1/360*g**6 + 33*g**2. Factor c(k).
-k*(k - 3)*(k + 2)*(3*k + 2)/3
Let 477 - 4*n**2 - 673 - 1316*n - 106 - 1010 = 0. Calculate n.
-328, -1
Suppose 11*a - 5930 = -5633. Let z(r) be the first derivative of -2*r - a - 1/5*r**4 - 12/5*r**2 - 6/5*r**3. Let z(l) = 0. What is l?
-5/2, -1
Let l(k) be the third derivative of 3/38*k**5 + 0 - 113*k**2 + 9/38*k**4 + 1/1995*k**7 + 1/95*k**6 + 0*k + 0*k**3. Factor l(x).
2*x*(x + 3)**2*(x + 6)/19
Solve 9/5*q**2 + 0 + 3/5*q**3 - 162/5*q = 0 for q.
-9, 0, 6
Let u be (-6)/9*(21/(-77) - (-240)/(-88)). Factor u*r**4 + 2/3*r**5 + 0 + 2*r**3 + 2/3*r**2 + 0*r.
2*r**2*(r + 1)**3/3
Suppose -1 = -2*u + 3*h + 8, 33 = 5*u + 3*h. Suppose 0*v = 2*v - u. Solve -3 - 9*s + 4*s**3 + s**3 + 3*s + s**3 + v*s**4 = 0.
-1, 1
Factor -2*u**4 + 60*u**4 - 3*u**2 + 3*u**3 - 21 + 3*u**3 - 38*u - 57*u**4 - 9*u**2.
(u - 3)*(u + 1)**2*(u + 7)
Let a = 2916 + -2914. Let t(q) be the second derivative of 0*q**a + 3/4*q**4 + 0 + 1/3*q**3 - 14*q. Find c, given that t(c) = 0.
-2/9, 0
Let s be (2/(-6))/(((-4)/(-2))/30). Let z be (-2)/(s + 3 - (-2)/2). Solve -23*p**3 + 4*p**z - p**4 + p**5 + 17*p**3 - 18*p + 26*p = 0.
-2, -1, 0, 2
Let l(h) be the third derivative of 7/270*h**5 - 23*h**2 + 1/36*h**4 + 0*h**3 + 0*h + 1/945*h**7 + 0 + 1/108*h**6. Factor l(j).
2*j*(j + 1)**2*(j + 3)/9
Let c(z) be the third derivative of -z**5/120 + 10*z**4 - 4800*z**3 + 166*z**2. Factor c(u).
-(u - 240)**2/2
Let s(i) be the second derivative of 3*i + 3/20*i**5 + 1/30*i**6 + 3*i**2 - 1/4*i**4 - 7/6*i**3 - 5. Solve s(f) = 0.
-3, -2, 1
Let q(y) be the second derivative of 1/80*y**5 + 2*y - 1/24*y**3 + 78 + 0*y**2 + 0*y**4. Find l, given that q(l) = 0.
-1, 0, 1
Let i(v) be the third derivative of -v**7/42 - 5*v**6/8 + 6*v**5 - 95*v**4/6 - v**2 + 2194*v - 2. Factor i(q).
-5*q*(q - 2)**2*(q + 19)
Let s(h) be the third derivative of h**5/270 + 5*h**4/27 + 4*h**3/3 - 3703*h**2. Find z such that s(z) = 0.
-18, -2
Let g = -117550 + 117554. Find i, given that i**g + 11/3*i**3 + 4*i**2 + 0 + 4/3*i = 0.
-2, -1, -2/3, 0
Let u(j) be the first derivative of -j**6/10 + 57*j**5/25 - 159*j**4/10 + 14*j**3 + 1617*j**2/10 + 1029*j/5 - 132. Factor u(y).
-3*(y - 7)**3*(y + 1)**2/5
Let b(n) be the first derivative of -49*n**5 - 12285*n**4 + 7075*n**3 + 12070*n**2 + 4020*n + 4. Let b(z) = 0. Calculate z.
