
Let l be 108/26 - 6/39. Let y(d) be the third derivative of -1/240*d**5 + 0*d**l + 0*d**3 + 0 - 1/840*d**7 - 1/240*d**6 - 4*d**2 + 0*d. Let y(m) = 0. What is m?
-1, 0
Let s(d) be the second derivative of 1/6*d**4 - 2/3*d**3 + 0*d**2 - 3 - 9*d. Solve s(f) = 0.
0, 2
Suppose 3*d - l - 106 + 100 = 0, -2 = -d - 3*l. Factor -2/21 + 2/21*p**d - 4/21*p + 4/21*p**3.
2*(p - 1)*(p + 1)*(2*p + 1)/21
Let c be (3/9)/(592/222). Let v(u) be the first derivative of -1/4*u**2 + 1/6*u**6 - 1/2*u**3 - 12 + 0*u + 3/10*u**5 - c*u**4. Let v(p) = 0. Calculate p.
-1, -1/2, 0, 1
Let b = -14 + 11. Let i(s) = -8*s**2 - 40*s - 83. Let d(k) = -15*k**2 - 80*k - 165. Let t(f) = b*d(f) + 5*i(f). Factor t(u).
5*(u + 4)**2
Let n(w) = 2*w**2. Let c(j) = -8*j**2 - 8*j - 8. Let s(o) = 2*c(o) + 6*n(o). Factor s(a).
-4*(a + 2)**2
Suppose 4 - 761*r**2 + 4 + 1528*r**2 + 2*r - 768*r**2 = 0. Calculate r.
-2, 4
Let o = -24535 + 221135/9. Let d = o - 106/3. Factor -2/3*x**2 - 2/9*x**3 - 2/3*x - d.
-2*(x + 1)**3/9
Let a(i) be the first derivative of 52 + 0*i + 0*i**3 + 4/5*i**5 + 3*i**4 + 0*i**2. Find o, given that a(o) = 0.
-3, 0
Let j(r) be the first derivative of 6*r + 3/2*r**2 - r**3 - 13. Factor j(l).
-3*(l - 2)*(l + 1)
Let b(c) be the second derivative of c**4/20 + 24*c**3/5 + 864*c**2/5 + 27*c. Solve b(s) = 0 for s.
-24
Let t(w) be the second derivative of -w**7/63 + 2*w**6/15 - w**5/6 - w - 44. Factor t(b).
-2*b**3*(b - 5)*(b - 1)/3
Let q(u) be the first derivative of -3/10*u**5 + 0*u**3 + 0*u**2 + 0*u - 1/8*u**6 - 3 + 9/16*u**4. Factor q(z).
-3*z**3*(z - 1)*(z + 3)/4
Let f(m) = -m**2 - m - 1. Let b(n) = 3*n**2 - 91*n - 1147. Let x(y) = -b(y) - 5*f(y). Factor x(s).
2*(s + 24)**2
Factor 88529281/5 + 56454/5*g**2 + 1/5*g**4 + 388/5*g**3 + 3650692/5*g.
(g + 97)**4/5
Let a = -1697 + 1700. Let w(l) be the second derivative of -3/2*l**4 + 0 + a*l**2 - 3*l + 2/5*l**5 - 10/3*l**3. Factor w(v).
2*(v - 3)*(v + 1)*(4*v - 1)
Let v(b) be the third derivative of 0 + 16*b**2 + 0*b + 1/9*b**4 + 1/108*b**6 - 8/27*b**3 + 1/15*b**5. Factor v(u).
2*(u + 2)**2*(5*u - 2)/9
Let v(f) be the first derivative of 0*f**3 - 30 + 4*f**5 + 0*f**2 + 0*f + 2*f**4 + 25/12*f**6. Solve v(d) = 0 for d.
-4/5, 0
Let m(i) be the third derivative of i**5/140 - i**4/28 + 54*i**2 + i. Factor m(x).
3*x*(x - 2)/7
Let s(h) be the third derivative of -1/6*h**4 + 0*h - 5/6*h**3 + 5*h**2 + 1/10*h**5 + 0 - 1/40*h**6. Let o(v) be the first derivative of s(v). Factor o(y).
-(3*y - 2)**2
Let a be ((-20)/(-100))/(438/72 + -6). Determine j so that -a*j - 1/5*j**2 - 11/5 = 0.
-11, -1
Suppose t - 72 = -3*t. Determine q, given that 28*q**2 - 4*q - t + 28*q - 36*q**2 = 0.
3/2
Suppose 4*u = 10*u - 36. Let v(t) = 2*t - 9. Let l be v(u). Factor l - 2*x + 1/3*x**2.
