0 = -6*h + 13*h. Let v be (-1)/3*(-6)/4. Factor -o + v*o**3 + h - 1/2*o**2.
o*(o - 2)*(o + 1)/2
Let p(u) be the second derivative of u**6/50 - 21*u**5/100 + u**4/4 + 7*u**3/10 - 9*u**2/5 + u + 4. Let p(i) = 0. What is i?
-1, 1, 6
Factor -1/3*q**4 + 0 - q**3 + 0*q - 2/3*q**2.
-q**2*(q + 1)*(q + 2)/3
Suppose 9*u - 168 = 5*u. Let w = -124/3 + u. Determine r so that 1/3*r**4 + 1/3*r**2 + w*r**3 + 0*r + 0 = 0.
-1, 0
Let a = 152/249 - -60/83. Find s, given that 4/3*s**3 - a*s - 4/3*s**2 + 4/3 = 0.
-1, 1
Let s(z) be the first derivative of z**6/2 + 2*z**5 - 3*z**4/2 - 8*z**3 + 11*z**2/2 + 6*z - 97. Suppose s(f) = 0. Calculate f.
-3, -2, -1/3, 1
Let v(m) = -213*m - 2978. Let d be v(-14). Factor -27/8*z + 0 - 9/8*z**2 + 15/8*z**3 - 3/8*z**d.
-3*z*(z - 3)**2*(z + 1)/8
Let q(u) be the third derivative of -u**9/3024 + u**7/840 + 23*u**3/6 - 23*u**2. Let a(s) be the first derivative of q(s). Factor a(t).
-t**3*(t - 1)*(t + 1)
Let j(u) be the second derivative of u**5/20 + 7*u**4/3 + 55*u**3/2 - 225*u**2 + 380*u. Determine x so that j(x) = 0.
-15, 2
Let y = -6574/5 + 1316. Solve -y*a**2 - 12/5*a**3 + 3*a - 6/5 - 3/5*a**5 + 12/5*a**4 = 0 for a.
-1, 1, 2
Let g = -10056 - -10058. Factor 4/3*w + 0 + 3*w**3 - 4*w**g.
w*(3*w - 2)**2/3
Suppose -9*h = 11 - 65. Suppose -h - 28*w**3 + 3*w + 30*w**3 + 11*w - 11*w**2 + w**2 = 0. Calculate w.
1, 3
Let w(h) be the third derivative of -h**7/3780 + h**6/180 - h**5/20 + 13*h**4/24 - 5*h**2. Let x(r) be the second derivative of w(r). Factor x(a).
-2*(a - 3)**2/3
Let m(g) = -g**3 + 21*g**2 + g - 10. Let i be m(21). Solve 6*v - 70*v**3 + 65*v**3 - v + 10 + v**2 - i*v**2 = 0 for v.
-2, -1, 1
Let g = 22 + -19. Find u, given that 12*u**2 - 46 + 27 + 12*u + 4*u**g + 23 = 0.
-1
Let x(r) be the first derivative of r**3/6 + 6*r**2 + 22*r + 553. Factor x(d).
(d + 2)*(d + 22)/2
Let a(r) = r**2 + 5*r - 3. Suppose v - 8 = q, 3*v = -4*q + 3*q. Let h be a(q). Determine y, given that h + 3/2*y**2 - 9/2*y = 0.
1, 2
Factor 3*c**3 + 671*c - 674*c + 0*c**3.
3*c*(c - 1)*(c + 1)
Let 58/3*q**2 + 12 - 6*q**3 + 2/3*q**4 - 26*q = 0. What is q?
1, 2, 3
Suppose -52*u**5 - 23*u**2 - 12 - 10*u**4 + 7*u**3 + 53*u**5 - 44*u + 17*u**4 - 8 = 0. Calculate u.
-5, -2, -1, 2
Let r(j) = j**2 - 15*j + 27. Let b be r(13). Suppose 0 = 2*z + 4*w + 8, -5*z = 4*w + b + 7. Find f, given that z*f + 3/7 - 3/7*f**2 = 0.
-1, 1
Let q(n) be the third derivative of 7/60*n**6 + 0*n**4 + 0*n - 17*n**2 - 2 + 1/10*n**5 + 1/21*n**7 + 0*n**3 + 1/168*n**8. Determine w, given that q(w) = 0.
-3, -1, 0
Factor 0 + 1/2*f**3 + 2*f - 2*f**2.
f*(f - 2)**2/2
Let m be -7*(14/(-49) + (-24)/(-98)). Determine q so that -6/7*q**3 + 0 + 4/7*q**2 + m*q**4 + 0*q = 0.
