
3*q**2*(q + 1)/5
Let l = 4 - 4. Let o(m) be the second derivative of l + 2*m + 1/24*m**4 + 1/4*m**2 - 1/6*m**3. Let o(k) = 0. Calculate k.
1
Factor -2/3 - 2/3*a**4 - 8/3*a**3 - 8/3*a - 4*a**2.
-2*(a + 1)**4/3
Let t(q) be the third derivative of 1/36*q**4 + 1/630*q**7 + 0*q**3 - 1/180*q**5 - 3*q**2 + 1/336*q**8 + 0 + 0*q - 1/72*q**6. Solve t(x) = 0.
-1, 0, 2/3, 1
Factor 122*x + 2*x**2 - 242*x + 118*x.
2*x*(x - 1)
Let i(d) = -d**3 - 17*d**2 - 18*d - 30. Let s be i(-16). Let g(v) be the first derivative of 0*v**2 + 4/3*v**3 + 0*v - 1/2*v**4 + s. Factor g(w).
-2*w**2*(w - 2)
Let y = 2989/18 - 166. Let l(r) be the first derivative of y*r**4 - 2/9*r + 1/3*r**2 + 1 - 2/9*r**3. Factor l(x).
2*(x - 1)**3/9
Let l(b) be the third derivative of b**6/180 + b**5/15 + b**4/4 + 4*b**3/9 - 38*b**2. Factor l(f).
2*(f + 1)**2*(f + 4)/3
Suppose -5*a + 0*a + 5*d = -30, 0 = -2*a - d. Let t be (-2)/(-6) - (-35)/63. Factor -2/3 + t*k - 2/9*k**a.
-2*(k - 3)*(k - 1)/9
Let c(r) = 5*r**2 + 5 + 2*r**3 - 11 - 3 - r. Let q(y) = 2*y**3 + 6*y**2 - 10. Let j(g) = -6*c(g) + 5*q(g). Factor j(a).
-2*(a - 2)*(a + 1)**2
Let d(v) be the first derivative of -v**4/20 - 3*v**3/5 - 27*v**2/10 - 27*v/5 + 6. Solve d(k) = 0 for k.
-3
Let s(j) be the second derivative of -3*j**5/4 - 35*j**4/12 - 25*j**3/6 - 5*j**2/2 - 4*j - 4. Factor s(b).
-5*(b + 1)**2*(3*b + 1)
Let w(a) be the second derivative of 1/60*a**6 - a - 1/75*a**5 + 0*a**3 - 1/175*a**7 + 0 + a**2 + 0*a**4. Let h(b) be the first derivative of w(b). Factor h(g).
-2*g**2*(g - 1)*(3*g - 2)/5
Suppose l - f = -5, l = 2*l - 5*f + 25. Solve 16/5*q**4 + l + 0*q - 8/5*q**5 - 2*q**3 + 2/5*q**2 = 0.
0, 1/2, 1
Suppose -4*d = -35 + 11. Suppose -x - d + 8 = 0. What is t in 4/11*t + 2/11 + 2/11*t**x = 0?
-1
Let a(b) be the second derivative of -b - 2*b**3 + 1/5*b**5 - 2/3*b**4 + 0*b**2 + 0. Determine l, given that a(l) = 0.
-1, 0, 3
Factor -1083/7 + 114/7*t - 3/7*t**2.
-3*(t - 19)**2/7
Let s = 67 - 64. Factor 0 - 2/3*c**s + 0*c + 2/3*c**2.
-2*c**2*(c - 1)/3
Let m(w) be the third derivative of -1/12*w**3 + 0 - 4*w**2 + 0*w**5 - 1/60*w**6 + 1/16*w**4 + 0*w. Determine u, given that m(u) = 0.
-1, 1/2
Let v(w) be the third derivative of w**7/420 + w**6/80 - w**5/40 - 11*w**4/48 - w**3/2 + w**2 + 18*w. Factor v(y).
(y - 2)*(y + 1)**2*(y + 3)/2
Let z = 19 - 10. Suppose v + 2*v**4 - 2*v**2 + 14*v**2 - z*v - 8*v**3 + 2 = 0. Calculate v.
1
Let m = -1 + 6. Suppose m*j = -4*i, -5*j = -3*i - i. Solve 6*f**2 - 2*f**3 + i*f + 0*f**2 - 3*f - f = 0.
0, 1, 2
Let d(w) be the third derivative of w**8/336 - w**7/105 + w**5/30 - w**4/24 + 32*w**2. Factor d(v).
v*(v - 1)**3*(v + 1)
Let j(u) be the third derivative of u**7/10080 - u**6/1440 + u**5/480 + 7*u**4/24 - 8*u**2. Let o(x) be the second derivative of j(x). Factor o(m).