(x - 3)**2/3
Suppose 179*w = 163*w + 48. Determine u, given that 4/3*u**w + 2/3*u**4 - 2/3*u - 4/3*u**2 - 2/3*u**5 + 2/3 = 0.
-1, 1
Let r(u) = -u**3 - 4*u**2 + 2*u + 5. Let y(i) = -i**2 + 1. Let s(k) = k**2 - k - 10. Let d be s(5). Let a(z) = d*y(z) - 2*r(z). Suppose a(h) = 0. Calculate h.
-1, 0, 2
Let k(s) be the third derivative of s**7/525 + s**6/75 - 2*s**5/25 + 5*s**2 - 2*s. Factor k(o).
2*o**2*(o - 2)*(o + 6)/5
Let p(f) be the first derivative of f**4/16 - f**3/2 + 11*f**2/8 - 3*f/2 - 61. Factor p(b).
(b - 3)*(b - 2)*(b - 1)/4
Let h(u) be the first derivative of 2*u**3/3 + 10*u**2 + 18*u - 114. Factor h(w).
2*(w + 1)*(w + 9)
Suppose 0 = -5*v + 2*i + 19, -5*v + 8*i + 17 = 7*i. Let h(l) = -l**2 + 15*l - 12. Let f be h(14). Determine q so that -v - 9/2*q - 3/2*q**f = 0.
-2, -1
Suppose 5*g - d - 2*d - 355 = 0, 0 = 4*d + 20. Let m be g/(-18) + 13 + -9. Determine u, given that 0*u - m*u**5 + 0 - 2/9*u**4 + 0*u**2 + 0*u**3 = 0.
-1, 0
Let w(a) be the first derivative of -2*a**3/27 + 19*a**2/9 + 40*a/9 - 11. Solve w(i) = 0.
-1, 20
Suppose 2*w = 4*p - w - 284, 2*p - w - 142 = 0. Factor x**2 + p*x**4 - 67*x**4 - x**2 + 12*x**3 - 16*x.
4*x*(x - 1)*(x + 2)**2
Let o(z) be the first derivative of 2*z**3/27 + 41*z**2/3 + 244*z/9 - 543. Factor o(j).
2*(j + 1)*(j + 122)/9
Let j(r) be the first derivative of r**6/840 - r**5/140 + r**4/56 - 7*r**3/3 - 6. Let k(q) be the third derivative of j(q). Let k(w) = 0. What is w?
1
Let t(v) be the first derivative of -v**4/30 + v**3/5 + 15*v - 4. Let a(m) be the first derivative of t(m). Find k, given that a(k) = 0.
0, 3
Solve 0 - 1/7*n**4 + 6/7*n**2 + 1/7*n**3 + 0*n = 0 for n.
-2, 0, 3
Suppose 0 = -7*k - 990 + 4847. Solve -k*m - m**2 + 551*m = 0 for m.
0
Suppose 102 = 63*h - 29*h. Let f(x) be the second derivative of 0*x**4 + 0*x**6 + 0*x**h + 0 + 0*x**5 - 11*x + 0*x**2 - 1/21*x**7. Factor f(t).
-2*t**5
Let x(z) be the first derivative of z**5/10 - z**4 + 11*z**3/3 - 6*z**2 + 9*z/2 + 11. What is f in x(f) = 0?
1, 3
Factor 1/12*k**2 + 37/12*k + 3.
(k + 1)*(k + 36)/12
Suppose -14*q + 13*q = -3. Let y be 1 - (11/q + -3). Factor -2/3*f + 0 + 1/3*f**2 + y*f**3.
f*(f - 1)*(f + 2)/3
Find z such that -z + 0 + 1/3*z**3 - 2/3*z**2 = 0.
-1, 0, 3
Let w(g) be the second derivative of -g**7/147 + 13*g**6/105 + 81*g**5/70 + 155*g**4/42 + 124*g**3/21 + 36*g**2/7 + 50*g. Find t such that w(t) = 0.
-2, -1, 18
Factor -14*u**2 + 1/2*u**3 - 13 + 53/2*u.
(u - 26)*(u - 1)**2/2
Let r(n) be the second derivative of -n**6/6 + 7*n**5/4 - 25*n**4/4 + 15*n**3/2 + 215*n. What is j in r(j) = 0?
0, 1, 3
Factor -88*s + 16 + 11/2*s**3 - s**2.
(s - 4)*(s + 4)*(11*s - 2)/2
Let q be 212/(-1484) + 2/14. Factor -1/3*u**4 - 1/3*u**3 + 0*u + q + 0*u**2.
-u**3*(u + 1)/3
Let i(w) be the first derivative of w**4/12 + w**3/8 - w**2/8 - w + 8. Let c(d) be the first derivative of i(d). Factor c(p).
