. Solve -1/3*u**2 + v - 2/3*u + 1/3*u**3 = 0 for u.
-1, 0, 2
Let w = 6 - 3. Suppose x - 3 + 0 = 0. Find i, given that i**x - 3 - 3*i**2 + i**2 + w + i = 0.
0, 1
Factor 3/4*s**2 - 63/2 - 57/4*s.
3*(s - 21)*(s + 2)/4
Let l be -4 + (1850/95)/5. Let i = 20/171 - l. Factor i*g**5 - 2/9*g + 4/9*g**4 - 4/9*g**2 + 0 + 0*g**3.
2*g*(g - 1)*(g + 1)**3/9
Let u(f) be the second derivative of 0*f**4 - 2/105*f**6 + 0*f**2 + 1/35*f**5 + 0*f**3 + 0 - 39*f. Determine o, given that u(o) = 0.
0, 1
Let i(w) = w**2 + w - 1. Let v(o) = -15*o**3 + 201*o**2 - 314*o + 124. Let j(g) = 4*i(g) + v(g). Factor j(l).
-5*(l - 12)*(l - 1)*(3*l - 2)
Let d be 4/26 + (-378)/(-6006)*-1. Factor 0 + 1/11*i**2 - d*i.
i*(i - 1)/11
Let g(s) = 2*s**3 - 163*s**2 - 754*s - 943. Let q(c) = -c**3 + 54*c**2 + 252*c + 314. Let p(o) = -6*g(o) - 17*q(o). Find l such that p(l) = 0.
-4
Let b = 188/33 + -59/11. Let -2/3 - 1/3*g + b*g**2 = 0. What is g?
-1, 2
Factor -2/3*i**5 + 0 + 14/3*i**4 + 40/3*i**2 - 16/3*i - 12*i**3.
-2*i*(i - 2)**3*(i - 1)/3
Let x = 489 + -1466/3. Factor x*n - 4/3*n**5 + 1/3*n**2 + 0 + 11/3*n**4 - 3*n**3.
-n*(n - 1)**3*(4*n + 1)/3
Let r = -1729/6 - -289. Let o(x) be the second derivative of 2*x**2 + 0 + 7*x - 1/10*x**5 + 1/3*x**3 - r*x**4 + 1/5*x**6. Let o(k) = 0. What is k?
-1, -2/3, 1
Let v(k) be the third derivative of -k**5/10 + 133*k**4/36 + 10*k**3/3 + 22*k**2 - 15*k. Let v(z) = 0. What is z?
-2/9, 15
Let h(j) be the second derivative of j**4/126 - 8*j**3/63 + j**2/3 + 217*j. Solve h(a) = 0 for a.
1, 7
Let p(d) = 5*d**5 - 24*d**3 - 10*d**2 + 19*d + 6. Let c(g) = -10*g**5 + 49*g**3 + 20*g**2 - 39*g - 11. Let r(t) = 4*c(t) + 9*p(t). Factor r(x).
5*(x - 2)*(x - 1)*(x + 1)**3
Let t(a) be the first derivative of -a**5/30 + 49*a**4/24 - 104*a**3/3 + 48*a**2 - 232. Let t(z) = 0. Calculate z.
0, 1, 24
Let d(s) be the third derivative of 12*s**2 + 0 - 1/30*s**5 + 0*s**3 + 1/60*s**6 + 0*s**4 - 1/420*s**7 + 0*s. Determine i, given that d(i) = 0.
0, 2
Let f = -20047 + 20049. Factor -1/5*x**f + 8/5 - 2/5*x.
-(x - 2)*(x + 4)/5
Let i(b) = -b**2 + 7*b + 2. Let u be i(7). Suppose 0 = a + c + 4, 4*a + c = -u*c - 12. Determine r so that -1/5*r**2 + a - 2/5*r**3 + 3/5*r**4 + 0*r = 0.
-1/3, 0, 1
Let q = 82 - 73. Suppose 4*f - 26 = -q*f. Factor 0 + 2/3*u**f + 2/3*u**3 + 0*u.
2*u**2*(u + 1)/3
Let q be (-31)/372 - (-85)/12. Let f(v) be the first derivative of q - 6*v + 8*v**2 - 32/9*v**3. Factor f(n).
-2*(4*n - 3)**2/3
Let p(l) = -3*l**3 + 63*l**2 + 15. Let v(o) = o**3 - 16*o**2 - 4. Let q(a) = -a**2 - 18*a + 23. Let w be q(-19). Let k(t) = w*p(t) + 15*v(t). Factor k(i).
3*i**2*(i + 4)
Let k(u) = u**3 + 5*u**2 - 4*u - 2. Let i be k(-5). Let t = i - 13. Find y such that -3*y**2 + 5*y**3 + 3*y**4 - 3*y + 3*y**3 - t*y**3 = 0.
