11*y.
2*(y + 1)**2*(y + 2)/11
Let x(h) be the second derivative of h**6/2880 - h**4/192 + h**3 + 2*h. Let j(y) be the second derivative of x(y). Find z, given that j(z) = 0.
-1, 1
Let v(t) = -2*t - 27. Let u be v(-15). Factor 0 - 2/9*a - 8/9*a**u + 10/9*a**2.
-2*a*(a - 1)*(4*a - 1)/9
Let p(b) be the second derivative of -b**6/720 - b**5/120 - b**4/72 + 2*b**2 - b. Let m(f) be the first derivative of p(f). Let m(t) = 0. What is t?
-2, -1, 0
Let n be ((-15)/(-25))/((-30)/(-25)). Let l(t) be the first derivative of 1/4*t**6 + 0*t - n*t**5 + 0*t**3 - 1 + 1/4*t**4 + 0*t**2. Solve l(a) = 0.
0, 2/3, 1
Let d(y) = 5*y**2 - 11*y - 2. Let w(c) = -c**2 + c + 1. Let z(i) = -d(i) - 2*w(i). Suppose z(u) = 0. Calculate u.
0, 3
Let g = 8 - -1. Let b = g + -6. Factor -2*f**4 - f**4 - 12*f**2 - 2*f - 9*f**3 - 9*f**b - 5*f**4.
-2*f*(f + 1)**2*(4*f + 1)
Let h(n) be the first derivative of n**6/6 + n**5/5 - n**4/2 - 2. Suppose h(t) = 0. What is t?
-2, 0, 1
Let q(v) = -9*v**2 + 17*v - 13. Let m(h) = -4*h**2 + 8*h - 6. Let r(t) = -13*m(t) + 6*q(t). Determine l so that r(l) = 0.
-1, 0
Let w(d) be the first derivative of d**2 + 24*d + 15. Let o be w(-12). Factor 0*h - 1/7*h**5 - 1/7*h**3 + o*h**2 + 0 - 2/7*h**4.
-h**3*(h + 1)**2/7
Suppose 4*g - 4*n + 5*n = 14, 4*n + 16 = 2*g. Determine p so that -38*p**3 - 4*p + 15*p**2 + 39*p**4 - g*p**5 - 10*p**5 + 0*p**2 + 2*p = 0.
0, 2/7, 1/2, 1
Suppose 2 = 11*y - 20. Find m such that -5/6*m**4 + 5/6*m**y + 0 - 1/3*m**3 + 1/3*m = 0.
-1, -2/5, 0, 1
Let a = -3/28919 - -3962560/6333261. Let f = a - -3/73. Suppose 2/3*n**2 - f + 0*n = 0. Calculate n.
-1, 1
Suppose 120 + 5*y**3 + 2*y - 7*y + 50*y**2 + 145*y = 0. Calculate y.
-6, -2
Let d be 25/2*20/100. Factor d*n**2 + 1/2*n + 0.
n*(5*n + 1)/2
Let t = 22 + -7. Let u = t - 11. Factor 0*b**u + 2*b**2 + 2*b**3 + 2*b**5 - 2*b**4 - 4*b**3.
2*b**2*(b - 1)**2*(b + 1)
Let k(s) = 5*s**3 - 13*s**2 + 2*s + 2. Let n(l) = 25*l**3 - 65*l**2 + 9*l + 9. Let g(y) = 11*k(y) - 2*n(y). Factor g(w).
(w - 2)*(w - 1)*(5*w + 2)
Let b(k) be the second derivative of 7/15*k**6 + 1/5*k**5 - 4/21*k**7 - k + 0*k**3 + 0 + 0*k**2 + 0*k**4. Let b(s) = 0. What is s?
-1/4, 0, 2
Let i(d) be the second derivative of 1/80*d**5 + 0*d**2 - d + 0 + 0*d**4 - 1/120*d**6 + 0*d**3. Factor i(o).
-o**3*(o - 1)/4
Let s = -1055/7 - -151. Solve 0*u - 2/7*u**2 + 0 + s*u**3 = 0 for u.
0, 1
Let p(u) = -4*u**3 - 9*u**2 + 10*u - 2. Let b(j) = j**3 + j**2 - j. Let f(d) = 20*b(d) + 4*p(d). Suppose f(h) = 0. What is h?
1, 2
Factor -15*s**4 + 5*s**5 - 64*s + 54*s + 2*s**2 + 5*s**3 + 13*s**2.
5*s*(s - 2)*(s - 1)**2*(s + 1)
Let n(j) = -16*j - 1. Let m be n(-1). Let s be m/(-10)*(-1 - 1). Factor -2*g**3 + 4*g**4 - 5*g**4 + 4*g**s.