0, 1, 2
Let y(o) be the third derivative of -o**6/30 + 4*o**5/15 + 7*o**4/6 - 20*o**3/3 + 29*o**2 + o. Suppose y(k) = 0. What is k?
-2, 1, 5
Let s(c) be the first derivative of -18 + 15/14*c**2 - 1/7*c**3 - 12/7*c. Let s(r) = 0. Calculate r.
1, 4
Let x = 409 + -406. Let v(m) be the first derivative of -6*m - 4 + 2*m**2 - 2/9*m**x. Factor v(j).
-2*(j - 3)**2/3
Let i(k) be the third derivative of k**5/90 - 23*k**4/36 + 22*k**3/9 - 2*k**2 - 41*k. Factor i(l).
2*(l - 22)*(l - 1)/3
Let k(y) be the first derivative of -y**6/8 - 11*y**5/5 - 9*y**4 - 5*y**3/6 + 291*y**2/8 - 45*y/2 - 88. Solve k(f) = 0 for f.
-10, -3, 1/3, 1
Let h(y) be the second derivative of y**4/96 + y**3/6 + y**2 - 21*y - 2. What is w in h(w) = 0?
-4
Let p(r) = 2*r + 17 - 27 + 0*r. Let d be p(7). Determine i, given that i**4 - 4*i**4 + d*i - i**4 + 20*i**3 + 12*i - 32*i**2 = 0.
0, 1, 2
Factor 2*p + 20/3 + 2/3*p**3 - 4*p**2.
2*(p - 5)*(p - 2)*(p + 1)/3
Factor 2/7*h**5 - 32/7*h**4 + 128/7*h**3 + 0*h**2 + 0*h + 0.
2*h**3*(h - 8)**2/7
Let g(u) be the first derivative of u**4/9 + u**3/3 + u**2/3 - 15*u - 6. Let x(r) be the first derivative of g(r). Factor x(v).
2*(v + 1)*(2*v + 1)/3
Let d(r) be the third derivative of r**8/5040 + r**7/420 + r**6/90 + r**5/30 - 11*r**2. Let g(z) be the third derivative of d(z). Factor g(p).
4*(p + 1)*(p + 2)
Let g(j) be the first derivative of -j**4/24 + 13*j**3/9 - 71*j**2/12 + 23*j/3 + 111. Let g(w) = 0. Calculate w.
1, 2, 23
Let n = 3026/3 + -1002. Let u(p) be the first derivative of 6 + 10*p - 25/2*p**2 + n*p**3 - 5/4*p**4. Factor u(c).
-5*(c - 2)*(c - 1)**2
Let d(u) be the second derivative of -18/7*u**2 - 2/7*u**3 + 0 - 8*u - 1/84*u**4. Factor d(y).
-(y + 6)**2/7
Let v be ((-15)/9)/(3/(-9)). Solve -23*u**v - 3*u - 20*u**3 - 10*u**4 - 20*u**2 - 7*u - 2 + 21*u**5 = 0 for u.
-1
Suppose 2*u - 18 = -3*o, -11 = 46*o - 51*o + 3*u. Determine k, given that 4/3*k + 4*k**2 - 8/3 - 4/3*k**3 - 4/3*k**o = 0.
-2, -1, 1
Let f(u) be the second derivative of -26*u + 0 + 3/35*u**5 + 0*u**2 + 0*u**3 + 0*u**4 - 1/35*u**6. Factor f(b).
-6*b**3*(b - 2)/7
Let u(t) be the second derivative of -t**7/84 + 3*t**5/40 - t**4/12 + 7*t - 1. Solve u(z) = 0.
-2, 0, 1
Suppose o + 2 = -f, 0 = 4*o - 3*f + 62 - 82. Determine n so that -3/8*n - 3/8*n**4 - 9/8*n**3 - 9/8*n**o + 0 = 0.
-1, 0
Let v(s) be the third derivative of s**5/20 + s**4/4 + s**3/2 + 9*s**2 + 1. Determine a so that v(a) = 0.
-1
Let h = 3/457 + 448/1371. Let x(c) be the first derivative of -h*c**3 + 0*c + 1/5*c**5 + 0*c**4 + 1/4*c**2 - 1/12*c**6 + 6. Determine i so that x(i) = 0.
-1, 0, 1
Let l = -11/4 - -49/12. Let n = 2710/3 - 903. What is t in -1/3*t**3 + n*t - l*t**2 + 0 + 4/3*t**4 = 0?
-1, 0, 1/4, 1
Let z(u) be the third derivative of u**6/36 + u**5/45 - 5*u**4/36 - 2*u**3/9 + 24*u**2. Let z(k) = 0. What is k?
-1, -2/5, 1
Solve -14*y**4 - 25*y**4 - 36 + 44*y**2 - 27*y**4 + 26*y**4 + 102*y - 64*y**3 - 5*y**5 - y**5 = 0 for y.
