be the first derivative of -b**4/4 - 3*b**3/2 - 3*b**2 - 4*b + 2. Let k(n) be the first derivative of h(n). Suppose k(m) = 0. Calculate m.
-2, -1
Let u(s) = -s**4 + s**3 - s**2 - s. Let w(c) be the third derivative of 4*c**7/105 - 7*c**6/120 - c**4/12 + c**2. Let b(z) = 6*u(z) - 3*w(z). Solve b(h) = 0.
0, 2/5, 1/2
Let 4/13 - 6/13*i + 2/13*i**2 = 0. Calculate i.
1, 2
Let n(v) be the second derivative of 0*v**2 - 3*v + 0*v**4 - 1/42*v**7 + 1/10*v**5 - 1/30*v**6 + 0*v**3 + 0. Factor n(t).
-t**3*(t - 1)*(t + 2)
Let f(d) be the first derivative of d**3 - 3*d - 7. Factor f(p).
3*(p - 1)*(p + 1)
Let h(d) be the first derivative of 1/21*d**4 + 0*d**2 + 2 - 1/70*d**5 - 1/21*d**3 + 3*d. Let u(i) be the first derivative of h(i). Factor u(b).
-2*b*(b - 1)**2/7
Find i, given that 5*i**3 + 13*i**4 + 5*i - 8 - 50*i**2 - 4*i**5 + 50*i - 11*i = 0.
-2, 1/4, 1, 2
Let s = -30 - -32. Solve 4/5*a**3 + 0*a**s + 2/5 - 4/5*a - 2/5*a**4 = 0.
-1, 1
Suppose 40 = 2*u - 4*u. Let h = 101/5 + u. Determine p, given that -1/5*p - 1/5 + h*p**3 + 1/5*p**2 = 0.
-1, 1
Let n = 59/3 - 115/6. Let q(d) = -3*d**3 + d**2 + 2*d + 1. Let v be q(-1). Factor 0*l + n*l**2 + 3/2*l**v + 0.
l**2*(3*l + 1)/2
Let c = -23 - -39. Factor c + 35*h + 2*h**3 + 20*h**2 + 2*h**3 - 3*h.
4*(h + 1)*(h + 2)**2
Let n(y) = -y**4 + 3*y**3 + y**2 - 3*y + 6. Let i(m) = -2*m**4 + 6*m**3 + 2*m**2 - 6*m + 11. Let t(z) = -6*i(z) + 11*n(z). Factor t(l).
l*(l - 3)*(l - 1)*(l + 1)
Suppose 13 = 2*n - 5*k, -7*k + 2*k = 5. Let w(g) be the third derivative of 0*g**n + 0 + 0*g - 1/270*g**5 + 2*g**2 + 0*g**3. Suppose w(b) = 0. What is b?
0
Suppose -2*j - 9 = j. Let y be (0 - j)*4/6. Factor 2 - 2 + y*c**2 - 4*c.
2*c*(c - 2)
Let o be 22/24 - 21/28. Let x(r) be the second derivative of -2/3*r**3 - r**2 - r + 0 - o*r**4. Find l, given that x(l) = 0.
-1
Let d**2 + 0 - d**3 - 1/3*d + 1/3*d**4 = 0. Calculate d.
0, 1
Let j(l) be the second derivative of -l**5/4 + 25*l**4/6 - 80*l**3/3 + 80*l**2 + 30*l. Factor j(p).
-5*(p - 4)**2*(p - 2)
Let n(s) = 0 + 4 + 3*s**3 + 1 - 4 - 2*s**2. Let w be n(1). Factor 29 - 27 - a + w*a**2 - 3*a.
2*(a - 1)**2
Let u(g) = -8*g**2 + 4*g + 4. Let w = 5 + -3. Let b(i) = 3*i**w - 2*i**2 - 1 + 0. Let v(j) = 6*b(j) + u(j). Factor v(p).
-2*(p - 1)**2
Let u(o) = o**3 - 14*o**2 + 2. Let f be u(14). Let j(h) be the third derivative of 0 + 3/4*h**4 + 7/30*h**5 + h**f + 0*h + 2/3*h**3. Let j(d) = 0. What is d?
-1, -2/7
Let u = -5/29 + 133/435. Let a = u - -38/15. Solve 2/3*q + 0 + 10/3*q**2 + a*q**3 = 0 for q.
-1, -1/4, 0
Let f(h) be the third derivative of h**7/2100 - h**6/450 + h**5/300 - h**3/6 - 2*h**2. Let u(t) be the first derivative of f(t). Factor u(w).
2*w*(w - 1)**2/5
Factor 0*f - 2/13*f**3 + 0 - 2/13*f**2.
