, 1
Let x(a) be the second derivative of a**5/210 - a**4/28 + 2*a**3/21 - a**2/2 + 4*a. Let w(m) be the first derivative of x(m). Suppose w(o) = 0. Calculate o.
1, 2
Let t(o) be the third derivative of o**6/30 + 7*o**5/15 - o**4/6 - 14*o**3/3 + 138*o**2. Let t(w) = 0. What is w?
-7, -1, 1
Let t = -14 + 16. Suppose -4 = -3*r + 4*a, 4*a = -r + t*a + 8. Factor -2/3 - 1/3*o**3 + 1/3*o - 1/3*o**r + o**2.
-(o - 1)**2*(o + 1)*(o + 2)/3
Suppose 8*t - 3*w - 57 = 4*t, 2*w - 17 = -t. Let p = t - 13. Factor 2/5*c**p + 0 - 4/5*c.
2*c*(c - 2)/5
Let p(g) be the second derivative of -g**7/147 + 4*g**6/105 - g**5/14 + g**4/21 - 570*g. Factor p(u).
-2*u**2*(u - 2)*(u - 1)**2/7
Let l = 36 - 31. Factor 2*b**2 + b - 7 + 11 + l*b.
2*(b + 1)*(b + 2)
Factor 22/3*h**2 + 0 - 121/3*h - 1/3*h**3.
-h*(h - 11)**2/3
Let j(r) be the second derivative of -1/2*r**3 + 7*r + 1/5*r**5 + 1/6*r**4 + 0 - r**2 + 0*r**6 - 1/42*r**7. Find k, given that j(k) = 0.
-1, 1, 2
Let r = 56 + -56. Let t(m) be the first derivative of -2/27*m**3 - 1/9*m**2 + 2 + r*m. Let t(k) = 0. What is k?
-1, 0
Let n be -1*254/(-4)*(0 + -2). Let g = n + 130. Suppose 5/2*h**4 + 0 - 10*h**2 + 12*h**g - 25/8*h**5 + 2*h = 0. What is h?
-2, 0, 2/5, 2
Let b(t) be the second derivative of -1/60*t**4 + 0 - 1/150*t**6 + 0*t**3 - 21*t + 1/50*t**5 + 0*t**2. Factor b(r).
-r**2*(r - 1)**2/5
Let c(q) be the first derivative of q**6/42 + 12*q**5/35 + 53*q**4/28 + 106*q**3/21 + 48*q**2/7 + 32*q/7 - 94. Let c(z) = 0. What is z?
-4, -2, -1
Let q(c) = -c**5 + 4*c**4 - 20*c**2 - 17*c. Let a(y) = 3*y**5 - 11*y**4 + 59*y**2 + 52*y. Let u(m) = 4*a(m) + 14*q(m). Find x such that u(x) = 0.
-1, 0, 3, 5
Suppose 11 = 5*h + 4*u, -11*u + 8*u = -4*h + 15. Solve -3/4*t**h + 0 - 21/8*t**2 + 3/8*t**4 - 3/2*t = 0.
-1, 0, 4
Let d(t) = t**3 + 14*t**2 + 14*t - 118. Let l be d(-12). Factor 2/11*n**3 - 2/11*n**l + 0 + 2/11*n**4 - 2/11*n.
2*n*(n - 1)*(n + 1)**2/11
Let h = 0 - -4. Suppose -h*m = -23 + 3. Let 2*i + 12*i**3 + 8*i**4 - 18*i**2 - 11*i**m + 8*i**2 - 5*i**5 = 0. Calculate i.
-1, 0, 1/2
Let l(f) = f**2 - 13*f + 14. Let q be l(12). Suppose -q*o = -3 - 3. Factor -3*k**5 - 3*k**2 - 6*k**4 + 3*k**2 + 0*k**5 - 3*k**o.
-3*k**3*(k + 1)**2
Let o(q) = 2 - 10*q**2 - 3*q - 15*q + 7*q**2 + q**2. Let i be o(-9). Let 2/3*h**3 + 0 + 4/3*h**i - 2/3*h**4 + 0*h = 0. What is h?
-1, 0, 2
Let t(a) = -12*a**5 + 4*a**4 + 30*a**3 + 4*a**2 - 14*a + 2. Let h(w) = -w**5 - w**4 + w**2 - w + 1. Let o(s) = -2*h(s) + t(s). Solve o(l) = 0.
-1, 0, 3/5, 2
Solve 5/4*v**3 + v + 0 + 2*v**2 + 1/4*v**4 = 0 for v.
-2, -1, 0
Let q(a) be the first derivative of a**6/3 - 8*a**5/5 + 5*a**4/2 - 4*a**3/3 - 257. Suppose q(f) = 0. What is f?
0, 1, 2
Let o = 4397/22010 + 1/4402. Factor 9/5*u**2 - 11/5*u**3 - o - 1/5*u + 4/5*u**4.