-g**3*(g - 2)
Factor -1/3*f**2 + 1/3*f**3 + 0*f + 0 + 1/3*f**4 - 1/3*f**5.
-f**2*(f - 1)**2*(f + 1)/3
Let b = 10 - 6. Suppose 0 = b*u + 2*u - 12. Let -1/2*k - 1 + 1/2*k**u = 0. Calculate k.
-1, 2
Let p be -107*(1/4 - 0). Let o = 27 + p. Determine n, given that 1/4*n**2 + 0*n + 1/2*n**3 + 0 + o*n**4 = 0.
-1, 0
Let b be -2 + 0/3 - -8. Determine z so that -b*z**3 - 4*z**2 + z**4 + 2*z**2 + 6*z - 3*z**4 + 4 = 0.
-2, -1, 1
Let a = -1654/21 + 238/3. Factor -2*g + a + 10/7*g**2.
2*(g - 1)*(5*g - 2)/7
Let d(r) be the first derivative of 3*r**4 - 7*r**3 + 3*r**2 + 3*r + 6. Let d(x) = 0. What is x?
-1/4, 1
Suppose 7*k + 0*k - 21 = 0. Let l(n) be the first derivative of 1 - 1/2*n**2 - 1/3*n**k + 0*n. Factor l(v).
-v*(v + 1)
Let x(u) be the third derivative of u**6/480 + u**5/120 - u**4/96 - u**3/12 + 10*u**2. Factor x(l).
(l - 1)*(l + 1)*(l + 2)/4
Let q = 33/8 + -397/104. Determine r, given that -4/13*r**2 - q*r**3 + 2/13 + 2/13*r**5 + 2/13*r + 2/13*r**4 = 0.
-1, 1
Let p(h) = -h**3 + h**4 - 2*h**4 + 2*h**3 + h. Let t(r) = -7*r**4 + 7*r**3 - r**2 + 3*r. Let z(u) = 3*p(u) - t(u). Find x, given that z(x) = 0.
0, 1/2
Let a(q) be the first derivative of 0*q - 1/2*q**4 - 2/3*q**3 + q**2 - 3 + 2/5*q**5. Suppose a(k) = 0. Calculate k.
-1, 0, 1
Let z(c) be the second derivative of 3*c**5/160 + c**4/4 - 9*c**3/16 + 2*c + 18. Factor z(n).
3*n*(n - 1)*(n + 9)/8
Let x(j) be the first derivative of j**6/3 - 8*j**5/5 + j**4 + 8*j**3/3 - 3*j**2 - 5. Determine t, given that x(t) = 0.
-1, 0, 1, 3
Let -7/2*b**3 + 2*b**5 + 0*b**4 + 1/2*b**2 + 3/2*b - 1/2 = 0. Calculate b.
-1, 1/2, 1
Suppose 13*i**3 - 10*i**2 - 11*i**3 + 8*i + 18 - 2*i = 0. What is i?
-1, 3
Let t(c) be the first derivative of -3*c + 3 + 0*c**3 - 1/2*c**2 + 1/12*c**4. Let u(d) be the first derivative of t(d). Factor u(b).
(b - 1)*(b + 1)
Let j(v) be the second derivative of v**7/6300 - v**6/1800 - v**5/150 + v**4/6 + 2*v. Let h(o) be the third derivative of j(o). Determine f so that h(f) = 0.
-1, 2
Let h be ((-868)/50)/((-12)/5). Let a = -41/6 + h. Factor -2/5*c**2 + 0*c + a.
-2*(c - 1)*(c + 1)/5
Let z(d) be the second derivative of 0 + 0*d**3 + 0*d**5 + 1/3*d**2 - 1/9*d**4 + 1/45*d**6 + 2*d. Let z(v) = 0. What is v?
-1, 1
Let f(j) = -j**5 - j**4 + j**3 + j**2 + j. Let i(m) = -2*m**5 + 2*m**4 + 12*m**3 + 10*m**2 + 5*m. Let w(s) = 3*f(s) - i(s). Factor w(b).
-b*(b + 1)**3*(b + 2)
Let r = -5 - -7. Factor -8/3*b**r - 7/3*b - 2/3 - b**3.
-(b + 1)**2*(3*b + 2)/3
Let v(w) be the third derivative of -w**5/210 - w**4/28 + 10*w**3/21 + 3*w**2 - 9. Determine a, given that v(a) = 0.
-5, 2
Let v(d) be the third derivative of -d**5/15 - 6*d**2. Factor v(f).
-4*f**2
Let p(r) = 3*r**2 + 5*r + 3. Let d(q) = -q**2 - q - 1. Suppose o - 4*o + 3 = 0. Suppose 0 = -f + o - 2. Let l(s) = f*p(s) - d(s). Factor l(b).
