
Let s(d) be the third derivative of 0*d - 1/720*d**6 + 0 + 1/80*d**5 - 1/24*d**4 - 1/3*d**3 + d**2. Let g(v) be the first derivative of s(v). Factor g(a).
-(a - 2)*(a - 1)/2
Let a(o) be the second derivative of -o**6/75 - o**5/25 + o**4/10 + 9*o. Solve a(n) = 0.
-3, 0, 1
Let r(k) be the first derivative of 2 + 1/2*k**6 + 0*k + 9/4*k**4 - 3/2*k**2 - 1/2*k**3 + 21/10*k**5. Solve r(y) = 0 for y.
-2, -1, 0, 1/2
Factor -2*f**2 + 4*f + 54 - 54.
-2*f*(f - 2)
Let s be 1/10*4*-20. Let x = s - -12. Factor b**3 + b**2 + 2*b**x - 3*b**3 - b**4.
b**2*(b - 1)**2
Factor 5*x**3 - 197 - 40*x - 183 + 140 + 26*x**2 - x**2.
5*(x - 3)*(x + 4)**2
Let k = 3 + 1. Let r(s) be the second derivative of 1/4*s**2 + 2*s - 1/48*s**k + 1/24*s**3 + 0. Factor r(a).
-(a - 2)*(a + 1)/4
Let n(j) be the third derivative of j**8/5040 - j**7/1260 + j**6/1080 - 4*j**3/3 + 6*j**2. Let g(v) be the first derivative of n(v). Factor g(m).
m**2*(m - 1)**2/3
Let k(c) be the second derivative of -3/5*c**2 + 3/100*c**5 + 1/10*c**4 - 5*c - 1/10*c**3 + 0. Solve k(z) = 0.
-2, -1, 1
Solve -2/5*x**2 + 12/5*x - 18/5 = 0.
3
Let f(y) be the third derivative of -9*y**2 + 0 - 1/6*y**3 + 0*y + 0*y**4 + 1/60*y**5. Factor f(c).
(c - 1)*(c + 1)
Solve 2*v**4 + 6*v**2 - 8*v - 4*v**4 + 393 - 401 + 4*v**3 = 0.
-1, 2
Let x(w) = -w**3 + 3*w**2 + 2*w - 3. Suppose -4 = j - 7. Let q be x(j). Let -32/3*k + 16/3*k**2 + 14/3*k**4 - 32/3 + 2/3*k**5 + 32/3*k**q = 0. Calculate k.
-2, 1
Determine a, given that -3/2 + 2*a - 1/2*a**2 = 0.
1, 3
Let a(w) be the third derivative of -1/48*w**4 + 0*w**6 + 0*w + 0 + 1/672*w**8 - 1/210*w**7 + 0*w**3 + 3*w**2 + 1/60*w**5. Suppose a(q) = 0. Calculate q.
-1, 0, 1
Let r(h) be the second derivative of h**4/12 - h**3/6 - 3*h**2/2 + 7*h. Let i be r(-2). Solve s**2 + 1/3*s**i + 2/3*s + 0 = 0.
-2, -1, 0
Let f = -15955/3 - -5365. Let p = -46 + f. Solve 0*v + p*v**2 + 0 - 2/3*v**3 = 0 for v.
0, 1
Let g(m) = -12*m**4 - 18*m**3 + 9*m**2 + 15*m + 3. Let h(v) = 24*v**4 + 37*v**3 - 18*v**2 - 30*v - 6. Let d(y) = -7*g(y) - 3*h(y). Let d(j) = 0. What is j?
-1, -1/4, 1
Let w(q) be the first derivative of -2*q**6 - 4*q**5 - q**4 + 4*q**3/3 - 5. Factor w(d).
-4*d**2*(d + 1)**2*(3*d - 1)
Factor -2*q**2 + 2*q - 17 + 4*q - 19 + 32.
-2*(q - 2)*(q - 1)
Let c(k) be the second derivative of k**7/189 - k**5/90 + 9*k. Factor c(t).
2*t**3*(t - 1)*(t + 1)/9
Let v(c) be the third derivative of c**5/30 - c**4/12 - 2*c**3/3 + c**2. Find i, given that v(i) = 0.
-1, 2
Factor 11*x - 4*x**4 + 10 - x**4 - 5 - 10*x**3 - x.
-5*(x - 1)*(x + 1)**3
Let j = 7 - -3. Let r(p) = -14*p**5 + 8*p**3 + 10*p**2 - 14*p - 10. Let s(b) = b**5 - b**2 + b + 1. Let h(w) = j*s(w) + r(w). Factor h(c).
-4*c*(c - 1)**2*(c + 1)**2
Let t = 421/6 - 70. Let l(f) be the first derivative of -t*f**2 + 0*f + 4 + 1/12*f**4 - 1/9*f**3 + 1/15*f**5. Let l(r) = 0. Calculate r.