(u - 1)**3*(4*u + 1)/5
Solve 3*o**3 + 3/2*o**4 + 0 - 3/2*o**2 - 3*o = 0 for o.
-2, -1, 0, 1
What is i in 0 + 84/5*i**2 + 3/5*i**4 + 0*i - 87/5*i**3 = 0?
0, 1, 28
Let o be 204/(-255) + 8/10. Let x(y) be the third derivative of 0*y + 0*y**3 - 6*y**2 - 1/4*y**4 - 1/20*y**5 + o. Suppose x(w) = 0. Calculate w.
-2, 0
Factor 0 + 68/7*h**4 + 24*h**3 + 6/7*h**5 + 0*h - 144/7*h**2.
2*h**2*(h + 6)**2*(3*h - 2)/7
Let y = 4155 - 4151. Factor 0*o**y + 3/5*o + 1/5*o**5 - 2/5 + 2/5*o**2 - 4/5*o**3.
(o - 1)**3*(o + 1)*(o + 2)/5
Let v(i) be the third derivative of -i**8/224 + 3*i**6/80 + i**5/20 + 14*i**2. Factor v(o).
-3*o**2*(o - 2)*(o + 1)**2/2
Let h(r) = 5*r**3 - 3*r**2 - 6. Let b(n) = -11*n**3 + 6*n**2 + 13. Let i(w) = -4*b(w) - 9*h(w). Let g be i(3). Factor 1 + 6*k + 5 + 2*k**2 - 2*k - 4*k**g.
-2*(k - 3)*(k + 1)
Let j be (0/((-4)/(-4) + -2))/(-2). Factor 3*b - b**2 - 8 + j*b - 3*b - 6*b.
-(b + 2)*(b + 4)
Let p(j) be the first derivative of j**6/1080 - 2*j**5/45 + 8*j**4/9 + 7*j**3/3 - j**2/2 - 38. Let i(u) be the third derivative of p(u). Factor i(x).
(x - 8)**2/3
Let b = -89/21 - -30/7. Let h(x) be the third derivative of 0*x - b*x**3 - 1/210*x**5 + 1/42*x**4 + 0 + 3*x**2. Solve h(s) = 0 for s.
1
Determine b so that 0*b**3 - b**3 + 30*b**2 - 80*b - 149*b + 23*b - 19*b = 0.
0, 15
Let a(j) be the third derivative of -1/40*j**6 + 1/60*j**5 + 0*j + 0 + 1/112*j**8 + 0*j**3 + 0*j**4 - 1/210*j**7 + 12*j**2. Suppose a(u) = 0. Calculate u.
-1, 0, 1/3, 1
Let q = 661/1640 - 1/328. Let p(g) be the first derivative of 1/10*g**2 + 4/5*g**3 - 3 - 2/25*g**5 - q*g + 1/2*g**4 - 1/10*g**6. Solve p(h) = 0 for h.
-1, 1/3, 2
Suppose 10 + 29 = 13*f. Let p(t) be the first derivative of 13*t**f + 69/5*t**5 + 81/4*t**4 + 0*t + 3*t**2 + 7/2*t**6 + 6. Factor p(l).
3*l*(l + 1)**3*(7*l + 2)
Suppose -6*v = -2*v. Let l(k) = k**2 + 2*k - k + 2 + 2*k**2 + v. Let j(m) = -3*m**2 - 3. Let d(i) = 2*j(i) + 3*l(i). Factor d(w).
3*w*(w + 1)
Let n(g) = 4*g**3 - 139*g**2 - 186*g + 220. Let t be n(36). Solve -12/7*r**t + 0 - 22/7*r**3 + 6/7*r**2 + 4/7*r = 0 for r.
-2, -1/3, 0, 1/2
Let m(h) be the first derivative of 2*h**6/3 - 24*h**5/5 + 8*h**4 + 91. Factor m(d).
4*d**3*(d - 4)*(d - 2)
Find r such that 15/4*r + 1/4*r**2 + 11 = 0.
-11, -4
Let i = -22 + 26. Let b be 10/(i/2) - (-16)/(-8). Factor 0 + 1/2*n + 3*n**b + 1/2*n**5 + 2*n**2 + 2*n**4.
n*(n + 1)**4/2
Let k(v) = v**3 + 5*v**2 - 13*v - 36. Let s be k(-6). Let x(f) = 4*f**2 + 22*f - 32. Let z(l) = 3*l**2 + 21*l - 32. Let y(i) = s*z(i) - 5*x(i). Factor y(p).
-2*(p - 4)**2
Factor -111*i**2 + 38*i**2 + 45*i**2 + 43*i**2 + 3*i**3.
3*i**2*(i + 5)
Let b(h) = 71*h - 2341. Let m be b(33). Determine j so that -8/3*j + 0 - 4/3*j**m = 0.
