n(o) be the second derivative of o**7/315 - o**6/18 + 2*o**5/5 - 3*o**4/2 + 3*o**3 + 23*o**2/2 - 2*o. Let d(w) be the first derivative of n(w). Factor d(k).
2*(k - 3)**3*(k - 1)/3
Let x(c) be the second derivative of 3*c**5/20 + 38*c**4 + 2888*c**3 + c + 235. Let x(m) = 0. Calculate m.
-76, 0
Factor -36*u - 20/3*u**3 - 18 - 24*u**2 - 2/3*u**4.
-2*(u + 1)*(u + 3)**3/3
Suppose -16/7*s + 0 + 1/7*s**2 = 0. What is s?
0, 16
Let b(v) be the third derivative of -v**5/70 - 9*v**4/14 - 17*v**3/7 + 151*v**2 + 2*v. Factor b(y).
-6*(y + 1)*(y + 17)/7
Let d(g) = g**3 - 5*g**2 + 3*g + 6. Let a be d(4). Factor -8*n**3 - 5*n**4 + 5*n + 5*n**5 - 2*n**3 - 31 + 10*n**a + 26.
5*(n - 1)**3*(n + 1)**2
Factor -1/6*m**2 - m - 5/6.
-(m + 1)*(m + 5)/6
Let l = 4807 + -4807. Find r such that l + 2/9*r**4 + 0*r + 2/9*r**5 + 0*r**2 + 0*r**3 = 0.
-1, 0
Let v(c) be the third derivative of -1/42*c**4 + 0 - 1/7*c**3 + 0*c + 1/210*c**5 - 3*c**2. Suppose v(g) = 0. Calculate g.
-1, 3
Let s(j) be the second derivative of 0*j**3 + 1/45*j**6 + 0*j**2 + 1/9*j**4 + 1/10*j**5 + 0 + 11*j. Determine x, given that s(x) = 0.
-2, -1, 0
Suppose 216 = -21*c + 12*c. Let w be c/18 + 4*29/78. Let -w*n**2 - 6/13 - 8/13*n = 0. What is n?
-3, -1
Let d(o) be the third derivative of o**8/1176 + 4*o**7/735 + o**6/210 - 2*o**5/105 - o**4/28 - 192*o**2. Let d(b) = 0. Calculate b.
-3, -1, 0, 1
Let o(m) = -m**2 + 13*m**2 - 16*m**3 + 4*m**3 + 6*m**4. Let c(p) = -11*p**4 + 24*p**3 - 24*p**2. Let a(x) = -3*c(x) - 5*o(x). Solve a(d) = 0 for d.
0, 2
Let s(u) be the first derivative of -6 - 5/3*u**3 + 5*u**2 + 0*u. Suppose s(r) = 0. What is r?
0, 2
Let 56*v**2 - 15*v - 38*v - 23*v**2 - 206 + 230 - v**4 - 3*v**3 = 0. What is v?
-8, 1, 3
Suppose 24 = -9*q + 24. Let b(r) be the third derivative of 0*r + q*r**3 - 1/45*r**5 + 1/18*r**4 + 0 + r**2 - 1/120*r**6. Factor b(a).
-a*(a + 2)*(3*a - 2)/3
Let c(r) = -r**2 + 7*r - 7. Let b be c(5). Suppose -d - b = -2*d. Factor -2*l - 48 + 24*l - d*l**2 + 2*l.
-3*(l - 4)**2
Let p(y) = -6*y**2 + 14*y - 16. Let a(m) = m**2 - m + 2. Let h(r) = 4*a(r) + p(r). Suppose h(v) = 0. What is v?
1, 4
Let b(c) be the third derivative of -c**6/90 - c**5/15 - c**4/6 + 2*c**3/3 + 3*c**2. Let n(z) be the first derivative of b(z). Factor n(x).
-4*(x + 1)**2
Let z = -13 + 21. Suppose 5*b = z*b. Let r**3 + 1/2*r + b + 3/2*r**2 = 0. Calculate r.
-1, -1/2, 0
Let i(k) be the first derivative of -k**4/4 + k**3/4 + 2*k**2 - 3*k - 187. Factor i(b).
-(b - 2)*(b + 2)*(4*b - 3)/4
Let n(q) = 170*q - 168. Let z be n(1). Factor 0 - 1/4*a**z + 0*a.
-a**2/4
Let j(m) = 5*m + 407. Let o be j(-81). Determine n so that -108/7*n**3 - 16*n**o - 16/7 + 96/7*n + 3*n**5 + 29/7*n**4 = 0.
-2, 2/7, 1/3, 2
Factor 80*n**3 + 9*n**4 - 11*n**4 + 722 + 0*n**4 + 876*n**2 + 1520*n + 4*n**4.