-2*f**2*(f + 1)/13
Let s = -880 - -880. Suppose 8/5*p**3 + 2/5*p**4 + 4/5*p + 2*p**2 + s = 0. Calculate p.
-2, -1, 0
Let x(j) be the second derivative of -3*j**5/40 + 3*j**4/8 - j**3/2 + 5*j. Factor x(d).
-3*d*(d - 2)*(d - 1)/2
Let l(u) be the second derivative of u**5/20 - 29*u**4/108 + 4*u**3/9 - 2*u**2/9 + 2*u. Factor l(g).
(g - 2)*(g - 1)*(9*g - 2)/9
Let r(s) be the third derivative of s**9/120960 - s**8/13440 + s**7/5040 - s**5/60 + 3*s**2. Let p(f) be the third derivative of r(f). Solve p(i) = 0.
0, 1, 2
Factor 86*u - 64*u**4 + 53*u - 80*u + 288*u**3 + 137*u - 420*u**2.
-4*u*(u - 1)*(4*u - 7)**2
Factor 2/5*c**3 + 8/5 + 0*c - 6/5*c**2.
2*(c - 2)**2*(c + 1)/5
Suppose -5*r + r + 8 = 0. Let j = 13 + -7. Find y such that -6*y**r + y**2 + j*y**2 + y**3 = 0.
-1, 0
Let g(y) be the first derivative of y**7/70 - 19*y**6/360 + y**5/15 - y**4/24 + 10*y**3/3 + 3. Let t(i) be the third derivative of g(i). Factor t(j).
(j - 1)*(3*j - 1)*(4*j - 1)
Suppose -5*p + 0*p - 20 = 0. Let o be ((-9)/6)/(2/p). Find f, given that 46*f**4 + f**5 - 3 + 4*f**4 + 30*f**2 - 60*f**o - 5*f**4 - 13*f**5 = 0.
-1/4, 1
Let d(s) be the third derivative of -3/80*s**5 - 5/32*s**4 + 0 + 0*s - 1/4*s**3 - 2*s**2. Factor d(u).
-3*(u + 1)*(3*u + 2)/4
Let c(t) be the first derivative of -9*t**5/35 + 3*t**4/28 + 17*t**3/7 + 57*t**2/14 + 18*t/7 - 5. Determine q so that c(q) = 0.
-1, -2/3, 3
Suppose -4*b + 11 = -29. Suppose -i + b = i. Factor 0 + 1/4*c + 0*c**3 + 1/2*c**2 - 1/2*c**4 - 1/4*c**i.
-c*(c - 1)*(c + 1)**3/4
Suppose -5*h = 2*z - 4*h - 9, 5*z = -2*h + 22. Let c(y) be the second derivative of 0 - y**2 - 4*y - 1/6*y**z + 2/3*y**3. Factor c(u).
-2*(u - 1)**2
Suppose 0 = -0*i + 2*i - 8. Let p(t) be the first derivative of 0*t + 0*t**2 + 1/6*t**i - 2/9*t**3 - 3. Factor p(g).
2*g**2*(g - 1)/3
Let s(u) be the first derivative of 8*u**6/9 - 28*u**5/5 + 73*u**4/6 - 86*u**3/9 + 8*u/3 - 26. Determine c, given that s(c) = 0.
-1/4, 1/2, 1, 2
Let f(d) be the third derivative of -1/180*d**5 + 0 + 0*d - 1/9*d**3 - 4*d**2 - 1/24*d**4. Factor f(s).
-(s + 1)*(s + 2)/3
Let q(d) = d**3 + 7*d**2 + 2. Let v be q(-7). Determine z so that 1/3*z**v - 1/3*z - 1/6*z**4 + 2/3*z**3 - 1/3*z**5 - 1/6 = 0.
-1, -1/2, 1
Suppose -i = -5*i. Suppose 2*q = -5*n + 20, 35 = 5*n - i*n + 5*q. Suppose 2/7*a + 8/7*a**n + 0 = 0. Calculate a.
-1/4, 0
Let i(s) be the first derivative of -s**4/4 + s**2/2 + 3. Let y be i(-1). Suppose -2/7*q**3 + 0*q + y + 2/7*q**2 = 0. What is q?
0, 1
Let r be (-9)/(-5) - (-6)/30. Let y(b) be the second derivative of -1/20*b**5 - 1/2*b**3 + 0 + b + 1/2*b**r + 1/4*b**4. Factor y(n).
-(n - 1)**3
Find u such that 1/3*u**3 - u**2 + 0 + 0*u = 0.
0, 3
Factor -12*v**3 + 22*v**2 - 36*v - 27*v + 47*v + 6*v**2.
-4*v*(v - 1)*(3*v - 4)
Factor 0 + 0*i + 4/9*i**2 + 2/9*i**4 + 2/3*i**3.
