 - 2/9*g**k - 2/9*g**2 + 0.
2*g*(g - 1)**2*(g + 1)/9
Suppose 2*b + b = 5*b. Let v(k) be the first derivative of -2 + 1/12*k**4 - 1/18*k**6 + 0*k**3 + 0*k**2 + 0*k**5 + b*k. Factor v(y).
-y**3*(y - 1)*(y + 1)/3
Suppose -2*i + 4 = -0*i. Factor 3*v**4 - 3 + v**4 - 7*v**4 - v**i + 7*v**2.
-3*(v - 1)**2*(v + 1)**2
Let o be -1 - (-2)/1 - (-14 + 13). Factor 0 - 22/3*n**4 - 8/3*n**5 + 2/3*n - 2/3*n**o - 6*n**3.
-2*n*(n + 1)**3*(4*n - 1)/3
Let h(l) be the third derivative of -l**5/60 - l**4/8 - 6*l**2. Solve h(x) = 0.
-3, 0
Let t(k) be the first derivative of k**8/672 + k**7/140 + k**6/240 - k**5/40 - k**4/24 + 3*k**2/2 - 2. Let x(l) be the second derivative of t(l). Factor x(r).
r*(r - 1)*(r + 1)**2*(r + 2)/2
Let d be 3/108 - 0/(-5). Let u(x) be the second derivative of 2*x + 0*x**3 + 0*x**2 - d*x**4 - 1/60*x**5 + 0. Determine k, given that u(k) = 0.
-1, 0
Let t(r) be the second derivative of -2*r**2 + 0 + 16/9*r**3 + 0*r**5 - 2/3*r**4 - 6*r + 2/45*r**6. Factor t(l).
4*(l - 1)**3*(l + 3)/3
Suppose 6*a + 168 - 180 = 0. Factor -2/5*f**a + 2/5*f - 2/5*f**3 + 2/5*f**4 + 0.
2*f*(f - 1)**2*(f + 1)/5
Let u(g) be the first derivative of -g**6/90 + g**5/15 - g**4/6 - 4*g**3/3 - 6. Let r(p) be the third derivative of u(p). Let r(o) = 0. Calculate o.
1
Let b be 1 - -1 - 322/8. Let y = b - -39. Factor y*s**2 + 1/4 + 3/4*s + 1/4*s**3.
(s + 1)**3/4
Let u(b) be the second derivative of -b**6/90 + b**4/36 + 6*b. Factor u(k).
-k**2*(k - 1)*(k + 1)/3
Let o = 4 + -2. Let a = 0 + o. Find c, given that 2/3*c + 0 - 4/3*c**a + 2/3*c**3 = 0.
0, 1
Suppose 11*u = -16*u. Factor -12/7*z**4 - 16/7*z**2 + 24/7*z**3 + 2/7*z**5 + u*z + 0.
2*z**2*(z - 2)**3/7
Determine f so that -2*f**3 + 3 + 1 - 4 - 2*f**2 = 0.
-1, 0
Let y(p) be the first derivative of -2*p**3/69 - 2*p**2/23 - 18. Suppose y(d) = 0. Calculate d.
-2, 0
Let m(h) be the first derivative of h**6/24 - h**4/8 + h**2/8 - 4. Factor m(u).
u*(u - 1)**2*(u + 1)**2/4
Suppose 0*l - l = 0. Let z be 12/54*(3 - l). Factor 1/3*q + z*q**2 + 0 + 0*q**3 - 2/3*q**4 - 1/3*q**5.
-q*(q - 1)*(q + 1)**3/3
Let y(c) be the first derivative of c**7/280 + c**6/60 - c**5/80 - c**4/8 + c**3/6 + 3*c**2/2 - 2. Let u(x) be the second derivative of y(x). Factor u(q).
(q - 1)*(q + 2)**2*(3*q - 1)/4
Let a(o) be the first derivative of -o**7/210 - o**6/180 + o**5/60 + o**4/36 - 7*o**2/2 + 3. Let y(x) be the second derivative of a(x). Factor y(q).
-q*(q - 1)*(q + 1)*(3*q + 2)/3
Solve -3/5*o**3 - 6/5*o**2 + 9/5*o + 0 = 0.
-3, 0, 1
Suppose p - r - r = 6, -4*p - r - 3 = 0. Factor -1/2*u - 1/2*u**5 + u**3 + p*u**2 + 0 + 0*u**4.
-u*(u - 1)**2*(u + 1)**2/2
Suppose -3*w - 4*h + 13 = -3*h, -2*w + h + 12 = 0. Solve 3*d**2 + 3*d**4 - 6 + 0*d**5 + 2*d**w + 0*d**5 - 15*d + 21*d**3 - 8*d**5 = 0.
