, 1
Let a(d) be the second derivative of d**6/480 - d**5/80 - 29*d**3/6 - 14*d. Let i(l) be the second derivative of a(l). Suppose i(b) = 0. Calculate b.
0, 2
Suppose 0 = 5*b + 2*d - 8, -b - 2*d - 3305 + 3313 = 0. Factor -5/3*p**4 + 10*p**3 + 0 - 25/3*p**2 + b*p.
-5*p**2*(p - 5)*(p - 1)/3
Let w(i) be the third derivative of -i**5/45 + 5*i**4/18 - 4*i**3/3 + 5*i**2 - 2. Factor w(s).
-4*(s - 3)*(s - 2)/3
Let o = -51 - -52. Let y = 7/4 - o. Factor 0 + 3/4*k**2 - y*k.
3*k*(k - 1)/4
Let s = -1 - -5. Let d be (-1 - -2)/((-5)/(-35)). Determine p so that -s*p**3 + d*p**4 + 4*p**4 - 3*p**4 - 4*p**5 = 0.
0, 1
Let l(s) be the first derivative of s**6/180 - 2*s**5/45 + s**4/12 + 8*s**2 - 18. Let g(w) be the second derivative of l(w). Solve g(h) = 0.
0, 1, 3
Let i(g) = -2*g**2 + 11*g + 16. Let h(o) = -16 - 8*o**2 - 10*o + 27*o**2 - 10*o**2 - 8*o**2. Let x(a) = -3*h(a) - 2*i(a). Find r such that x(r) = 0.
-4
Let x be -1 + 9 + (81 - 88). Factor x + 3/4*y - 1/4*y**2.
-(y - 4)*(y + 1)/4
Let o(y) be the second derivative of -2*y**5/15 + 5*y**4/36 + y**3/3 - 11*y**2 + 17*y. Let i(m) be the first derivative of o(m). Find u such that i(u) = 0.
-1/3, 3/4
Let o = 11388 - 11388. Determine y so that 0 + 6/11*y**2 + 4/11*y + o*y**3 - 2/11*y**4 = 0.
-1, 0, 2
Suppose 4 - 12 = n. Let h be (-30)/(-8) + (-2)/n. Find s such that -21 - 4*s - s**3 + 17 + h*s**3 + 5*s**2 = 0.
-2, -2/3, 1
Let g(z) = -24*z + 52. Let r(a) = a. Let k(v) = g(v) + 20*r(v). Let y be k(13). Determine q so that y*q + 0 - 2/9*q**3 - 2/9*q**4 + 2/9*q**5 + 2/9*q**2 = 0.
-1, 0, 1
Let h(l) be the second derivative of -l**4/6 - 20*l**3 - 900*l**2 - 3*l + 21. Factor h(k).
-2*(k + 30)**2
Let u be 4/(-1) + 3 + 4. Let c = 5 - u. Factor 27*f - 7*f - 20*f**4 - 60*f**c + 55*f**3 + 5*f**4.
-5*f*(f - 2)*(f - 1)*(3*f - 2)
Let y(x) be the second derivative of -x**4/84 + x**3/42 + 3*x**2/7 + x + 151. Factor y(j).
-(j - 3)*(j + 2)/7
Let n(s) = -2*s. Let h(x) = 2*x**3 + 26*x**2 - 6*x - 26. Let i(c) = -h(c) + 2*n(c). Factor i(d).
-2*(d - 1)*(d + 1)*(d + 13)
Let x(u) = -4*u - 2. Suppose -b - 7 = 2*d, -d - 23 = -3*d + 5*b. Let z be x(d). Solve 3 + 0 + 7*k - 13*k + 3*k**z = 0 for k.
1
Let w(u) be the second derivative of u**5/170 + 41*u**4/102 - 4*u**3/51 - 164*u**2/17 + 9*u - 2. Factor w(v).
2*(v - 2)*(v + 2)*(v + 41)/17
Let q(o) be the first derivative of 25 + 1/8*o**6 + 3/16*o**4 + 0*o + 7/20*o**5 - 1/4*o**3 - 1/4*o**2. Factor q(r).
r*(r + 1)**3*(3*r - 2)/4
Let f(x) be the second derivative of 3*x + 0 - 5/2*x**2 + 1/15*x**6 - 2/3*x**3 - 3/4*x**4 - 1/10*x**5. Let t(u) be the first derivative of f(u). Factor t(r).
2*(r - 2)*(r + 1)*(4*r + 1)
Suppose -3*o - 24 = -303. Suppose 146 + 38 = 4*b + 4*h, -3*h + o = 2*b. Factor -11*v**2 - 10 - 16*v**2 + b*v - 9*v - 2.