-2, 0
Factor -1/6*u**4 - 2/3*u**3 - 5/6*u**2 + 0 - 1/3*u.
-u*(u + 1)**2*(u + 2)/6
Let j = 1/5 + -3/16. Let x(f) be the second derivative of -1/12*f**3 + 6*f - 1/16*f**4 + 0*f**2 + 0 - j*f**5. Determine k, given that x(k) = 0.
-2, -1, 0
Factor 1 + 9/2*k**3 - 9/2*k - k**2.
(k - 1)*(k + 1)*(9*k - 2)/2
Let p(u) be the third derivative of -1/8*u**6 + 0 + 0*u**3 + 1/6*u**5 + 0*u**4 + 1/42*u**7 - 14*u**2 + 0*u. Factor p(m).
5*m**2*(m - 2)*(m - 1)
Let c(j) = 60*j**2 - 62*j**2 + 16*j + 40 + 5*j. Let r be c(12). Find n, given that 0*n**2 + 0 - 9/4*n**3 + 3*n + 3/4*n**r = 0.
-1, 0, 2
Let f(t) be the second derivative of -25*t - 1/33*t**3 - 1/66*t**4 + 0 + 2/11*t**2. Solve f(d) = 0 for d.
-2, 1
Let h = -71 - -55. Let l be -2*(4/1)/h. What is y in 1/2*y - 1/2*y**2 + 1/2 - l*y**3 = 0?
-1, 1
Let -54 + 56*s - 7*s**2 + 22*s**2 - 4*s**2 - 13*s**2 = 0. What is s?
1, 27
Let h(w) be the third derivative of -w**6/300 + w**5/15 - 3*w**4/20 + 8*w**2 - 15*w. Factor h(s).
-2*s*(s - 9)*(s - 1)/5
Let k(b) be the second derivative of 1/4*b**4 + 3/2*b**3 + 2*b + 0 + 3*b**2. Factor k(h).
3*(h + 1)*(h + 2)
Let s(t) be the first derivative of -2*t**5/45 + t**4/3 - 16*t**3/27 - 2*t**2/3 + 2*t - 56. What is m in s(m) = 0?
-1, 1, 3
Let z(k) be the second derivative of k**4/48 + k**3/4 - 39*k. Let z(b) = 0. Calculate b.
-6, 0
Let x(a) be the first derivative of -3*a**5/5 + 12*a**4 - 28*a**3 - 112. Find z such that x(z) = 0.
0, 2, 14
Solve 40/13*l + 8/13*l**3 - 8/13 - 34/13*l**2 = 0.
1/4, 2
Let o(a) be the first derivative of -a**7/210 - a**6/45 - 11*a**3/3 + 1. Let u(s) be the third derivative of o(s). Find z such that u(z) = 0.
-2, 0
Let p be 0 + -1*(-31)/1. Suppose 17 = n - 3*c, 0 = -n + 5*c + p - 4. Let 11*d**2 + 7*d**2 - 2*d - 3*d**n - 4*d**2 = 0. Calculate d.
0, 2/11
Suppose 318 - 132 = 6*w. Let l = w - 181/6. Factor 0*m + 1/6*m**5 + 4/3*m**3 + 0 + 2/3*m**2 + l*m**4.
m**2*(m + 1)*(m + 2)**2/6
Let n(v) be the third derivative of -1/540*v**6 - 2/3*v**3 + 0*v**4 + 1/90*v**5 + 0 + 0*v + 3*v**2. Let i(k) be the first derivative of n(k). Factor i(c).
-2*c*(c - 2)/3
Let x = 143 - 139. Let b(p) be the second derivative of 1/20*p**5 - 3*p + 0 + 1/6*p**x + 0*p**2 + 1/6*p**3. Factor b(t).
t*(t + 1)**2
Let x(k) = -k + 4. Let a be x(-3). Let f be 2/3*(-5 + 8). Factor -2*g**f - 10*g**4 + a*g**3 + 0*g**4 - g**3 + 4*g**4 + 2*g**5.
2*g**2*(g - 1)**3
Let r(s) be the second derivative of -s**7/70 - 3*s**6/25 + 11*s**4/10 - 3*s**3/2 + 474*s. Solve r(u) = 0 for u.
-5, -3, 0, 1
Suppose 1 = 4*l - 11, -141 = -x + 4*l. Let n be 10/(-6) + x/27. Let 0*z + 0 + 2*z**n + 2*z**3 + 2/3*z**2 + 2/3*z**5 = 0. What is z?
-1, 0
Suppose 0 = -4*g - 5*n + 40, -3*g - 7 = -2*g - 3*n. Suppose -6*l + g*l + 8 = 0. Factor 2*q**3 - 17*q + 11*q + 4*q**2 + l*q.
2*q*(q + 1)**2
Let u(l) be the second derivative of l**