-3, -2, 1/3, 1
Let t(p) be the second derivative of -3*p**6 + 0*p**3 - 7*p + 0*p**2 - 2*p**4 - 1/2*p**7 - 27/5*p**5 + 0. Determine s so that t(s) = 0.
-2, -2/7, 0
Factor -3/2*o**3 + 3/2*o + 21/2*o**2 - 21/2.
-3*(o - 7)*(o - 1)*(o + 1)/2
Let w(f) be the second derivative of -f**6/6 - 5*f**5/4 - 5*f**4/4 + 25*f**3/6 + 10*f**2 - 2*f - 228. Solve w(m) = 0.
-4, -1, 1
Let j = -216 + 221. Let q(x) be the third derivative of 0 + 0*x + 2*x**2 + 1/120*x**6 + 1/12*x**4 - 1/20*x**j + 0*x**3. Find o such that q(o) = 0.
0, 1, 2
Let u = -132 - -136. Let z(t) be the first derivative of -1/2*t**u + t**2 + 0*t + 0*t**3 + 7. Suppose z(y) = 0. What is y?
-1, 0, 1
Let t(z) = -z**4 + z**2 - z + 1. Let c(v) = -2*v**5 + 38*v**4 - 20*v**3 - 98*v**2 + 144*v - 62. Let o(n) = -c(n) - 10*t(n). Solve o(k) = 0 for k.
-2, 1, 13
Let k(q) = -2*q + 3. Let u be k(-6). Let h(g) = g**3 - g**2 - g. Let m(x) = -20*x**3 + 35*x**2. Let y(o) = u*h(o) + m(o). Factor y(w).
-5*w*(w - 3)*(w - 1)
Factor -21*b**2 - 7658*b**4 - 21*b**2 + 69*b**3 + 7628*b**4 + 3*b**5.
3*b**2*(b - 7)*(b - 2)*(b - 1)
Find t, given that 3/5*t**2 + 0 - 6/5*t = 0.
0, 2
Let i(f) be the second derivative of 0*f**3 + 1/90*f**5 + 0 - 4*f - 1/54*f**4 + 1/63*f**7 + 0*f**2 + 1/27*f**6. Factor i(l).
2*l**2*(l + 1)**2*(3*l - 1)/9
Factor -96*u**3 - 19*u + 51*u**3 + 64*u + 40 - 40*u**2.
-5*(u - 1)*(u + 1)*(9*u + 8)
Let n(m) = m**2. Let k(l) = -17*l**2 + l + 21. Let w(x) = -8*x**2 + 10. Let t(i) = 4*k(i) - 9*w(i). Let f(b) = 2*n(b) - t(b). What is o in f(o) = 0?
-3, 1
Let x be 126/(-28) + 2/4. Let f be -5 - ((-150)/42 + x). Suppose 6/7*c**3 + 0*c + f*c**2 + 2/7*c**5 + 0 - 10/7*c**4 = 0. Calculate c.
-1, 0, 3
Let x = -5163 + 36150/7. Suppose -6/7 + x*m - 3/7*m**2 = 0. What is m?
1, 2
Let y(j) be the first derivative of -2*j**3 - 76*j**2 + 104*j + 50. Factor y(i).
-2*(i + 26)*(3*i - 2)
Let j(x) = x**3 + 8*x**2 + x - 6. Let z be j(-8). Let l be ((-2)/3)/(z/4284). Solve 4913*o**3 - 3 - 1734*o**2 - 2 - 3 + l*o = 0 for o.
2/17
Let o(f) be the first derivative of -f**6/6 - 5*f**5/4 - 5*f**4/4 + 15*f**3/2 - 3*f + 15. Let z(t) be the first derivative of o(t). Find u, given that z(u) = 0.
-3, 0, 1
Determine x, given that -x**2 - x**3 + 228 - 228 - 4*x + 6*x = 0.
-2, 0, 1
Solve -7*j - 75 - 30*j**2 - 12*j**2 + 43*j**2 - 3*j = 0.
-5, 15
Let t(r) = r**3 + 8*r**2 - 336*r - 2680. Let s be t(-8). Factor 6 + 8/3*b**3 - s*b + 2/3*b**4 - 4/3*b**2.
2*(b - 1)**2*(b + 3)**2/3
Let a(s) be the first derivative of 5*s**3/3 + 35*s**2 - 75*s + 106. Find u, given that a(u) = 0.
-15, 1
Let d(x) be the third derivative of -7*x**2 - 2*x**3 - 1/3*x**4 + 1/15*x**5 + 0 + 0*x. Let d(z) = 0. Calculate