**5/20 + 27*x**4/16 - 2*x**3 + 16. Factor g(w).
-3*w**2*(w - 8)*(w - 1)/4
Let x = 37/130 - -1/65. Let i(a) be the first derivative of -1/2*a**3 + 1/8*a**6 - 4 + 0*a + x*a**5 - 3/8*a**2 + 0*a**4. Factor i(p).
3*p*(p - 1)*(p + 1)**3/4
Let f be (2 - (-640)/(-45)) + (-4)/(-18). Let m be 20/48 - 4/f. Let -m + 3/4*k - 3/4*k**3 + 3/4*k**2 = 0. Calculate k.
-1, 1
Let o(n) be the first derivative of 135*n**4/4 + 60*n**3 + 40*n**2 + 9*n - 16. Let a(c) be the first derivative of o(c). Factor a(p).
5*(9*p + 4)**2
Solve -115*y + 21*y - 26*y - 125 + 5*y**2 = 0.
-1, 25
Let n(t) = t**3 - 2*t**2 - t - 4. Let d(g) = 33*g**3 - 89*g**2 + 36*g - 16. Let j(k) = -d(k) + 6*n(k). Factor j(h).
-(h - 2)*(h - 1)*(27*h + 4)
Suppose -2*k + 27 = -3*p + 4, -2*p = 4*k - 22. Let x(l) be the second derivative of -3/10*l**6 + 21/20*l**5 - 2*l**3 + 0 + 0*l**4 - k*l + 0*l**2. Factor x(b).
-3*b*(b - 2)*(b - 1)*(3*b + 2)
Let c(k) be the third derivative of k**7/315 - 37*k**6/540 + 43*k**5/270 + 13*k**4/108 - 22*k**3/27 - 317*k**2. Find o such that c(o) = 0.
-2/3, 1, 11
Let v(n) = -2*n**4 - 11*n**3 - 5. Let o(h) = h**4 + h**3 + 1. Let f(y) = 5*o(y) + v(y). Factor f(g).
3*g**3*(g - 2)
Solve 0 - 2/5*u**5 + 6/5*u**3 + 8/5*u - 16/5*u**2 + 4/5*u**4 = 0.
-2, 0, 1, 2
Let n(f) be the second derivative of 5*f**7/42 + f**6/3 - 3*f**5/4 - 5*f**4/3 + 10*f**3/3 - 12*f + 3. What is s in n(s) = 0?
-2, 0, 1
Let k(q) be the third derivative of q**7/252 - 7*q**6/180 + 2*q**5/15 - q**4/9 + q**3 - 8*q**2. Let z(j) be the first derivative of k(j). Factor z(x).
2*(x - 2)**2*(5*x - 1)/3
Let y(q) be the second derivative of 0 + 2/15*q**6 + 3/20*q**5 - 1/12*q**4 - 3*q + 0*q**2 + 0*q**3. What is t in y(t) = 0?
-1, 0, 1/4
Suppose -38 + 76 = 19*n. Factor -3*h + 12/5*h**n - 3/5*h**3 + 6/5.
-3*(h - 2)*(h - 1)**2/5
Let f = -358/5 - 2326/15. Let v = -226 - f. Let -1/3 + v*w - 1/3*w**2 = 0. What is w?
1
Solve 62/7*g - 8 - 2/7*g**3 - 4/7*g**2 = 0.
-7, 1, 4
Let q(x) be the first derivative of 0*x**4 - 1/20*x**5 - 1/180*x**6 + 0*x**2 + 0*x - 1/3*x**3 - 4. Let r(a) be the third derivative of q(a). Factor r(y).
-2*y*(y + 3)
Solve -12*z**3 - 13419/4*z**4 - 12 + 390*z**2 + 12*z - 11907/4*z**5 = 0.
-1, -2/7, 2/9
Let c = -15 - -1. Let n be (-4)/c - (706/(-126) + 5). Factor n*x**2 + 2/9*x**3 + 0 + 8/9*x.
2*x*(x + 2)**2/9
Solve 17*q**3 + 8*q + 36*q**3 - 25*q**3 + 16*q**2 - 7*q**2 + 19*q**2 + 8*q**4 = 0.
-2, -1, -1/2, 0
Let y(k) be the second derivative of -k**7/840 - k**6/30 - 2*k**5/5 - 5*k**4/3 - 21*k. Let t(u) be the third derivative of y(u). Factor t(a).
-3*(a + 4)**2
Suppose -4*g - 8 = 3*w, -5*g - 2 = 3*w - 4*g. Let p be w/(-1) + (-6)/(-24). Solve -p*x**2 + 0 + 1/2*x = 0 for x.
0, 2
Solve 8/9*x**2 - 44/9*x**3 + 10/9*x**5 + 4/9*x**4 - 28/9 + 50/9*x = 0 for x.