(m - 1)**2/4
Let q(g) be the first derivative of -3*g**5/170 - 11*g**4/204 - 2*g**3/51 + 4*g**2 + 2. Let l(h) be the second derivative of q(h). Suppose l(w) = 0. What is w?
-1, -2/9
Let g(u) be the first derivative of u**5/20 - u**3/12 - 2. Factor g(a).
a**2*(a - 1)*(a + 1)/4
Let f = 1499 + -34483/23. Let g = 97/69 - f. Suppose 0*c**2 - g*c**4 + 0 + 0*c + c**5 + 2/3*c**3 = 0. Calculate c.
0, 2/3, 1
Let y be (-560)/(-72) + (-4)/(-18). Solve t**2 - y + 6 + 2 + t = 0.
-1, 0
Let n(u) = 11*u**4 + 17*u**3 + 19*u**2 - 13*u + 13. Let o(i) = 5*i**4 + 8*i**3 + 9*i**2 - 6*i + 6. Let v(b) = 6*n(b) - 13*o(b). What is d in v(d) = 0?
-1, 0, 3
Find d, given that 3/2*d**2 + 1/4*d**4 + 1/4 - d**3 - d = 0.
1
Factor -8*o**2 - 4*o**2 + o**2 - 5*o**2 - 14*o**4 - 38*o**3 + 8*o.
-2*o*(o + 1)*(o + 2)*(7*o - 2)
Factor 54/5 + 54/5*w + 2/5*w**3 + 18/5*w**2.
2*(w + 3)**3/5
Let x(i) be the second derivative of 5*i**4/12 - 5*i**2/2 - 26*i. Find c, given that x(c) = 0.
-1, 1
Let s = -3 + 6. Let a be (1/s)/((-3)/(-6)). Factor 2/3*i**3 + a*i**2 - 2/3 - 2/3*i.
2*(i - 1)*(i + 1)**2/3
Let z(p) be the first derivative of 2*p**3/7 + p**2 + 4*p/7 - 20. Suppose z(t) = 0. What is t?
-2, -1/3
Let g be (-1 - -2)/((-5)/(-20)). Let n(b) be the second derivative of 1/90*b**6 + 0*b**g + 0 - 1/60*b**5 + 0*b**2 + 0*b**3 - 2*b. Factor n(v).
v**3*(v - 1)/3
Let c = -6 - -5. Let r be c/(-3) + 5/3. Factor -2/5*b - 2/5*b**3 - 4/5*b**r + 0.
-2*b*(b + 1)**2/5
Let t(a) = -1 - 1 - 7*a**2 - 7*a + 1 - 1 - a**3. Let f be t(-6). Factor -1 + i + 5 - i**3 - f.
-i*(i - 1)*(i + 1)
Suppose -3*n - 9 = 3*g, n - 4*g - 22 = -0*g. Let v = 56 - 223/4. Solve 0 + v*i**n + 1/4*i = 0 for i.
-1, 0
What is i in 0*i + 0 + 1/3*i**3 - 1/3*i**2 = 0?
0, 1
Let l(n) be the first derivative of 8*n**5/35 - 13*n**4/14 + 2*n**3/7 + 16*n**2/7 - 8*n/7 - 9. Find v, given that l(v) = 0.
-1, 1/4, 2
Let q(i) be the third derivative of i**9/37800 + i**8/16800 - i**7/6300 - i**6/1800 - i**4/12 + 2*i**2. Let b(j) be the second derivative of q(j). Factor b(g).
2*g*(g - 1)*(g + 1)**2/5
Let z(s) = -8*s**4 + 8*s**3 + 2*s**2 - 2*s + 6. Let l = -2 - 4. Let p(w) = -w**4 + w**3 + 1. Let f(y) = l*p(y) + z(y). Factor f(r).
-2*r*(r - 1)**2*(r + 1)
Let y be 247/78 - 3/1. Let l(z) be the second derivative of 0*z**3 + 0*z**2 - 4/15*z**6 - y*z**4 + 0 - 1/2*z**5 + z. Factor l(o).
-2*o**2*(o + 1)*(4*o + 1)
Let z(k) be the first derivative of 1/12*k**3 + 0*k + 0*k**2 + 1/20*k**5 + 1/8*k**4 - 3. Let z(y) = 0. Calculate y.
-1, 0
Let f(p) = -9*p + 2. Let r be f(6). Let d be r/(-16) - 6/(-8). Factor 0*c**2 - 1/2*c**d + 0 - 1/4*c**3 - 1/4*c**5 + 0*c.
-c**3*(c + 1)**2/4
Let m(z) = -z**3 - 7*z**2 - 5*z + 8. Let x = -8 - -2. Let s be m(x). Factor 2/3*h**4 - s*h**3 + 2*h**2 - 2/3*h + 0.
