second derivative of -j**5/120 + j**4/36 - j**3/36 + 29*j. Solve s(m) = 0 for m.
0, 1
Let v(g) = -g**3 - 7*g**2 - 14*g - 6. Let b be v(-4). Let d(h) be the first derivative of 0*h - h**b + 4 - 1/3*h**3. Find w such that d(w) = 0.
-2, 0
Let l(o) be the second derivative of -o**7/3360 - o**6/720 - o**5/480 + o**3/3 + o. Let h(j) be the second derivative of l(j). Find s, given that h(s) = 0.
-1, 0
Let o be (-81)/(-21) + 2/14. Factor o*c**2 - 12*c**2 + 6*c**2.
-2*c**2
Let t(k) be the third derivative of k**8/33600 - k**7/4200 + k**6/1200 - k**5/600 - 5*k**4/24 - 3*k**2. Let i(a) be the second derivative of t(a). Factor i(r).
(r - 1)**3/5
Let g be 5*(2 - 44/10). Let m be 0 + -1*g/22. Suppose -m - 2/11*o**2 - 8/11*o = 0. Calculate o.
-3, -1
Find m such that 4/9*m**3 - 2/9*m - 2/9*m**5 + 0 + 0*m**4 + 0*m**2 = 0.
-1, 0, 1
Let z = -14 - -17. Let x = z - 1. Suppose 2/11*n**4 + 0*n**x + 2/11*n**3 + 0 + 0*n = 0. Calculate n.
-1, 0
Let u = -2/63 - -79/504. Let t(b) be the second derivative of -u*b**3 + 0 + 3*b + 1/4*b**2 - 5/48*b**4. Factor t(n).
-(n + 1)*(5*n - 2)/4
Let v(g) = g**3 + 3*g**2 + 3*g + 2. Let n be v(-2). Determine q so that 3*q + 0*q**2 - 2*q**3 + n*q**2 - q = 0.
-1, 0, 1
Suppose 4*m + 10 - 42 = 4*r, 5*r = -3*m - 16. Suppose -h + 3 = -2*h, -c - 5*h = 15. Factor -2/11*b**m + 4/11*b**2 + c - 2/11*b.
-2*b*(b - 1)**2/11
Let g be 2 - (2 - (0 + 2)). Let y be (0 - (-1)/(-3))/((-10)/15). Factor l - y*l**g + 0.
-l*(l - 2)/2
Suppose -57*s - 2*s = -177. Factor -1/4*v + 1/4*v**s - 1/4*v**2 + 1/4.
(v - 1)**2*(v + 1)/4
Let o(t) be the third derivative of t**9/20160 - t**7/1680 + t**5/60 - 5*t**2. Let y(l) be the third derivative of o(l). Factor y(g).
3*g*(g - 1)*(g + 1)
Let n(d) = -d**2 - d - 1. Let i(p) = 2*p. Let b = 6 + -8. Let t(q) = b*n(q) - 3*i(q). Factor t(v).
2*(v - 1)**2
Let g(t) be the third derivative of t**9/23520 - t**8/11760 - t**7/882 - t**6/315 + t**5/6 - 6*t**2. Let v(y) be the third derivative of g(y). Factor v(a).
2*(a - 2)*(3*a + 2)**2/7
Let x(j) be the first derivative of 1/12*j**4 - 2 + 1/2*j**2 + 0*j + 2/105*j**5 - 2/21*j**3. Let q(w) be the second derivative of x(w). Factor q(v).
2*(v + 2)*(4*v - 1)/7
Let w(v) be the first derivative of -4*v**6/15 + 6*v**5/25 + v**4/10 - 3. Find a such that w(a) = 0.
-1/4, 0, 1
Let b(m) be the first derivative of -48*m + 24*m**3 + 48*m**2 + 81/5*m**5 - 54*m**4 + 1. Solve b(z) = 0.
-2/3, 2/3, 2
Let w = -648667/161 + 4029. Let l = w - -316/483. Determine d, given that 0*d**2 + 1/3*d**4 - 1/3 + 2/3*d - l*d**3 = 0.
-1, 1
Let k(l) = 2*l**2 - 21. Let r be k(0). Let y be (2/3)/((-35)/r). Factor -y*t**3 - 1/5 + 1/5*t**2 + 2/5*t.
-(t - 1)*(t + 1)*(2*t - 1)/5
Let o(c) be the third derivative of -c**7/840 + 7*c**6/720 - 7*c**5/240 + c**4/24 - 5*c**3/6 - 4*c**2. Let p(b) be the first derivative of o(b). Factor p(k).