-2, -7/5, 1
Let w(q) be the third derivative of q**7/1155 + q**6/660 - q**5/165 - 230*q**2. Solve w(k) = 0 for k.
-2, 0, 1
Let t(y) be the first derivative of -y**4/2 - 38*y**3/3 - 99*y**2 - 162*y + 136. Determine c, given that t(c) = 0.
-9, -1
Let u(t) = -4*t + 50. Let q be u(12). Suppose 0 = 5*j + 3*w - 9, -4*j + 10 = q*w - w. Factor 5/2*d**2 + 0 + d + 1/2*d**4 + 2*d**j.
d*(d + 1)**2*(d + 2)/2
Let b = -38 + 44. Let m = 0 + 2. Suppose 0*d**m - 4 - d**2 - b*d**2 - 20*d + 9*d**3 = 0. What is d?
-1, -2/9, 2
Let x(u) be the first derivative of 3*u**5 + 3*u**4 - 4*u**3 - 2 + 0*u**2 + 0*u - 3/2*u**6. Solve x(l) = 0.
-1, 0, 2/3, 2
Let n(k) be the second derivative of k**4/6 - 10*k**3/3 - 11*k**2 - 2*k - 16. Solve n(p) = 0.
-1, 11
Let u(l) be the second derivative of -2/3*l**4 + 8/3*l**3 + 0 - l + 1/15*l**5 - 5/2*l**2. Let r(q) be the first derivative of u(q). Solve r(f) = 0 for f.
2
Let y(r) be the second derivative of -r**4/24 - 19*r**3/6 - 361*r**2/4 + 5*r - 79. Suppose y(z) = 0. Calculate z.
-19
Let s(v) = v**3 - 5*v**2 + 6*v - 3. Let o be s(4). Suppose -5*a - 4*f = -o*f - 9, -2*a = 4*f - 8. Factor 6*d + 6*d**a - 5*d**3 - 3*d + d**3 + d**3 - 6*d**4.
-3*d*(d - 1)*(d + 1)*(2*d + 1)
Let t = 1/255 - -1/34. Let u(a) be the second derivative of -1/27*a**3 + 1/135*a**6 + 0 - t*a**5 + 6*a + 1/18*a**4 + 0*a**2. What is c in u(c) = 0?
0, 1
Suppose -9*z = -223 + 205. Let t(b) be the third derivative of -1/10*b**5 - 1/24*b**4 + 0 - 2/105*b**7 + 0*b**3 + 5*b**z + 0*b - 3/40*b**6. Factor t(x).
-x*(x + 1)**2*(4*x + 1)
Let h(r) be the first derivative of -3*r**5/10 - 3*r**4/8 + r**3 + 273. Determine v so that h(v) = 0.
-2, 0, 1
Factor 86/5*v**3 - 176*v**2 + 0 - 2/5*v**4 - 968/5*v.
-2*v*(v - 22)**2*(v + 1)/5
Let f(v) be the second derivative of 3*v**5/100 - 3*v**4/5 + 70*v. Factor f(n).
3*n**2*(n - 12)/5
Suppose 0 = 5*o - r - 8 - 20, 2*o + 5*r + 5 = 0. Suppose 0 = -4*d + 6*d - o*b - 4, 0 = d + 5*b - 2. Factor -1/6*c**d - 1/6 - 1/3*c.
-(c + 1)**2/6
Let q be (-6)/9 + 403/(-3). Let t be ((-9)/(-5))/((-54)/q). Solve -t*s + 9/2*s**2 + 3/2 - 3/2*s**3 = 0.
1
Let l(c) be the second derivative of 7*c**6/720 - c**5/48 - c**4/24 + 4*c**3/3 - 29*c. Let r(m) be the second derivative of l(m). Suppose r(p) = 0. What is p?
-2/7, 1
Solve 23/4*i**3 + 7/4*i**4 + 5/2 + 17/4*i - 57/4*i**2 = 0 for i.
-5, -2/7, 1
Let -s + 3*s**3 - 6 - 6*s**2 - 13*s - 7*s - 6 = 0. Calculate s.
-1, 4
Suppose 9 - 24 = -3*l. Let i(v) = -l*v**2 + 25 - 25 + 14*v. Let z(h) = -2*h**2 + 5*h. Let j(c) = 3*i(c) - 8*z(c). What is r in j(r) = 0?
-2, 0
Let f = -302 + 434. Let g be f/(-36) - (-2 + -2*1). Solve 1/6*a**4 + 1/6*a**2 + 0 + 0*a - g*a**3 = 0.
0, 1
Let b = -9917/12 + 828. Let t(z) be the first derivative of 3/20*z**5 - 13/16*z**4 + b*z**3 + 1/2*z - 11/8*z**2 + 1. Factor t(r).