-1, -1/2, 1, 2
Let r(c) be the first derivative of c**6/18 + c**5/5 + c**4/4 + c**3/9 + 15. Let r(w) = 0. What is w?
-1, 0
Let a(t) be the first derivative of 5*t**3/3 + 65*t**2/2 - 70*t - 46. Factor a(s).
5*(s - 1)*(s + 14)
Let r(d) be the second derivative of -d**6/15 + d**5/6 - d**4/9 - 6*d. Suppose r(p) = 0. What is p?
0, 2/3, 1
Let d(w) = 5*w**3 + 4*w**2 + 3*w. Let y(c) = 9*c**3 + 7*c**2 + 5*c. Let f(r) = -7*d(r) + 4*y(r). Factor f(i).
i*(i - 1)*(i + 1)
Let l(o) = -o**2 + 40. Let j be l(6). Factor 0 - 2/9*b**2 - 2/9*b**5 + 2/9*b**3 + 2/9*b**j + 0*b.
-2*b**2*(b - 1)**2*(b + 1)/9
Let j = -26 - -28. Let n(o) be the second derivative of o**7/42 - o**5/10 + o**3/6 - o. Let g(p) = p**5 - 2*p**3 + p. Let h(u) = j*g(u) - 3*n(u). Factor h(t).
-t*(t - 1)**2*(t + 1)**2
Factor -16/5*v**3 + 4/5 - 16/5*v + 24/5*v**2 + 4/5*v**4.
4*(v - 1)**4/5
Let z = 109/5 + -213/10. Let w(g) be the first derivative of 1/2*g**2 + 1/6*g**3 + z*g - 3. Factor w(v).
(v + 1)**2/2
Let f(z) be the second derivative of -3*z + 0 - 3/70*z**5 + 4/21*z**4 + 2/7*z**2 - 1/3*z**3. Find l, given that f(l) = 0.
2/3, 1
Let u(r) be the first derivative of -3*r + 2 + 1/6*r**4 - r**3 + 2*r**2. Let p(l) be the first derivative of u(l). What is v in p(v) = 0?
1, 2
Let i(z) be the first derivative of -z**4/4 + z**3/2 - 2*z + 4. Let w(m) be the first derivative of i(m). Factor w(c).
-3*c*(c - 1)
Let g(x) be the first derivative of x**3/3 - x**2/2 - x - 3. Let a(r) = -1. Suppose -4*t - 5 = t. Let s(k) = t*g(k) - a(k). Factor s(p).
-(p - 2)*(p + 1)
Let a(o) be the third derivative of o**7/13860 - o**6/990 + o**5/165 - o**4/12 - 5*o**2. Let u(p) be the second derivative of a(p). Factor u(b).
2*(b - 2)**2/11
Let u(h) be the second derivative of -2*h**7/15 + 52*h**6/75 - 34*h**5/25 + 16*h**4/15 + 2*h**3/15 - 4*h**2/5 + 14*h. Factor u(v).
-4*(v - 1)**4*(7*v + 2)/5
Let d(p) = p**3 - 5*p**2 + 6*p - 6. Let y be d(4). Suppose -2*a - 2*q - 4 = 0, y = 5*a - q - 0. Solve 0*n + a*n + 2*n**3 + 2*n + 4*n**2 = 0 for n.
-1, 0
Suppose 0 = 2*v + 6, -3*v + 4 = -4*n - 7*v. Let p(h) be the first derivative of -1/2*h + 1/2*h**n + 1/6*h**3 - 1/4*h**4 - 1. Factor p(i).
-(i - 1)*(i + 1)*(2*i - 1)/2
Let f(n) = n**2 - 3*n - 2. Suppose -s + 1 = -3. Let p be f(s). Suppose -z**2 - 4*z**3 - 3*z**p + 6*z + z**4 - 2 - 2*z**5 + 5*z**4 = 0. Calculate z.
-1, 1
Let b(t) be the third derivative of 1/30*t**6 - 1/6*t**4 + 0*t - 1/15*t**5 + 0 + 6*t**2 + 2/3*t**3. Find l, given that b(l) = 0.
-1, 1
Let g = -3 + 5. Let p(w) = w**2 + 3. Let j be p(0). Factor 2*i**4 + g*i**3 - 3*i**4 + 0*i**j + 3*i**4 - 2*i - 2*i**2.
2*i*(i - 1)*(i + 1)**2
Suppose 6 = -2*g + 4. Let h be (4 + -4)/(1/g). Solve 0*d**2 + 0*d**3 + 1/2*d**4 + h*d + 0 = 0.
0
Let a be (2/4 - 132/88) + 3. Let -6/7*g**a - 4/7 - 2/7*g**3 + 2/7*g**4 + 10/7*g = 0. What is g?
-2, 1
Solve -2/17*y**3 + 12/17*y**2 + 0 + 0*y = 0.