-201, -2/7, 1
Let o(m) be the third derivative of 0 - 30*m**2 + 0*m**3 - 1/12*m**4 + 0*m + 1/30*m**5. Factor o(u).
2*u*(u - 1)
Suppose -9*i = 4*i - 4186. Suppose -i*y + 322*y + 4*y**5 - 8*y**4 - 12*y**3 = 0. Calculate y.
-1, 0, 3
Let y(p) be the first derivative of 2*p**3/9 + 64*p**2/3 - 790*p - 2789. Solve y(u) = 0.
-79, 15
Solve 540*g**2 - 2*g**3 - 3443*g**2 + 12*g**3 - 2039*g**2 + 5918*g - 986 = 0 for g.
1/5, 1, 493
Suppose 3*m - 23 - 1 = 0. Suppose -m*t = -33 + 1. Factor -t*d**3 + d**2 - 3*d**2 + 14*d**3 - 2*d**3.
2*d**2*(4*d - 1)
Let k be ((-65)/(-52))/(2/(-56)). Let i be (-85)/k - (-1 + 2). Factor -6/7 + 2/7*o**3 - i*o - 2/7*o**2.
2*(o - 3)*(o + 1)**2/7
Let s = 197 - 167. Factor o**5 - 2*o**3 - 4*o**4 + s*o**2 - 26*o**2 + 0*o**3 + 4*o**3 - 3*o.
o*(o - 3)*(o - 1)**2*(o + 1)
Determine q so that -31/2*q**2 - 289/4*q - 1/4*q**3 - 57 = 0.
-57, -4, -1
Let h be -9 + 4 + (-11 - (3198/(-12))/13). Determine w, given that -6*w**3 - h*w**2 + 27/2*w - 3 = 0.
-2, 1/4, 1
Let r(a) be the first derivative of a**6/780 + a**5/195 - a**4/52 + 7*a**2/2 - 4*a - 50. Let c(w) be the second derivative of r(w). Factor c(g).
2*g*(g - 1)*(g + 3)/13
Let m = -34892/3 - -11636. Let x(d) be the second derivative of 4/3*d**3 - 1/6*d**4 + 7*d + 1/120*d**5 - m*d**2 + 0. Factor x(n).
(n - 4)**3/6
Let o = 272291/51054 - 1/17018. Solve o*t + 4*t**2 + 2/3*t**3 + 0 = 0 for t.
-4, -2, 0
Let c(f) be the third derivative of 0*f + 1/12*f**4 - 1 + 4*f**3 - 1/60*f**6 - 2/5*f**5 + 53*f**2. Determine z so that c(z) = 0.
-12, -1, 1
Solve 2496*y + 4*y**2 + 11 + 2687*y + y**2 - 5443*y + 3049 = 0 for y.
18, 34
Let r = -2584601/5 - -516921. Factor -1/5*w + r + 1/5*w**3 - 4/5*w**2.
(w - 4)*(w - 1)*(w + 1)/5
Let g = 3838 - 3836. Factor 505*c - 5/2*c**g - 51005/2.
-5*(c - 101)**2/2
Let d be (-474)/88 - (-6)/4. Let k = -40/11 - d. Determine u, given that 1/4*u**5 + k*u + 1/2 - u**2 + 1/2*u**4 - 1/2*u**3 = 0.
-2, -1, 1
Factor 388/3*a**2 + 768 + 1/3*a**4 + 704*a - 44/3*a**3.
(a - 24)**2*(a + 2)**2/3
Let v(r) be the first derivative of -r**3/3 - 71*r**2/2 - 558*r - 8652. Factor v(m).
-(m + 9)*(m + 62)
Let w(r) be the third derivative of 4*r**7/105 + r**6/2 - 17*r**5/15 + 1268*r**2 - 1. Suppose w(x) = 0. Calculate x.