2*(n + 1)**2*(n + 19)**2
Let z(f) = f + 1. Let y(p) = 3*p + 8. Let a(n) = -y(n) + 2*z(n). Let b be a(-8). Factor 2*i**3 - 18*i - 4*i**2 + 8*i**b + 20*i.
2*i*(i + 1)**2
Let y be 6 + (-8)/(-48) + -6. Factor -1/6 + 2/3*d - d**2 - y*d**4 + 2/3*d**3.
-(d - 1)**4/6
Let j = 457 - 8225/18. Let s(v) be the first derivative of 1/8*v**4 - j*v**3 - 1/18*v**6 - 1/12*v**2 + 4 + 1/30*v**5 + 0*v. Suppose s(n) = 0. What is n?
-1, -1/2, 0, 1
Let g(k) be the second derivative of 1/3*k**4 + 1/5*k**5 + 14*k - 10/3*k**3 + 6*k**2 + 0. Suppose g(h) = 0. What is h?
-3, 1
Factor 4/3*a**3 + 0 + 0*a - 4*a**5 + 0*a**2 - 8/3*a**4.
-4*a**3*(a + 1)*(3*a - 1)/3
Let v(a) = 240*a**2 - 1735*a + 11830. Let h(t) be the first derivative of 17*t**3/3 - 62*t**2 + 845*t + 44. Let z(f) = 85*h(f) - 6*v(f). Factor z(b).
5*(b - 13)**2
Let y be 4/(-7) + (-32)/(-7). Find u such that 1 - 4*u**2 - 1 - 4*u**2 + 4*u**y - 4*u**3 = 0.
-1, 0, 2
Suppose -5*y + 0*y = -10. Suppose 4*p = 3*f + 13, 2*p = 3*f - 0*f + 5. Let -3*u**2 - 2 + 3*u**2 + u**y - 3*u**2 - p*u = 0. What is u?
-1
Suppose 15*q - 127 = 68. Suppose -33 = -4*d - q. Suppose -46/3*m + 176/9*m**4 - 230/9*m**2 + 32/9*m**d - 2 + 178/9*m**3 = 0. What is m?
-3, -1/4, 1
Suppose -3*c = g, 2*g - 4 = 2*c - 12. Factor -3/2*r**2 + 1/2*r + c - 1/2*r**3 + 1/2*r**4.
(r - 2)*(r - 1)*(r + 1)**2/2
Let c(w) be the third derivative of 1/2*w**4 + 0 - 1/20*w**5 - 3/2*w**3 + 0*w - 4*w**2. Find d, given that c(d) = 0.
1, 3
Factor 26/7*l**2 + 0 - 4*l.
2*l*(13*l - 14)/7
Let t(z) = z**2 - 2*z - 11. Suppose -6*m + 25 = 1. Let d(w) = 1. Let y(b) = m*t(b) + 44*d(b). Factor y(x).
4*x*(x - 2)
Let q = -1272 + 1275. Solve 27/5 - q*g**2 - 9/5*g - 3/5*g**3 = 0 for g.
-3, 1
Let l(u) be the first derivative of -5*u**6/6 - u**5 + 25*u**4/4 + 5*u**3/3 - 20*u**2 + 20*u + 438. Factor l(o).
-5*(o - 1)**3*(o + 2)**2
Suppose 1/4*i + 1/4*i**2 - 3/2 = 0. Calculate i.
-3, 2
Let h(n) be the first derivative of n**3/3 - 7*n**2 + 8*n - 2. Let i be h(14). Factor 2*l**2 - 7*l + 7*l + i*l - 8 - 2*l**3 + 0*l**2.
-2*(l - 2)*(l - 1)*(l + 2)
Solve -26*j**3 - 4*j**2 - 12*j**2 + 5*j**2 + 24*j - 11*j**2 + 2*j**5 + 22*j**4 = 0 for j.
-12, -1, 0, 1
Let b = -2/4809 + 22444/4809. Factor -b*s - 6*s**2 + 4/3.
-2*(s + 1)*(9*s - 2)/3
Let s(w) be the second derivative of 0*w**3 - 3/2*w**2 + 0 - 22*w + 1/4*w**4. Let s(m) = 0. Calculate m.
-1, 1
Let l be -3*2/9*3. Let t be 3*(8/3 + l). Factor -2*p**t - 10*p + 10*p + 0*p**2.
-2*p**2
Let b(w) be the second derivative of -w**7/15 + 16*w**6/75 - 11*w**5/50 + w**4/15 - 403*w. Factor b(q).
-2*q**2*(q - 1)**2*(7*q - 2)/5
Suppose 2*n = -4*s + 14, -5*n - 3*s - 9 + 30 = 0. Let -3/2*o**n - 9/2*o - 3/2 - 9/2*o**2 = 0. What is o?