0, 6
Let d(z) be the second derivative of -1/42*z**4 - 2/7*z**2 - 1/7*z**3 - z + 0. Factor d(r).
-2*(r + 1)*(r + 2)/7
Let f(i) be the second derivative of i**4/18 + 2*i**3/9 - 8*i**2/3 + 21*i. Factor f(g).
2*(g - 2)*(g + 4)/3
Let i(c) be the third derivative of -2*c**7/105 + c**6/30 + c**5/5 - c**4/6 - 4*c**3/3 - 5*c**2. Solve i(h) = 0.
-1, 1, 2
Let n = -37/3 + 13. Let m = -3 - -6. Suppose 4/3 - 4/3*g**2 + 2/3*g**m - n*g = 0. Calculate g.
-1, 1, 2
Factor -2*b**3 - 24*b + 1 + 9 - 12*b**2 - 11 - 15.
-2*(b + 2)**3
Suppose -21*s + 4*p = -16*s - 22, -2*p + 2 = 4*s. Solve -8/5*r**4 - 2/5*r**5 - 12/5*r**3 - 2/5*r - 8/5*r**s + 0 = 0 for r.
-1, 0
Suppose 2 = -m - 5. Let q = 11 + m. Factor -16/9*x**q + 0*x**2 + 0*x - 10/9*x**5 + 8/9*x**3 + 0.
-2*x**3*(x + 2)*(5*x - 2)/9
Let j(f) be the second derivative of 5/12*f**4 - 1/20*f**5 - 9/2*f**2 + 0 - 1/2*f**3 + 9*f. Determine l so that j(l) = 0.
-1, 3
Suppose -5*r = -2*r - 9. Suppose -5*q - j + 30 = 3*j, r*q + j = 11. Factor -2/7*a**q - 2/7*a**3 + 0 + 2/7*a**4 + 2/7*a.
2*a*(a - 1)**2*(a + 1)/7
Determine m, given that 8 + 0 + 65*m**2 + 12 + 0 + 60*m + 30*m**3 + 5*m**4 = 0.
-2, -1
Let g be 2 - 2 - 0*4/16. Factor 2/3*t**4 + 0 + 2/9*t**5 + g*t + 2/3*t**3 + 2/9*t**2.
2*t**2*(t + 1)**3/9
Let b(d) be the third derivative of 0*d - 1/10*d**5 - 6*d**2 + 1/40*d**6 + 1/35*d**7 + 0*d**3 + 0 - 1/8*d**4. Suppose b(l) = 0. Calculate l.
-1, -1/2, 0, 1
Let t(w) be the first derivative of 9*w**6/8 - 9*w**5/10 - 39*w**4/8 + 9*w**3 - 45*w**2/8 + 3*w/2 + 13. Solve t(k) = 0 for k.
-2, 1/3, 1
Let s(k) be the first derivative of k**5/20 + k**4/6 + 2*k - 5. Let o(q) be the first derivative of s(q). Factor o(a).
a**2*(a + 2)
Let i be 30/14 + 1/(-7). Factor 2*c**2 - 1 + c**5 - 5*c - 2*c**5 + 0*c**i - c**4 + 4*c + 2*c**3.
-(c - 1)**2*(c + 1)**3
Let m(v) = -80*v**4 + 20*v**3 + 215*v**2 + 125*v - 15. Let c(s) = -20*s**4 + 5*s**3 + 54*s**2 + 31*s - 4. Let o(g) = -25*c(g) + 6*m(g). Factor o(n).
5*(n - 2)*(n + 1)**2*(4*n - 1)
Find y, given that -1/3*y**4 + 0 + 0*y - 2/3*y**2 + y**3 = 0.
0, 1, 2
Let a(c) be the second derivative of 0*c**2 - 4*c + 1/30*c**6 + 0 + 0*c**3 + 1/12*c**4 - 1/10*c**5. Solve a(d) = 0.
0, 1
Let i = 0 + 2. Factor 2*x**i + x - 4*x + x**2.
3*x*(x - 1)
Suppose -2/7*y**4 + 2*y - 18/7*y**2 + 10/7*y**3 - 4/7 = 0. What is y?
1, 2
Let n(z) be the first derivative of 0*z**2 + 4/9*z**3 + 1/3*z**5 - 4 + 0*z + 1/18*z**6 + 2/3*z**4. Factor n(h).
h**2*(h + 1)*(h + 2)**2/3
Suppose -4/7*b**4 + 0 + 0*b**3 + 2/7*b + 4/7*b**2 - 2/7*b**5 = 0. What is b?
-1, 0, 1
Let i(u) = -7*u - 1. Let d(z) = -z. Let q(a) = 6*d(a) - 2*i(a). Let j(s) = -s**2 + 17*s + 3. Let o(w) = 2*j(w) - 5*q(w). What is n 