-2*(b + 1)**2
Let f(y) be the first derivative of -y**6/8 + 3*y**5/20 + 3*y**4/8 - y**3/2 - 3*y**2/8 + 3*y/4 + 3. Factor f(w).
-3*(w - 1)**3*(w + 1)**2/4
Factor 459*p**2 - 229*p**2 - 235*p**2 + 5.
-5*(p - 1)*(p + 1)
Let b(p) be the first derivative of -p**7/630 - p**6/180 - p**5/180 - p**2 - 4. Let h(k) be the second derivative of b(k). Determine t so that h(t) = 0.
-1, 0
Factor 809*f**3 - 18 - 18 - 13*f**2 - 808*f**3 + 48*f.
(f - 6)**2*(f - 1)
Determine t, given that t**2 + 0 + 2/3*t**3 + 1/3*t = 0.
-1, -1/2, 0
Let i(g) be the third derivative of 0*g + 2/15*g**5 + 1/6*g**4 + 3*g**2 + 0*g**3 + 0 + 1/30*g**6. Factor i(o).
4*o*(o + 1)**2
Find p such that 1/2*p + 0 + 1/4*p**4 + 0*p**3 - 3/4*p**2 = 0.
-2, 0, 1
Let i(w) be the third derivative of 2/3*w**3 + 0*w + 1/60*w**5 + 0 + 4*w**2 - 1/6*w**4. Factor i(r).
(r - 2)**2
Let w be 4 + (0 - (2 + 2/1)). Suppose 3*k = 4*k - 4. Find d, given that 20/3*d**3 + 13/3*d**2 + 3*d**k + w + 2/3*d = 0.
-1, -2/9, 0
Factor -3/5*q + 3/5*q**3 + 3/5 - 3/5*q**2.
3*(q - 1)**2*(q + 1)/5
Let h = -427 - -6409/15. Let k(y) be the first derivative of 2/5*y**2 - 3/20*y**4 - 2/25*y**5 + 0*y + h*y**3 + 4 + 1/30*y**6. Solve k(q) = 0.
-1, 0, 2
Let d(k) = k**3 + k**2 + k. Let z(f) = 32*f**3 + 6*f**2 - 12*f + 4. Let q(m) = 10*d(m) - z(m). Factor q(n).
-2*(n - 1)*(n + 1)*(11*n - 2)
Let j(q) be the first derivative of -q**3/18 - 5*q**2/12 + q - 37. What is r in j(r) = 0?
-6, 1
Let q(n) be the second derivative of 0 - 3/5*n**5 + n + 8*n**2 + 13/3*n**4 - 32/3*n**3. Solve q(d) = 0 for d.
1/3, 2
Let b(p) be the second derivative of p**4/66 + p**3/33 - 4*p. What is n in b(n) = 0?
-1, 0
Suppose -4*y + 6 + 6 = 0. Determine g, given that y - g**2 - 1 - 3 + 2*g + 0 = 0.
1
Let t(s) be the first derivative of -3*s**4/8 + 9*s**2/4 - 3*s + 9. Factor t(u).
-3*(u - 1)**2*(u + 2)/2
Let r be 15 - (2 + (-6)/4). Let h = 15 - r. Solve -d - 1 + h*d**3 + 3/4*d**2 - 1/4*d**4 = 0 for d.
-1, 2
Suppose 0*p = -5*p + 25. Let j = -2 + p. Factor 4*v**j - 3*v**2 + 3*v - 4*v + 3*v - 3*v**3.
v*(v - 2)*(v - 1)
Suppose 0 = -3*k + 2*j - 8, -j = -4*k - 4*j + 12. Factor k - 1/5*a - 3/5*a**2.
-a*(3*a + 1)/5
Let w(q) be the first derivative of -q**4/14 + 20*q**3/21 - 17*q**2/7 + 16*q/7 - 9. Factor w(m).
-2*(m - 8)*(m - 1)**2/7
Let j(d) be the second derivative of -d**5/30 + d**3/9 - 10*d. Suppose j(v) = 0. Calculate v.
-1, 0, 1
Factor -12/7 + 6/7*a**2 + 2*a.
2*(a + 3)*(3*a - 2)/7
Let k(d) be the second derivative of d**5/5 + 2*d**4/3 + 2*d**3/3 + d. Suppose k(i) = 0. What is i?
-1, 0
Suppose 1 = 2*b - 3. Suppose -4*o - 5*k = o, 3*o + b*k - 3 = 0. Find h, given that 0 + 0*h**2 + 1/2*h**4 + 0*h + 0*h**o - 1/2*h**5 = 0.
0, 1
Let y(o) be the first derivative of o**4/8 + 5*o**3/6 + 3*o**2/4 - 9*o/2 - 7. Factor y(w).
(w - 1)*(w