-1, 0, 1
Let s(y) be the second derivative of y**4/18 - 4*y**3/9 + y**2 + 64*y. Factor s(v).
2*(v - 3)*(v - 1)/3
Let h(a) = 2*a - 9. Let r(i) = 3*i - 14. Let t(q) = 8*h(q) - 5*r(q). Let u be t(4). Factor u*o - 6*o + 4*o**2 - 26 + 26.
4*o*(o - 1)
Let u(i) = -32*i**2 + 124*i - 572. Let v(k) = -13*k**2 + 48*k - 229. Let x(a) = -5*u(a) + 12*v(a). Solve x(d) = 0.
4, 7
Suppose -23*i + 16*i - 21 = 0. Let z(g) = g**3 - g**2 + 2*g - 2. Let q(m) = m**3 - m**2 + 4*m - 4. Let n(u) = i*q(u) + 5*z(u). Factor n(a).
2*(a - 1)**2*(a + 1)
Let h(d) = 29*d**3 - 65*d**2 + 43*d - 24. Let g(u) = -10*u**3 + 22*u**2 - 14*u + 8. Let s(p) = 17*g(p) + 6*h(p). Let s(m) = 0. Calculate m.
1, 2
Suppose -o = -3*o - 10, 5*k + 2*o = 5. Suppose 4*r**2 + 3*r**4 - 16*r**k - 4*r**2 - 3*r**5 - 6*r + 25*r**3 - 3*r**2 = 0. Calculate r.
-1, 0, 1, 2
Let r(z) be the second derivative of z**4/3 + 14*z**3/3 - 36*z**2 + 132*z. Let r(x) = 0. What is x?
-9, 2
Let u(f) be the first derivative of 6/5*f**5 - 3/4*f**4 + 0*f**3 - 1/2*f**6 + 0*f + 0*f**2 + 26. Let u(t) = 0. Calculate t.
0, 1
Factor -44*z + 19*z + 24 + 7*z + 4*z**2 + 94*z + 8*z**2.
4*(z + 6)*(3*z + 1)
Solve 4*r + 2290*r**2 + 2286*r**2 - r**3 - 4573*r**2 = 0 for r.
-1, 0, 4
Let u(f) = f**3 + 7*f**2 - 19*f - 16. Let s be u(-8). Let h be 60/s + (-3)/6. Factor h*p**5 - p**3 + 1/3*p**4 - 2/3*p + 0 - 5/3*p**2.
p*(p - 2)*(p + 1)**3/3
Let b be 18 - 4 - 918/81. Determine z so that 4/3*z**5 - 8/3*z**4 - 8/3*z**3 - b + 4/3*z + 16/3*z**2 = 0.
-1, 1, 2
Let q(u) be the second derivative of -42*u + 1/18*u**4 - 16/9*u**3 + 64/3*u**2 + 0. Suppose q(p) = 0. What is p?
8
Let h(b) be the third derivative of b**5/140 - 5*b**4/168 - b**3/21 + b**2 - 7. Factor h(w).
(w - 2)*(3*w + 1)/7
Let a(g) be the first derivative of g**4/46 + 32*g**3/23 + 768*g**2/23 + 8192*g/23 + 141. Suppose a(h) = 0. What is h?
-16
Factor 3/2 - 1/4*u**4 - 1/8*u**5 + 19/4*u**2 + 37/8*u + 3/2*u**3.
-(u - 4)*(u + 1)**3*(u + 3)/8
Let p(z) be the second derivative of 3*z**5/10 - 9*z**4/4 + z**3/2 + 18*z**2 - 2*z - 2. Solve p(m) = 0.
-1, 3/2, 4
Suppose -4*v - z = 265, -v + 5*z = 20 + 20. Let s = v - -65. What is l in 4/3 - 2/3*l**3 + s*l**2 + 2*l = 0?
-1, 2
Factor 0*d**2 - 4/9*d + 2/9*d**4 - 2/9 + 4/9*d**3.
2*(d - 1)*(d + 1)**3/9
Factor -4 - 50*w**3 - 14 + 9590*w**2 - 9580*w**2 + 42*w.
-2*(w + 1)*(5*w - 3)**2
Let w = -22779 + 22781. Find h, given that -4/5*h**3 - 108/5 - 36/5*h**w - 108/5*h = 0.
-3
Factor -4 + 386*f**3 - 480*f**2 + 183*f**3 - 29*f - 173*f**3 + 436*f**3 + 113*f.
4*(4*f - 1)**2*(13*f - 1)
Let h = -17 - -16. Let u be (-33)/(-5)*(-5)/h. Factor -u*m - 8 + 93*m - 4*m**2 - 48*m.
-4*(m - 2)*(m - 1)
Suppose -8 = -2*a - 2. Suppose 7*d**4 + 0*d - 11*d**4 - 2*d + 1 + 2*d**a + 3*d**4 = 0. Calculate d.