2*h*(h - 1)**3/3
Let b(k) = -3*k**3 + 13*k**2 - 26*k + 10. Let s = -9 - -11. Let w(u) = -u**2 - u - 1. Let y(d) = s*w(d) - b(d). Factor y(n).
3*(n - 2)**2*(n - 1)
Let g be 4/8 - 1/2. Suppose g*l = 3*l. Suppose 1/2*a**2 + l*a + 0 = 0. What is a?
0
Let p be 50/15*(-6)/(-4). Suppose p*a - l = 10, -4*a - 18 = 4*l - 50. Factor 0*g**a + 2*g - 3*g**3 - 5*g + 6*g**2.
-3*g*(g - 1)**2
Let s = -231 + 132. Let t be (-315)/s + 4/(-22). Factor -2/11*r**4 - 6/11*r**t - 6/11*r**2 + 0 - 2/11*r.
-2*r*(r + 1)**3/11
Let f(h) be the third derivative of h**7/70 + 2*h**2. Factor f(c).
3*c**4
Let m be 69/(-15) + 4 + 1. Factor m*t**2 + 4/5 - 6/5*t.
2*(t - 2)*(t - 1)/5
Let r be (2 - 3) + -1 + 5. Determine d, given that d**r + 2*d**2 - d**3 + 0*d**2 - 2*d**3 = 0.
0, 1
Suppose -153*m = -164*m + 22. Factor -2/11*r - 2/11*r**5 + 0 + 0*r**4 + 4/11*r**3 + 0*r**m.
-2*r*(r - 1)**2*(r + 1)**2/11
Let g(m) be the third derivative of m**8/504 - m**7/210 + m**5/180 + 7*m**2. Determine i so that g(i) = 0.
-1/2, 0, 1
Let g(a) be the second derivative of a**7/840 + a**6/288 - 7*a**5/480 - a**4/48 - 2*a**3/3 - 6*a. Let b(w) be the second derivative of g(w). Factor b(t).
(t - 1)*(t + 2)*(4*t + 1)/4
Let t(b) be the third derivative of b**6/120 + b**5/60 - b**4/24 - b**3/6 - 38*b**2. Determine l so that t(l) = 0.
-1, 1
Let f(q) be the second derivative of 3*q**7/35 - 4*q**6/15 + 13*q**5/50 - q**4/15 + 5*q. Factor f(z).
2*z**2*(z - 1)**2*(9*z - 2)/5
Let u(s) = 5*s**3 + s - 10. Let b(h) = 11*h**3 - h**2 + 2*h - 21. Let n(m) = -6*b(m) + 13*u(m). Let y be n(6). Solve j**2 + y*j - 2*j**2 + j - 5*j = 0 for j.
-2, 0
Determine m so that -m + 16*m - 17*m**2 - 10*m**3 - 6*m**5 - 3*m**2 + 20*m**4 + m**5 = 0.
-1, 0, 1, 3
Let d(b) = 2*b**2 - 5*b - 9. Let q be d(4). Solve 1/5*j**4 + 0*j - 2/5*j**5 + 2/5*j**q - 1/5*j**2 + 0 = 0.
-1, 0, 1/2, 1
Suppose -d = -5*d + 3*v + 6, -3*d = 2*v - 13. Let a(k) be the second derivative of 1/90*k**6 + 0 + 1/12*k**4 + 1/20*k**5 - k + 0*k**2 + 1/18*k**d. Factor a(l).
l*(l + 1)**3/3
Suppose 51*n - 36 = 39*n. Determine s, given that 0 + 3/7*s + 24/7*s**4 + 0*s**2 - 9/7*s**5 - 18/7*s**n = 0.
-1/3, 0, 1
Let d(b) = -2*b**3 - b**2 + 17*b - 5. Let l(i) = 6*i**3 + 4*i**2 - 50*i + 16. Let n(s) = -8*d(s) - 3*l(s). Let n(p) = 0. What is p?
-4, 1
Let x = 119/40 - 19/8. Suppose 3/5*v + 6/5 - x*v**2 = 0. What is v?
-1, 2
Let p(j) be the second derivative of -2*j**7/21 - 4*j**6/5 - 13*j**5/5 - 4*j**4 - 8*j**3/3 - j. Factor p(o).
-4*o*(o + 1)**2*(o + 2)**2
Let q(k) be the third derivative of 0 + 0*k + 0*k**5 + 1/28*k**4 - 2/21*k**3 - 1/420*k**6 - 6*k**2. Factor q(c).
-2*(c - 1)**2*(c + 2)/7
Let f(n) = 9 - n + 2*n**2 - 3*n**2 + n**3 - n**2 - 5*n**2. Let a be f(7). Factor -1/2*w**a - 1/2*w**3 + 0*w + 0.
-w**2*(w + 1)/2
Let r(h)