-3*(3*v - 2)**2
Factor -41*b + 57 + 15*b**2 - b**2 - 2*b**3 + 13*b - 41.
-2*(b - 4)*(b - 2)*(b - 1)
Let q(n) be the third derivative of n**8/336 + n**7/35 + n**6/15 - 176*n**2 + 3. Factor q(y).
y**3*(y + 2)*(y + 4)
Factor 7*d**2 - 11 - 35*d + d**2 - 3*d**2 + 41.
5*(d - 6)*(d - 1)
Let w(d) be the first derivative of -2*d**6/11 - 2*d**5/5 + d**4/22 + 4*d**3/11 - 65. Find l such that w(l) = 0.
-3/2, -1, 0, 2/3
Let h(q) be the third derivative of 0*q - 4/135*q**5 + 1/180*q**6 - 5/36*q**4 + 0 + 20*q**2 - 4/27*q**3. Find f, given that h(f) = 0.
-1, -1/3, 4
Suppose -11*d**2 + 20 + 3*d - 12*d + 16*d**2 - 20*d + 4*d = 0. What is d?
1, 4
Let r(h) be the second derivative of 2*h + 2/21*h**3 - 8 + 1/42*h**4 + 0*h**2. Factor r(s).
2*s*(s + 2)/7
Let o(u) be the third derivative of 20/3*u**3 + 1/8*u**6 - 11*u**2 + 0*u - 5/6*u**5 + 0 + 5/6*u**4. Factor o(q).
5*(q - 2)**2*(3*q + 2)
Let t(v) = -2*v**2 - 2*v + 3. Let b(l) = 2*l**2 + 3*l + 1. Let k(f) = f**2 + f. Let z(q) = b(q) - 3*k(q). Let m(x) = 2*t(x) - 6*z(x). Factor m(u).
2*u*(u - 2)
Let q be (-1)/((-22)/30 - 6/(-15)). Determine g, given that -10*g**q + 25 - 25*g**2 - 7*g + 2*g + 15*g**3 = 0.
-1, 1, 5
Let h = 268 + -2137/8. Let u(r) be the first derivative of 1/2*r**2 + 5/6*r**3 + 0*r - h*r**4 - 4. Determine m so that u(m) = 0.
-2/7, 0, 1
Suppose -c = 5*i - 9, 0*i + c = -2*i + 3. Find a such that -90*a**2 + 8 - 28*a - 4*a**3 + 70*a**i + 20*a**3 = 0.
-1, 1/4, 2
Let i(j) be the third derivative of 0*j + 0*j**3 + 1/48*j**5 + 1/24*j**4 - 7/480*j**6 + 0 - 29*j**2 - 1/420*j**7. Factor i(l).
-l*(l - 1)*(l + 4)*(2*l + 1)/4
Let o(m) = -m**3 + 22*m**2 + 29*m + 4. Let j(s) = 2*s**3 - 42*s**2 - 59*s - 10. Let f(z) = -6*j(z) - 15*o(z). Factor f(p).
3*p*(p - 27)*(p + 1)
Let m(l) be the third derivative of -l**8/2856 + l**6/510 - l**4/204 + 62*l**2. Find p, given that m(p) = 0.
-1, 0, 1
Let k = -32 - -33. Let y be (k/(-7))/((-12)/(-21) + -1). Factor -2/3 - y*d**2 + d.
-(d - 2)*(d - 1)/3
Suppose -5*i + 1035 = -5*l, -2*l - 386 = -i + 6*i. Let h = l - -203. Determine q so that 4/13*q + h + 2/13*q**2 + 2/13*q**5 - 6/13*q**3 - 2/13*q**4 = 0.
-1, 0, 1, 2
Suppose -5*g - 5*g = -30. Suppose 2 = c + 3*t, -g*c - 3*t + 4 = -c. Determine o, given that 2/5*o + 0 + 0*o**c - 2/5*o**3 = 0.
-1, 0, 1
Suppose 0 = 2*n - 6*n + 400. Determine s so that -n*s**4 + 12*s**3 - 8*s + 54*s**3 + 8*s**2 - 8*s**2 + 42*s**5 = 0.
-2/7, 0, 2/3, 1
Let g(z) be the third derivative of z**8/5040 + z**7/1260 - z**6/90 + 7*z**5/60 - 15*z**2. Let i(u) be the third derivative of g(u). Let i(w) = 0. What is w?
-2, 1
Suppose 48 = -7*d - 15. Let h = d - -14. Find u, given that -1/4*u**4 + 0*u**2 + 1/4*u**h + 0 + 0*u + 0*u**3 = 0.