(p + 1)*(4*p - 1)/4
Factor -1 + 1/3*k**2 - 2/3*k.
(k - 3)*(k + 1)/3
Suppose -267*d + 269*d = -4*u + 12, 11 = 3*u + d. Find v, given that -2/7*v - 2/7*v**u - 8/7*v**2 + 0 - 8/7*v**4 - 12/7*v**3 = 0.
-1, 0
Let i(b) be the second derivative of b**4/4 + 62*b**3 - 375*b**2/2 + 494*b. Determine c so that i(c) = 0.
-125, 1
Factor -8/5*r**2 + 2/5*r**5 - 14/5*r**3 - 4/5*r**4 + 0*r + 0.
2*r**2*(r - 4)*(r + 1)**2/5
Let z(d) = 19*d - 10. Suppose -5*c = -9*c + 12. Let k be z(c). Let 12*g**3 + 5*g**4 - 4*g**4 + k*g + 61*g + 81 + 54*g**2 = 0. What is g?
-3
Let u(o) be the second derivative of 2*o**5/35 + 17*o**4/42 + 16*o**3/21 + 3*o**2/7 - 79*o. Find q, given that u(q) = 0.
-3, -1, -1/4
Suppose -3*u + 16 = -5*n + 17, -4*n + 23 = 5*u. Let q - 1/2*q**n + 0 = 0. What is q?
0, 2
Let n(l) = 4*l - 3. Let d be n(2). Suppose 3*a**2 - 9*a + d*a + 2*a + 8*a = 0. What is a?
-2, 0
Let x(n) be the second derivative of 0 - 8*n - 2/105*n**7 + 1/75*n**6 + 1/50*n**5 + 0*n**4 + 0*n**3 + 0*n**2. Suppose x(f) = 0. What is f?
-1/2, 0, 1
Suppose -2*z + z - 22 = -4*m, -3*m + 2*z + 14 = 0. Factor 3 - 2*x - 4*x + m*x**3 - 3*x**4 - 2*x**3 + 2*x**3.
-3*(x - 1)**3*(x + 1)
Let a = 32 + -23. Solve -b - 5*b**2 + a*b + 1 - 3 - b = 0 for b.
2/5, 1
Let o be 3*(30/9)/(-5). Let f(v) = -20*v + 5*v**2 + 11 - v**2 - v**2 + 14. Let w(c) = 6*c**2 - 41*c + 49. Let p(k) = o*w(k) + 5*f(k). What is r in p(r) = 0?
3
Suppose 8*p = 2*p + 72. Factor -200*j + p - 203*j + 391*j - 3*j**2 + 6*j**2.
3*(j - 2)**2
Let 32/3*z**2 + 26/3*z + 1/6*z**5 + 8/3 + 5/3*z**4 + 37/6*z**3 = 0. Calculate z.
-4, -2, -1
Let q = 63763 - 320001/5. Let j = q - -238. Suppose j*s**2 - 4/5 - 2/5*s**3 + 2/5*s = 0. What is s?
-1, 1, 2
Let x(w) be the third derivative of -w**5/12 + 55*w**4/24 + 65*w**3/3 + w**2 - 64*w. Factor x(h).
-5*(h - 13)*(h + 2)
Solve -4/9*o + 2/3*o**4 + 0 + 2/9*o**5 + 2/9*o**3 - 2/3*o**2 = 0 for o.
-2, -1, 0, 1
Let m(n) = -7*n**2 + 51*n - 11. Let l be m(7). Let f(v) be the first derivative of -1 + 1/8*v**4 + 0*v**l + 0*v + 0*v**2. Solve f(j) = 0 for j.
0
Let j(f) be the second derivative of f**8/3360 - f**7/210 + f**6/30 - 2*f**5/15 + 17*f**4/6 + 2*f. Let z(x) be the third derivative of j(x). Solve z(y) = 0.
2
Let k(y) be the second derivative of -2*y**2 + 8*y + 2/21*y**7 - 2/5*y**5 + 2/3*y**4 + 2/3*y**3 - 2/15*y**6 + 0. Determine q so that k(q) = 0.
-1, 1
Let l be 14 + -2*(-12)/(-8). Let r = l - 7. Factor r*b - 8*b**3 + 5*b**3 - 2*b**2 + b**3.
-2*b*(b - 1)*(b + 2)
Let f = 13 - 8. Suppose -o - m - 1 = 0, -2*o - o + 7 = m. Suppose i**2 + i**3 + f*i**3 + 2*i**4 + 2*i**2 + i**o = 0. Calculate i.
-1, 0
Determine o, given that -46 + 10 + 1389*o - 2*o**2 - 1427*o = 0.
-18, -1