-1, 1
Let u(o) be the third derivative of 0*o + 1/1176*o**8 - 11/105*o**5 - 1/105*o**7 + 13/84*o**4 + 28*o**2 + 3/70*o**6 + 0 - 1/7*o**3. Solve u(j) = 0 for j.
1, 3
Factor -3/4 + 15/4*u - 9/2*u**2.
-3*(2*u - 1)*(3*u - 1)/4
Suppose 41 - 245 = -68*d. Let f(i) be the second derivative of -9*i - 1/9*i**d - 1/72*i**4 - 1/4*i**2 + 0. Factor f(n).
-(n + 1)*(n + 3)/6
Suppose -524*f**3 + 966*f**2 - 538*f**3 + 24 + 279*f**3 - 260*f + 343*f**4 - 540*f**3 = 0. Calculate f.
2/7, 3
Let b be 1*(-5 - -8 - -15). Factor -11*f**4 + 24*f**4 - b*f**4 - 5 + 10*f**2.
-5*(f - 1)**2*(f + 1)**2
Let i = -1009/8 + 128. Let m = 3419/2282 + 2/1141. Factor i*q - m*q**2 - 3/4 + 3/8*q**3.
3*(q - 2)*(q - 1)**2/8
Suppose -940 = 8*p - 8860. Factor 995 - m**4 + 10*m**3 - 4*m**4 - p - 10*m.
-5*(m - 1)**3*(m + 1)
Let x be (-15 - -5) + 58/3 - 9. Let -1/6*l**4 + 0 - 1/2*l**3 + 0*l - x*l**2 = 0. What is l?
-2, -1, 0
Let m = -422 + 422. Let m*q**2 + 1/4*q**3 + 0 - 1/4*q = 0. What is q?
-1, 0, 1
What is s in 0*s + 0*s**2 - 1/2*s**3 + 0 + 1/4*s**5 + 1/4*s**4 = 0?
-2, 0, 1
Let m(s) = -3*s**4 - 2*s**3 + s**2 + 4*s - 2. Let o(d) = -d**2 + d - 1. Let v(r) = r**2 + r - 6. Let w be v(3). Let u(g) = w*o(g) - 3*m(g). Factor u(n).
3*n*(n - 1)*(n + 1)*(3*n + 2)
Let u = -13 + 16. Let m(w) be the second derivative of -2/3*w**3 + 0 - 2*w**2 - u*w - 1/12*w**4. Factor m(h).
-(h + 2)**2
Let 2*s**2 + 83*s + 64*s - 119*s + 29 - 3 = 0. Calculate s.
-13, -1
Determine l, given that -119/4*l**2 + 1/4*l**3 - 121/4 - 241/4*l = 0.
-1, 121
Suppose 5*c + 3*o - 30 = 8*o, 5*o = 3*c - 24. Factor -c*j**2 - 12*j**4 + 3*j + 18*j**3 - 9*j**2 - 131*j**5 + 0*j**3 + 134*j**5.
3*j*(j - 1)**4
Let q(d) be the first derivative of 1/30*d**5 + 1/12*d**4 + 0*d**2 - 19 - 1/6*d**3 + 0*d. Solve q(c) = 0.
-3, 0, 1
Let g(z) = 3*z**4 + z - 1. Let n(w) = -12*w**4 + 9*w**3 - 27*w**2 - 74*w - 31. Let x(k) = -5*g(k) - n(k). Determine b, given that x(b) = 0.
-4, -1, 3
Let s be (15/(-25) + 1)/((-36)/330) + 4. Factor -s*n**3 + 1/3*n**2 - 4 + 8/3*n.
-(n - 2)**2*(n + 3)/3
Let b(t) be the second derivative of 78125*t**7/42 - 19375*t**6/3 + 31825*t**5/4 - 12455*t**4/3 + 3320*t**3/3 - 160*t**2 - 254*t. Find n such that b(n) = 0.
4/25, 1
Solve 52/11*x + 2/11*x**2 - 10*x**4 + 0 - 156/11*x**3 - 4/11*x**5 = 0 for x.
-26, -1, 0, 1/2
Let x = 20031 + -20027. Let 0*m - 1/2*m**x + 0 + 0*m**2 + 1/4*m**3 + 1/4*m**5 = 0. Calculate m.
0, 1
Let s(a) be the second derivative of 0*a**4 + 0 + 3/70*a**6 + 0*a**3 + 5*a - 1/70*a**5 + 0*a**2. Determine o so that s(o) = 0.
0, 2/9
Let r(q) be the first derivative of -3*q**4/14 - 22*q**3/21 + 19*q**2/7 - 10*q/7 - 31. Let r(d) = 0. Calculate d.
-5, 1/3, 1
Let n(v) be the third derivative of v**6/720 - v**5/48 - 2*v**3 + 27*v**2. Let a(z) be the first derivative of n(z). Factor a(u).
u*(u - 