-17/2, 0, 1
Let f(c) = -c**3 - 6*c**2 - 5*c - 12. Let j be f(-6). Factor 51*t - 24 - t**2 - 19*t - j*t.
-(t - 12)*(t - 2)
Let z(o) = -2*o**3 + 7*o**2 - 16*o + 14. Let f(h) = -469*h**3 - h**2 + 470*h**3 + h - 2*h. Let q(b) = 15*f(b) + 5*z(b). Factor q(p).
5*(p - 2)*(p - 1)*(p + 7)
Let j(w) be the third derivative of 2/15*w**5 + 0*w - 11/6*w**4 + 1/3*w**6 + 1/84*w**8 + 0 + 10/3*w**3 - 2/15*w**7 - 61*w**2. Determine v, given that j(v) = 0.
-1, 1, 5
Let p(c) be the second derivative of 35*c**4/2 + 179*c**3/6 + 17*c**2 - 4671*c. Factor p(j).
(7*j + 2)*(30*j + 17)
Let s(u) = -2316*u + 60220. Let i be s(26). What is j in 0 - 12/5*j**2 + 8/5*j - 48/5*j**3 - 28/5*j**i = 0?
-1, 0, 2/7
Let v(z) be the third derivative of -z**7/490 - 29*z**6/280 + 31*z**5/70 - 1904*z**2. Determine j, given that v(j) = 0.
-31, 0, 2
Let i(j) = -203 - 4 + 27*j - 76 + 3*j**2 + 21*j. Let b(n) = 2*n**2 + 24*n - 141. Let o(y) = -5*b(y) + 3*i(y). Factor o(f).
-(f - 12)**2
Let o be 4/11*(-24)/48*(0 + -1). Suppose -o*x**2 + 0 - 24/11*x = 0. Calculate x.
-12, 0
Let r(y) be the second derivative of y**4/6 - 4*y**3/3 - 5*y**2 - 3283*y - 2. Find d such that r(d) = 0.
-1, 5
Suppose 6*s = 459 + 45. Let r be ((-24)/(-182))/((-648)/s - -8). Factor 0 + 0*v - 4/13*v**3 + r*v**2 - 2/13*v**4.
-2*v**2*(v - 1)*(v + 3)/13
Suppose -47 - 18 = 5*m. Let k = m + 21. Determine v so that -4*v + 7*v**3 - k*v**3 + 2*v**3 + 20*v**2 - 20 + 3*v**3 = 0.
-5, -1, 1
Let c(z) be the third derivative of z**6/150 - 7*z**5/75 - 65*z**4/6 + 6422*z**3/15 + 1424*z**2 - z. Factor c(n).
4*(n - 13)**2*(n + 19)/5
Suppose f = 7*f - 1596. What is r in 155*r**3 - 20*r**4 + 24*r**2 - f*r**2 - 38*r**2 - 80*r = 0?
-1/4, 0, 4
Determine u so that 3*u**3 + 15*u**2 + 27*u**2 - 10*u**2 + 36*u - 2*u**3 - 72 + 3*u**3 = 0.
-6, -3, 1
Let z = 2160 + -2156. Let a(c) be the second derivative of 0 - 5/8*c**2 - 11*c + 1/24*c**z - 1/8*c**3. Factor a(b).
(b + 1)*(2*b - 5)/4
Determine p so that 1/8*p**2 + 0 - 45/8*p = 0.
0, 45
Suppose 780 + 5/3*o**3 + 290/3*o**2 + 535*o = 0. What is o?
-52, -3
Let i = 134 - 98. Suppose -4*y - u = -i, u = -5*y + 6*u + 70. Find r, given that -51*r**2 + y*r + 11*r**2 + 25*r**3 - 5*r**4 + 10*r = 0.
0, 1, 2
Let u(f) be the first derivative of f**3 - 5*f**2 + 8*f + 18. Let s b