(r - 2)*(r - 1)**2*(3*r - 1)/4
Let s(r) = 9*r**3 + 3*r - 2. Let v be s(1). Let 4*g - 2/5*g**2 - v = 0. Calculate g.
5
Let z be -4 + (-5)/((-20)/(-12)) + 4. Let m be (-3)/(-9) - z*4/(-144). Suppose 1/2*f**3 - 1/4*f**4 - 1/4*f + 1/2*f**2 - 1/4 - m*f**5 = 0. What is f?
-1, 1
Let 39/4*n**3 + 9 - 51*n - 201/4*n**2 = 0. What is n?
-1, 2/13, 6
Let h(a) be the third derivative of a**6/240 - a**5/20 + a**4/4 + 7*a**3/3 - 12*a**2. Let u(x) be the first derivative of h(x). Factor u(s).
3*(s - 2)**2/2
Let m = 2389 - 2387. What is s in 6/5*s**3 + 3/5*s**m + 0 + 3/5*s**4 + 0*s = 0?
-1, 0
Suppose -168 = -12*l + 84. Let s be 1/((-7)/l - 10/(-12)). Determine y so that y + 1/2*y**s + 1/2 = 0.
-1
Let j(r) = 2*r**2 + 13*r + 7. Let g be j(-6). Let x(d) be the first derivative of -4*d**2 - g + 2/3*d**3 + 6*d. Determine l so that x(l) = 0.
1, 3
Let r(w) be the third derivative of 0 - w**2 - 1/60*w**6 + 0*w + 1/30*w**5 - 1/105*w**7 + 0*w**3 + 1/12*w**4. Factor r(l).
-2*l*(l - 1)*(l + 1)**2
Let n(j) be the second derivative of j**5/5 + 11*j**4/6 + 4*j**3/3 - 5*j**2 - 21*j - 2. Find x, given that n(x) = 0.
-5, -1, 1/2
Let m = -3 - -38. Let f(k) = k**5 + 6*k**4 + 4*k**3 - 6*k**2 + 2*k. Let b(d) = -d**4 - d**3 + d**2. Let w(p) = m*b(p) + 5*f(p). Let w(u) = 0. Calculate u.
-1, 0, 1, 2
Let p(q) be the first derivative of q**6/6 + q**5/5 - 2*q**4 - 8*q**3/3 + 8*q**2 + 16*q - 152. Factor p(m).
(m - 2)**2*(m + 1)*(m + 2)**2
Let d(s) = 3*s**2 + 29*s - 27. Let v(g) = 2*g**2 + 15*g - 14. Suppose -6 = -4*l - 26. Let o(r) = l*v(r) + 3*d(r). Factor o(z).
-(z - 11)*(z - 1)
Let g(q) = -12*q**4 - 64*q**3 - 122*q**2 - 44*q + 18. Let u(d) = 2*d**4 + d**3 + d**2 - d + 1. Let l(r) = -g(r) - 2*u(r). Find c such that l(c) = 0.
-5, -2, -1, 1/4
Let v = 442801/240 - 1845. Let u(l) be the third derivative of 0*l**3 + 1/120*l**5 - 9*l**2 + 0 + 0*l + 0*l**4 - v*l**6. Factor u(o).
-o**2*(o - 1)/2
Suppose -2*l - f = -13, 5*f - 62 = 2*l - 105. Let i(k) be the third derivative of -1/480*k**6 - l*k**2 + 0 + 0*k**3 + 1/60*k**5 + 0*k - 1/24*k**4. Factor i(b).
-b*(b - 2)**2/4
Let v(b) be the first derivative of 5*b**4/2 - 25*b**3 + 45*b**2 - 188. Factor v(d).
5*d*(d - 6)*(2*d - 3)
Let c(j) = -j**4 - 2*j**3 - j**2. Let v(x) = -2*x**4 - 3*x**3 - 3*x**2 - 4*x. Let r(i) = -6*c(i) + 2*v(i). Factor r(w).
2*w*(w - 1)*(w + 2)**2
Let k be ((-34)/(-18))/(-1)*1890/(-180). Let f = -1297/66 + k. Let 0 + 0*j + 0*j**2 - f*j**3 + 0*j**4 + 2/11*j**5 = 0. Calculate j.
-1, 0, 1
Let z(k) be the second derivative of -k**5/8 + k**4/8 + k**3/6 - 297*k. Factor z(l).
-l*(l - 1)*(5*l + 2)/2
Let d be -3 + (-6)/2*(1 - 3). Let o be d/2*(-9)/(-54). Determine z, given that 0*z**2 + o*z + 0 - 1/4*z**3 = 0.
-1, 0, 1
Solve 6 + 2*k**4 - 4*k**2 + 2*k*