-(k - 2)*(k - 1)*(2*k - 1)/2
Let l(i) = i**3 + i**2 - i. Let z(k) = 6*k**3 - 3*k**2 - 5*k. Let h(f) = 20*l(f) - 4*z(f). Factor h(p).
-4*p**2*(p - 8)
Let o(b) be the first derivative of -b**6/1800 - b**5/600 + b**4/60 - 7*b**3/3 + 7. Let f(m) be the third derivative of o(m). Suppose f(v) = 0. Calculate v.
-2, 1
Factor u**4 + 9/2 + 33/2*u + 37/2*u**2 + 15/2*u**3.
(u + 1)*(u + 3)**2*(2*u + 1)/2
Let l(o) be the second derivative of -6*o**2 + 0 + 18*o**3 + 4*o - 81/4*o**4. Factor l(f).
-3*(9*f - 2)**2
Let o(u) be the first derivative of 3*u**5/20 - 27*u**4/16 + 21*u**3/4 - 57*u**2/8 + 9*u/2 + 33. Factor o(t).
3*(t - 6)*(t - 1)**3/4
Let o(q) = -q**2 - 7*q - 2. Let d be o(-6). Let j be d - (0/2 + 1). Factor 0*f**4 - 2*f**3 - f**5 + 2*f**4 + f**j.
-f**3*(f - 1)**2
Let s(y) be the first derivative of -y**7/350 - y**6/200 + 7*y**2/2 - 6. Let w(x) be the second derivative of s(x). Factor w(j).
-3*j**3*(j + 1)/5
Let n be 30/(-105) + 218/126. Let c(s) be the first derivative of -4/3*s - 1/15*s**5 - 1/2*s**4 - 2 - n*s**3 - 2*s**2. Factor c(d).
-(d + 1)**2*(d + 2)**2/3
Determine q, given that -100/7*q**3 - 2*q**5 - 30/7*q + 80/7*q**2 + 4/7 + 60/7*q**4 = 0.
2/7, 1
Let z(a) = 3*a**3 - 4*a**2 - 6*a + 7. Let k(l) = -l**3 + 1. Let n(q) = 6*k(q) - 2*z(q). Factor n(m).
-4*(m - 1)*(m + 1)*(3*m - 2)
Suppose -k + 1 = 0, 3*u = 5*k + 2 - 4. Suppose 9 = 5*w - u. Factor 10*y + 19*y**w - 1 + 2*y + 64*y**3 - 67*y**2.
(4*y - 1)**3
Let q(h) be the second derivative of 0 - 2/3*h**2 + 1/9*h**3 - h + 1/18*h**4. Solve q(l) = 0 for l.
-2, 1
Let d(y) be the second derivative of 5*y**4/6 - y**3 - 2*y**2 + 20*y. Determine a, given that d(a) = 0.
-2/5, 1
Suppose -h = 3*h. Suppose 0 = 2*d - h*d. Factor 0*q + 4/3*q**3 + d + 2/3*q**4 + 2/3*q**2.
2*q**2*(q + 1)**2/3
Let g(l) be the second derivative of l**9/17640 - l**8/4704 + l**7/4410 + l**4/3 - 4*l. Let o(s) be the third derivative of g(s). Solve o(z) = 0.
0, 2/3, 1
Let g = 4/11 + -5/44. Suppose -7*t = -2*t - 10. Factor 0*r - g*r**4 - 1/4 + 1/2*r**t + 0*r**3.
-(r - 1)**2*(r + 1)**2/4
Factor -1/2*k**3 - 1/2 - 3/2*k**2 - 3/2*k.
-(k + 1)**3/2
Let x(g) be the third derivative of -g**6/420 - g**5/105 - g**4/84 + 5*g**2. Factor x(i).
-2*i*(i + 1)**2/7
Let m be -3 - 2/(12/(-22)). Let x be (10/25)/(18/10). Factor 0 - 4/9*v - x*v**3 - m*v**2.
-2*v*(v + 1)*(v + 2)/9
Let l = 461/4 + -115. Let q(n) be the first derivative of -n**2 - 1 - l*n**4 - n**3 + 0*n. Factor q(h).
-h*(h + 1)*(h + 2)
Suppose -5*r = -s - 0*s + 5, 2*s = 5*r. Let k = 6 + r. Suppose 0*q + 0 - 2/3*q**2 - 2/3*q**3 + 2/3*q**k + 2/3*q**5 = 0. Calculate q.
-1, 0, 1
Let n be (-4 + 3)/(2/(-4)). Determine t, given that -t**n + 2*t**2 - 10*t**3 + 4*t**2 - t**2 + 4*t**4 = 0.