0, 1
Let i(f) = -f**4 + 3*f**3 - f**2 + 5. Let k(n) = -2*n**4 + 10*n**3 - 2*n**2 + 14. Suppose -2*o + 7*o = 25. Let u(x) = o*k(x) - 14*i(x). Let u(m) = 0. What is m?
-1, 0
Suppose 13*l - 19*l = 84. Let v be (0 - 3)*l/56. Factor 9/4*f**2 + v*f**4 + 3*f**3 - 3*f - 3.
3*(f - 1)*(f + 1)*(f + 2)**2/4
Let v(w) be the third derivative of -2/35*w**7 + 1/15*w**6 + 2/15*w**5 - 1/2*w**4 + 1/84*w**8 + 0*w + 2/3*w**3 + 0 + w**2. Suppose v(i) = 0. What is i?
-1, 1
Let t(y) be the first derivative of y**3/3 + 7*y**2/2 + 10*y + 80. Factor t(s).
(s + 2)*(s + 5)
Let t be (1/3 - 48/36)*(-1410)/329. Factor -9/7*f**2 - t*f - 9/7.
-3*(f + 3)*(3*f + 1)/7
Let d(t) be the third derivative of t**8/1680 - t**7/210 - t**6/200 + 3*t**5/20 - 9*t**4/20 + 4*t**2 - 60. Factor d(b).
b*(b - 3)**2*(b - 2)*(b + 3)/5
Let y(w) be the first derivative of -3*w**5/5 + 27*w**4/2 - 108*w**3 + 357*w**2 - 441*w + 29. Factor y(h).
-3*(h - 7)**2*(h - 3)*(h - 1)
Suppose -6*d = -3*d - 15. Solve -28*b**5 + 9*b**d + 16*b**5 + 6*b**4 = 0.
0, 2
Suppose 0 = -4*z + 2*v - 238, 4*z + 241 = -3*v + 8*v. Let b = z - -61. Factor 0 - 1/5*r**b + 1/5*r.
-r*(r - 1)/5
Let y(p) be the third derivative of -1/120*p**6 + 0*p**3 + 0 + 1/120*p**5 + 16*p**2 + 1/24*p**4 - 1/420*p**7 + 0*p. Determine g so that y(g) = 0.
-2, -1, 0, 1
Let b(u) be the second derivative of -17*u - 7/6*u**2 + 0 + 1/36*u**4 - 1/3*u**3. Let b(j) = 0. Calculate j.
-1, 7
Let d(y) be the first derivative of -1/150*y**5 + 0*y + 1/75*y**6 + 1/15*y**3 - 5*y**2 - 1/15*y**4 - 12. Let g(l) be the second derivative of d(l). Factor g(n).
2*(n - 1)*(n + 1)*(4*n - 1)/5
Let p(l) = -l**2 - 8*l - 7. Let o be p(-6). Factor 3*n**2 + n**4 + 5*n - 2*n**3 + o*n**3 - 4*n + 0*n**3.
n*(n + 1)**3
Let y = 281 + -13487/48. Let k(r) be the third derivative of 0*r - 1/12*r**3 + 1/240*r**6 + 0 + 1/120*r**5 - y*r**4 + r**2. What is t in k(t) = 0?
-1, 1
Let b(s) be the first derivative of -2*s**3/9 - 4*s**2/3 - 2*s + 55. Find r such that b(r) = 0.
-3, -1
Let y be (-1)/(-3) + 2/(-42). Let w = 17 + -17. Factor w*i - y*i**3 + 0 - 2/7*i**2.
-2*i**2*(i + 1)/7
Determine j so that -82/17 - 84/17*j - 2/17*j**2 = 0.
-41, -1
Let x(w) be the first derivative of w**5/12 - 5*w**3/6 + 13*w**2/2 + 7. Let d(b) be the second derivative of x(b). Factor d(r).
5*(r - 1)*(r + 1)
Suppose -3 - 21 = o. Let g be 2/(-11) + o/(-11). Factor -2*x + 2*x - 5*x**3 + 3*x**g + 3*x**4 - x**3.
3*x**2*(x - 1)**2
Find u, given that 34*u - 784 - 18*u - 10*u + 37*u - u**2 + 13*u = 0.
28
Let q(a) be the first derivative of -5/4*a**4 + 0*a**2 + 0*a + 0*a**3 - 17. Factor q(o).
-5*o**3
Let x = 5354 + -26763/5. Factor -3*p**3 + 0 + 2/5*p + 19/5*p**4 - x*p**5 + 1/5*p**2.
-p*(p - 1)**3*(7*p + 2)/5
Solve 2/23*p**2 + 6/23*p - 36/23 = 0 for p.
-6, 3
Find g, given that 0*g - 1/2*g**3 + 0*g**2 + 0 = 0.
0
Let c(h) be the first derivative of -3*h