-1, 0, 1
Let f(p) be the third derivative of p**6/1320 + p**5/132 + 7*p**4/264 + p**3/22 + 7*p**2. Factor f(g).
(g + 1)**2*(g + 3)/11
Suppose 3*c + 22 = 5*p, -2*p + c = 5*c - 14. Let u = p - -6. Factor -2*t + 4 + t**3 + t**2 + u*t**3 - 10*t + 4*t**4.
(t + 2)**2*(2*t - 1)**2
Let h = -10 - -43. Factor -28*b**2 - 62 - h*b + 2*b**3 + 8 + 87*b + 10*b**2.
2*(b - 3)**3
Let d be (-36)/90*(-5)/7. Factor d*j**3 + 0*j - 2/7*j**4 + 0*j**2 + 0.
-2*j**3*(j - 1)/7
Suppose 0 = -0*k + k. Suppose 5*s - 7 = -3*d, -d = -2*s + 5 - 0. Factor 1/2*u + 1/2*u**s + k.
u*(u + 1)/2
Let k = 13/2 + -6. Find o such that 0*o + 1/2*o**2 - k = 0.
-1, 1
Let s(r) be the second derivative of -r**7/210 + r**6/50 - r**4/15 - 11*r. Factor s(u).
-u**2*(u - 2)**2*(u + 1)/5
Let q(p) be the third derivative of p**11/1663200 - p**9/151200 + p**7/25200 + p**5/30 - 3*p**2. Let w(r) be the third derivative of q(r). Factor w(o).
o*(o - 1)**2*(o + 1)**2/5
Suppose 0 = -2*u - 2*u + 12. Let -2 + 6*y + 2*y**3 - u*y**2 - 3*y**2 + 0 = 0. Calculate y.
1
Factor -2/5*d**3 - 6/5*d**2 + 6/5 + 2/5*d.
-2*(d - 1)*(d + 1)*(d + 3)/5
Let u(v) be the second derivative of -v**5/20 - v**4/12 + v**3/6 + v**2/2 + 5*v. Factor u(w).
-(w - 1)*(w + 1)**2
Let s(k) = k**2 + 4*k - 5. Let v be s(-5). Solve v*i - i**3 + 8*i**3 - 3*i + 4*i**3 + 1 - 3*i**2 - 6*i**4 = 0.
-1/2, 1/3, 1
Let f(u) be the first derivative of 7 + 1/15*u**5 - 1/6*u**2 + 0*u + 1/12*u**4 - 1/9*u**3. Solve f(j) = 0.
-1, 0, 1
Find z such that 50/9*z**2 - 38/9*z**3 - 32/9*z + 8/9 - 2/9*z**5 + 14/9*z**4 = 0.
1, 2
Suppose 0 = 4*y + 2*p - 2 - 0, p = 5*y + 1. Suppose y = 5*l + 4*v - v - 10, 0 = -l + 2*v + 2. Let 3/4*u**3 + 3/4*u**l + 1/4*u + 1/4*u**4 + 0 = 0. What is u?
-1, 0
Let -70*z**2 + 8*z**3 + 3*z + 82*z**2 + z**3 = 0. What is z?
-1, -1/3, 0
Let c(t) = t**3 - 2*t**2 + t. Let i(y) = y**2 - 2. Let n be i(2). Let v be c(n). Let -2/7*a**3 - 6/7*a - 6/7*a**v - 2/7 = 0. What is a?
-1
Suppose w = 2*w - 3. Let n(m) = -4*m + 4*m - m**2 + w*m - 4*m. Let b(h) = h**2 + 3*h. Let o(i) = -b(i) - 3*n(i). Factor o(r).
2*r**2
Let n(c) be the first derivative of 2*c**3/27 - 2*c**2/9 - 12. Factor n(s).
2*s*(s - 2)/9
Let z(d) be the first derivative of 1/9*d**3 - 6 + 1/12*d**4 - 1/36*d**6 - 1/12*d**2 - 1/6*d - 1/30*d**5. Determine k so that z(k) = 0.
-1, 1
Let l(n) be the first derivative of n**6/6 + 11*n**5/20 + 9*n**4/16 + n**3/12 - n**2/8 - 7. Factor l(g).
g*(g + 1)**3*(4*g - 1)/4
Let x(a) be the second derivative of 0*a**2 + 0*a**4 - 2*a + 0*a**3 + 0 + 1/20*a**5. Determine t, given that x(t) = 0.
0
Let z(a) be the second derivative of -a**6/105 - a**5/35 + 2*a**3/21 + a**2/7 + 5*a. Let z(u) = 0. Calculate u.