2*i**2*(i + 1)*(i + 2)/9
Let h be (-2 - (-1 - 1))/2. Let f = -3 + 7. Suppose -2/7*k**5 + h*k + 2/7*k**3 + 0 + 2/7*k**2 - 2/7*k**f = 0. Calculate k.
-1, 0, 1
Let t(s) be the third derivative of -s**6/540 + s**5/180 + s**4/18 - s**3/3 - 3*s**2. Let g(k) be the first derivative of t(k). Solve g(m) = 0.
-1, 2
Factor 4/3*q - 4/3*q**2 + 0.
-4*q*(q - 1)/3
Let s(h) = h**2 + 4*h + 5. Let w be s(-3). Let x be 1/(-3) + 1 + 1. Factor -1/3*k**3 - x*k - 4/3*k**w - 2/3.
-(k + 1)**2*(k + 2)/3
Suppose -3*f + 2*w = -17, 2*f + 3*w - 2 = 5. Let j = f - 3. Determine k so that 3 - 11 - 11*k - 2*k**j + 3*k = 0.
-2
Let p(u) be the first derivative of u**6/300 - 2*u**5/75 + u**4/12 - 2*u**3/15 + 2*u**2 - 1. Let i(c) be the second derivative of p(c). Factor i(f).
2*(f - 2)*(f - 1)**2/5
Let x(a) be the third derivative of -1/30*a**3 + 0*a**4 + 3*a**2 + 1/300*a**5 + 0*a + 0. Factor x(n).
(n - 1)*(n + 1)/5
Let w(l) be the third derivative of 0*l**3 - 1/66*l**4 - 3*l**2 + 0 + 1/330*l**5 + 0*l. Factor w(j).
2*j*(j - 2)/11
Let o be ((-3)/(-3))/3 - 0. Let g(x) be the second derivative of 0 - o*x**3 - 1/12*x**4 - x + 0*x**2. What is w in g(w) = 0?
-2, 0
Suppose 4*b - 15 = b. Suppose 3 = -b*c + 18. Let x(j) = -2*j**3 - 7*j**2 - 16*j - 11. Let v(d) = -d**2 + 1. Let g(u) = c*v(u) + x(u). Factor g(z).
-2*(z + 1)*(z + 2)**2
Let o(l) be the third derivative of 1/140*l**6 - 3/56*l**4 + 3/490*l**7 + 0*l - 1/14*l**3 - 1/70*l**5 - 6*l**2 + 0 + 1/784*l**8. Factor o(q).
3*(q - 1)*(q + 1)**4/7
Let v(m) be the first derivative of 0*m**3 + 1/8*m**4 + 2 + 1/20*m**5 - 1/4*m**2 - 1/4*m. Factor v(y).
(y - 1)*(y + 1)**3/4
Let w(z) be the first derivative of 2*z**5/5 - z**4/3 - 8*z**3/9 + 2*z**2/3 + 2*z/3 - 49. Solve w(q) = 0.
-1, -1/3, 1
Let a(b) = -12*b**4 + 4*b**3 + 13*b**2 + 7*b - 4. Let u(y) = -12*y**4 + 3*y**3 + 12*y**2 + 6*y - 3. Let c(n) = -3*a(n) + 4*u(n). Factor c(l).
-3*l*(l - 1)*(2*l + 1)**2
Let u = -53 + 57. Let z(f) be the first derivative of -1/2*f**u + 3 - f**2 - 4/3*f**3 + 0*f. Suppose z(c) = 0. Calculate c.
-1, 0
Let v be -6 - -1 - (-1 + 0). Let o = 6 + v. Solve -8/3 + o*a**3 - 8/3*a + 10/3*a**2 = 0 for a.
-2, -2/3, 1
Let p = 1723/2 - 836. Let j = p + -25. Factor 1/2*t - 1/2*t**3 + 1/2*t**2 - j.
-(t - 1)**2*(t + 1)/2
Let d(s) be the second derivative of s**5/10 - s**4/6 - 2*s**3/3 - 9*s. Let d(h) = 0. What is h?
-1, 0, 2
Let b = 15 + -17. Let j be -4 + (1 - (-1 + b)). Factor -27/5*z**3 + 36/5*z**4 + 6/5*z**2 - 3*z**5 + j + 0*z.
-3*z**2*(z - 1)**2*(5*z - 2)/5
Let b(p) = -3*p**3 - 15*p**2 - 59*p - 49. Let s(a) = 10*a**3 + 45*a**2 + 175*a + 147. Let m(r) = -21*b(r) - 6*s(r). Suppose m(z) = 0. Calculate z.
-7, -1
Let c(k) = -k**4 - k**3 - k**2 + k - 1. Let y(g) = -30*g**4 - 35*g**3 - 30*g**2 + 25*g - 25. Let x(i) = 25*c