0, 1/2, 2
Suppose 5*x + 17 = m - 3*m, -4*x = 20. Factor m*q**2 + q**2 - 3*q**4 + q - 2*q**2 - q**3.
-q*(q - 1)*(q + 1)*(3*q + 1)
Let t(v) = -3*v**3 - 3*v. Suppose -8*n = -9*n + 6. Let b(j) = j. Let u(m) = n*b(m) + t(m). Factor u(i).
-3*i*(i - 1)*(i + 1)
Let i(z) be the third derivative of -z**8/1512 - 2*z**7/945 + z**5/135 + z**4/108 + 15*z**2. Suppose i(u) = 0. Calculate u.
-1, 0, 1
Let y(t) be the second derivative of t**7/15 + t**6/5 + t**5/10 - t**4/6 + t**2/2 - 4*t. Let j(l) be the first derivative of y(l). Factor j(a).
2*a*(a + 1)**2*(7*a - 2)
Let u(o) be the second derivative of -o**6/9 - 4*o**5/15 + 2*o**4/9 + 4*o. Solve u(r) = 0 for r.
-2, 0, 2/5
Suppose -1 = r - 3*m - 0, 5*m = -10. Let a(l) = l + 8. Let t be a(r). Suppose 3*s**3 - s**3 - 6*s - 6 + 1 + t = 0. Calculate s.
-1, 2
Let q be (-8)/24 - (-13)/3. Let i(p) be the second derivative of 1/12*p**q + 3*p + 1/2*p**2 + 1/3*p**3 + 0. Factor i(l).
(l + 1)**2
Let v(k) be the second derivative of -k**7/14 + 3*k**6/10 - 3*k**5/10 - 5*k. Determine y so that v(y) = 0.
0, 1, 2
Let m(y) be the second derivative of -2*y**6/5 + 21*y**5/20 - y**4/2 - y**3/2 + 6*y. Let m(v) = 0. Calculate v.
-1/4, 0, 1
Suppose 3*h - 22 = -7. Suppose 10*z = h*z + 10. Factor -2*c**3 - 2*c**z + 0 + 3 + c**3 + c - 1.
-(c - 1)*(c + 1)*(c + 2)
Let a be (3/2)/(3/6). Factor -1 - i**2 + a - 5 + 4*i**2.
3*(i - 1)*(i + 1)
Let v be (-2)/(-2) - (-11 - -10). Solve 2/7*x**v + 0*x + 0 = 0.
0
Factor -80*j**3 + 20*j**2 - 218*j**5 + 0*j + 25*j**4 + 0*j + 343*j**5.
5*j**2*(j + 1)*(5*j - 2)**2
Let d = 20 - 18. Let t(i) be the second derivative of -2/15*i**3 + 0 - 1/5*i**2 + d*i - 1/30*i**4. Determine f so that t(f) = 0.
-1
Let t(m) = -m**2 - 17*m. Let j(q) = -q**2 - 17*q - 1. Let f(u) = -2*j(u) + 3*t(u). Let d be f(-17). Factor -1/3*x**d - 1/3 + 2/3*x.
-(x - 1)**2/3
Let n(d) be the second derivative of d**5/10 - d**4/30 + 9*d. Factor n(v).
2*v**2*(5*v - 1)/5
Find z, given that 4/3*z**2 + 16/3*z + 16/3 = 0.
-2
Let 42*s**3 + 8*s - s**2 - 3*s**2 - 74*s**3 - 20*s**4 = 0. Calculate s.
-1, 0, 2/5
Factor 0*g**2 + 4*g**2 - 11*g**4 + 15*g**4 + 8*g**3.
4*g**2*(g + 1)**2
Let n(u) be the third derivative of -1/240*u**5 + 0 + 3*u**2 + 0*u + 0*u**4 + 1/2*u**3 + 1/720*u**6. Let v(c) be the first derivative of n(c). Factor v(w).
w*(w - 1)/2
Let x(v) = -5*v**4 - 6*v**3 + 4*v**2 + 1. Let k(o) = 4*o**4 + 5*o**3 - 3*o**2 - 1. Let j(t) = -6*k(t) - 5*x(t). Factor j(z).
(z - 1)**2*(z + 1)**2
Suppose z = 5*w - 20, -w - 4*w - 2*z = -20. Let i = 0 + 3. Suppose i*k**4 + k**w - 3*k**4 = 0. What is k?
0
Let q(c) be the first derivative of c**6/36 - c**5/15 + c**3/9 - c**2/12 + 13. Find s such that q(s) = 0.
-1, 0, 1
Let d be 1 + (-64)/12 + 5. Factor 0*x + d*x**2 - 2/3.
2*(x - 1)*(x + 1)/3