-1, 1
Let t(q) be the third derivative of q**6/24 - q**5/2 + 5*q**4/2 - 20*q**3/3 + 15*q**2. Factor t(i).
5*(i - 2)**3
Let i(u) = -2*u**3 + 7*u**2 - 16*u + 5. Let x(q) = 4*q**3 - 13*q**2 + 32*q - 9. Suppose 5*w + 0*w = -35. Let c(y) = w*i(y) - 3*x(y). Let c(z) = 0. What is z?
1, 2
Let h(q) = -7*q**3 - 3*q**2 + 12*q + 19. Let c(t) = 11*t**3 + 4*t**2 - 18*t - 29. Let n(x) = 5*c(x) + 8*h(x). Let v be n(-5). Factor -1/2*b**v + b - 1/2.
-(b - 1)**2/2
Let w(c) be the third derivative of 2/135*c**5 + 5/108*c**4 + 0 + 1/540*c**6 + 0*c + 2/27*c**3 - c**2. Determine j, given that w(j) = 0.
-2, -1
Let t(g) be the third derivative of -g**8/336 - g**7/30 - 7*g**6/60 - 2*g**5/15 - 30*g**2. Find i such that t(i) = 0.
-4, -2, -1, 0
Let i(r) = r**2 - 5*r + 2. Let n be i(5). Factor -15*v**4 - 30*v**n + 15*v - 4 + 16*v**5 + 30*v**3 + 1 - 13*v**5.
3*(v - 1)**5
Suppose 25 = 5*f - 3*l, 0*l = 5*f - l - 15. Let s = -7 + 8. Let s - 2*t**f - 2*t + 1 - 3*t**3 + 5*t**3 = 0. Calculate t.
-1, 1
Let z(r) be the third derivative of r**7/70 - r**5/6 + r**3/2 - 4*r**2. Let h(j) = 3*j**4 - 9*j**2 + 3. Let m(g) = -4*h(g) + 3*z(g). Let m(x) = 0. What is x?
-1, 1
Let y be 3 - 4/((-6)/3). Suppose m + 2 = -4*q, y*q + m = -4*m - 10. Determine p so that 0 + 0*p**3 + 1/2*p**5 + 0*p - 1/2*p**4 + q*p**2 = 0.
0, 1
Let b be (-252)/(-105) + (-6)/(-5) + -2. Factor 1/5*v**3 + b + 12/5*v + 6/5*v**2.
(v + 2)**3/5
Let v(i) be the first derivative of 2*i**3/9 + 4*i**2/3 + 8*i/3 + 40. Factor v(x).
2*(x + 2)**2/3
Let y(n) = 9*n + 30. Let o be y(-3). Factor -1/2*w**2 - 1/4*w - 1/4*w**o + 0.
-w*(w + 1)**2/4
Let l(t) be the first derivative of -t**4/7 - 20*t**3/21 - 2*t**2 - 12*t/7 + 21. Determine c so that l(c) = 0.
-3, -1
Let d(i) be the third derivative of i**5/48 + 5*i**4/48 + 5*i**3/24 - 2*i**2. Factor d(p).
5*(p + 1)**2/4
Let r = 4 - -3. Suppose 4*g - r = 5. Let 0*w + 0*w**2 - 1/2*w**g + 0 = 0. Calculate w.
0
Let h = 445/2 + -222. Suppose 0 + 1/4*r**2 + h*r = 0. What is r?
-2, 0
Let d(r) be the first derivative of -r**7/63 + r**5/30 + 4*r - 2. Let p(c) be the first derivative of d(c). Solve p(h) = 0.
-1, 0, 1
Let s(v) be the second derivative of v**8/7560 - v**7/3780 - v**6/1620 + v**5/540 + v**3/6 - 4*v. Let d(g) be the second derivative of s(g). Factor d(o).
2*o*(o - 1)**2*(o + 1)/9
Solve -6/7*z**3 + 0 + 3*z**2 + 12/7*z = 0.
-1/2, 0, 4
Suppose -36 = 4*d - 7*d. Let p(f) = f**2 - f + 1. Let s(i) = 5*i**3 + 3*i**2 + 4*i - 3. Let m(k) = d*p(k) + 4*s(k). Factor m(v).
4*v*(v + 1)*(5*v + 1)
Find q such that -2*q**2 + 2/3*q**3 + 8/3 + 0*q = 0.
-1, 2
Let a(v) be the second derivative of 0*v**2 + 1/12*v**3 + 0*v**5 + 0 - 3*v - 1/30*v**6 + 1/12*v**4 - 1/84*v**7. Let a(m) = 0. What is m?
-1, 0, 1
Let g(d) = 2*d**2 - 17*d + 15. Let f(q) = q - 1. Let w(i) = 22*f(i)