-1
Find j such that 2/3 + 8*j + 12*j**3 + 58/3*j**2 = 0.
-1, -1/2, -1/9
Let y(b) = b**3 - b**2 - b. Let t(c) = 7*c**4 + 48*c**3 + 64*c**2 + 4*c. Let i(j) = t(j) - 5*y(j). Solve i(g) = 0 for g.
-3, -1/7, 0
Factor 8*q - 24*q**2 - 14*q - 16 + 6*q**2 + 50*q.
-2*(q - 2)*(9*q - 4)
Solve -8*z - 123 - 2*z**4 - 252*z**2 + 90*z**3 + 369 + 90 = 0 for z.
-1, 2, 42
Let n(a) be the first derivative of 2*a**5/35 + a**4/28 - 11*a**3/21 + 11*a**2/14 - 3*a/7 - 395. Factor n(m).
(m - 1)**2*(m + 3)*(2*m - 1)/7
Let h be 6/3*(9 - 5)/2. Let y(g) be the first derivative of 0*g + 2/3*g**2 + 1 + 121/12*g**h + 44/9*g**3. Suppose y(u) = 0. Calculate u.
-2/11, 0
Let x(u) be the second derivative of -u**5/105 - 3*u**4/28 - 4*u**3/21 - 2*u**2 - 19*u. Let b(j) be the first derivative of x(j). Factor b(r).
-2*(r + 4)*(2*r + 1)/7
Let u(p) = 2*p - 4. Let c be u(0). Let g = c + 13. Factor -4*d**3 - 9 + 5*d + 3*d**3 + d**2 + 21 - g.
-(d - 3)*(d + 1)**2
Find d such that 4*d**4 + 4*d**2 + 16*d - 6 + 2*d**5 - 2*d**2 - 10*d**3 + 14 - 6*d**4 = 0.
-1, 2
Let o = 427 - 427. Determine z, given that o*z**2 - 1/2 + z**3 - z + 1/2*z**4 = 0.
-1, 1
Let u be (-392)/(-441) + ((-14)/35)/(3/5). Solve u*a**2 + 4/9 - 7/9*a + 1/9*a**3 = 0.
-4, 1
Let i = 55705/4 - 13926. Factor -1/4*k**2 - i - 1/2*k.
-(k + 1)**2/4
Let d = 2615/14 + -1304/7. Factor 1 + 3/2*n + d*n**2.
(n + 1)*(n + 2)/2
Let b(z) be the third derivative of z**6/120 - z**5/10 + z**4/2 - 4*z**3/3 - 147*z**2 + 2. Factor b(d).
(d - 2)**3
Let p(u) = -75*u**3 - 1578*u**2 - 72921*u - 1093521. Let l(f) = -18*f**3 - 395*f**2 - 18230*f - 273380. Let x(z) = 21*l(z) - 5*p(z). Solve x(q) = 0 for q.
-45
Let v(p) be the third derivative of p**7/210 - p**6/3 + 10*p**5 - 500*p**4/3 + 5000*p**3/3 + 12*p**2 - 1. Factor v(l).
(l - 10)**4
Let s(o) = -3*o**5 - o**3 + 11*o + 7. Let f = -113 + 120. Let b(p) = -p**5 - p**3 + 5*p + 3. Let m(h) = f*b(h) - 3*s(h). Factor m(z).
2*z*(z - 1)**2*(z + 1)**2
Let u be (1 - (3 + 2) - 1)/(-1). Let n(h) be the third derivative of -1/100*h**6 - 4*h**2 + 0 + 11/180*h**4 + 2/45*h**3 + 0*h + 2/75*h**u. Factor n(d).
-2*(d - 2)*(3*d + 1)**2/15
Factor -w**3 + 2*w**2 - 37 + 31 - 2*w**2 + 9*w - 2*w**3.
-3*(w - 1)**2*(w + 2)
Let n be ((-2)/5)/(26/(-150)). Let t = n - 111/65. What is u in 9/5*u - 12/5*u**2 + 0 + t*u**3 = 0?
0, 1, 3
Find r, given that 141*r**2 + 57*r**2 + 24*r**3 - 33*r**2 + 6655 - 19*r**3 + 1815*r = 0.
-11
Let l(h) be the first derivative of -h**6/30 + h**5/5 - h**4/2 + 2*h**3/3 - h**2/2 + 9*h - 10. Let m(p) be the first derivative of l(p). Factor m(u).
-(u - 1)**4
Let w be 6/5 + 36/(-105). Find x such that -2/7*x**2 - 4/7*x + w = 0.
-3, 1
Let y(d) be the third derivative of -d**6/280 + 13*d**5/140 + 29*d**4/56 + 15*d**3/14 - 254*d**2. Find l, given that y(l) = 0.
-1, 15
Let h(o) be the first derivative of -2*o**3/