ind z, given that 0 + 1/3*z**o + 1/3*z = 0.
-1, 0
Suppose 0 = 21*v - 26*v + 20. Let i(g) be the second derivative of 0 + 1/4*g**3 + 0*g**2 + 27/40*g**5 - 3/4*g**v + g. Factor i(s).
3*s*(3*s - 1)**2/2
Let n(g) = 3*g**2 - g + 9. Let q(r) = -2*r**2 - 5. Let k(x) = 3*n(x) + 5*q(x). Let c be k(-3). Factor -3*v**3 + 3*v - 1 - v**2 + 0*v**c + 3 - 1.
-(v - 1)*(v + 1)*(3*v + 1)
Let j be (-1)/(-2)*(-22 - -22). Factor -1/4*x**2 + 0 + j*x.
-x**2/4
Let l(k) = -2*k. Let y be l(-1). Let g be (-2)/7 + (-32)/(-63). Suppose 0 + g*j + 2/3*j**y = 0. What is j?
-1/3, 0
Let m(z) be the third derivative of z**8/20160 + z**7/5040 - z**6/360 - z**5/60 + 4*z**2. Let a(l) be the third derivative of m(l). Factor a(b).
(b - 1)*(b + 2)
Let l(o) be the first derivative of -o**6/75 - o**5/50 + o**4/30 + o**3/15 + 3*o - 3. Let u(q) be the first derivative of l(q). Suppose u(h) = 0. Calculate h.
-1, 0, 1
Let y(d) be the third derivative of 0 + 2/945*d**7 + 1/540*d**6 + 0*d + 0*d**5 + 5*d**2 + 1/1512*d**8 + 0*d**4 + 0*d**3. Factor y(g).
2*g**3*(g + 1)**2/9
Let n(q) be the first derivative of -q**5/5 + 3*q**4/4 + 3*q**3 + 5*q**2/2 + 21. Factor n(u).
-u*(u - 5)*(u + 1)**2
Let i(g) be the first derivative of -g**5/10 - g**4/8 + g**3/2 + 5*g**2/4 + g - 21. Factor i(c).
-(c - 2)*(c + 1)**3/2
Let z = -44 - -46. Let q(g) be the third derivative of 1/270*g**5 + 0*g - 1/54*g**4 - 2*g**z + 0 + 1/27*g**3. Factor q(y).
2*(y - 1)**2/9
Let c be 15/(-156) + 5/20. Let 8/13*g**3 - 8/13*g + c - 2/13*g**2 = 0. What is g?
-1, 1/4, 1
Let a(g) be the first derivative of 5 - 1/21*g**6 + 1/7*g**2 - 4/35*g**5 + 0*g**4 + 4/21*g**3 + 0*g. Let a(o) = 0. What is o?
-1, 0, 1
Determine o so that -1/7*o**2 + 2/7 + 1/7*o = 0.
-1, 2
Let d(n) = -2*n - 6. Let f be d(-4). Suppose 0 = -f*h, 3*p = -0*p + 3*h. Factor -2*m**2 + 2 + p*m + m - m.
-2*(m - 1)*(m + 1)
Let r(d) be the third derivative of d**8/21 - 13*d**7/210 + d**6/45 - d**3/6 + d**2. Let o(g) be the first derivative of r(g). Factor o(u).
4*u**2*(4*u - 1)*(5*u - 2)
Let j(z) = -z**3 + z**2 + 2*z. Let s(d) = d**3 - 3*d. Let m(n) = -3*j(n) - 2*s(n). Factor m(p).
p**2*(p - 3)
Let x(a) be the second derivative of -35*a**4/12 - 20*a**3/3 - 5*a**2/2 - 10*a. Factor x(w).
-5*(w + 1)*(7*w + 1)
Let x(c) be the third derivative of -c**5/90 - c**4/12 - 2*c**3/9 - 17*c**2. Determine f so that x(f) = 0.
-2, -1
Let w be 1/(-1) - -1*6/1. Find u such that 6/5*u**3 - 2/5*u**4 + 2/5*u**2 + 0 - 4/5*u**w - 2/5*u = 0.
-1, 0, 1/2, 1
Let i be (7/(-4 - 17))/(14/(-12)). Let i*o**3 + 0 + 2/7*o + 4/7*o**2 = 0. Calculate o.
-1, 0
Let u(j) be the second derivative of 1/9*j**3 - 1/3*j**2 + 0 - j - 1/30*j**5 + 1/18*j**4. Factor u(c).
-2*(c - 1)**2*(c + 1)/3
Let q(o) be the first derivative of -2/27*o**3 - 1/18*o**4 + 0*o**2 + 0*o + 3. Factor q(a).
-2*a**2*(a + 1)/9
Let r be 1 - -8 - (0/(-2) - -3). Find h, given that 8/3*h**5 + 0 - 6*h**4 - 4/3*h**3 - 4/3*h + r*h**2 = 0.
-1, 0, 1/4, 1, 2
Let b(d) be the first derivative of 35*d**6/24 + 6*d**5/5 - 31*d**4/16 - 2*d**3 - d**2/2 - 13. Determine u, given that b(u) = 0.
-1, -2/5, -2/7, 0, 1
Let v(t) be the second derivative of -t**5/8 - 65*t**4/24 - 20*t**3 - 45*t**2 - 35*t. Solve v(b) = 0 for b.
-6, -1
Solve -810/17*c**5 + 0 - 684/17*c**4 - 184/17*c**3 + 0*c - 16/17*c**2 = 0.
-2/5, -2/9, 0
Let i = 20 + -14. Let y(p) be the third derivative of 1/144*p**8 + 0 - 3*p**2 + 0*p - 1/9*p**3 + 4/45*p**5 + 13/315*p**7 + 17/180*p**i - 1/72*p**4. Factor y(z).
(z + 1)**4*(7*z - 2)/3
Let p(q) = -q**3 - 4*q**2 - 5*q - 4. Let b be p(-3). Let w(d) be the first derivative of 0*d - 3/10*d**b - 3/5*d**3 - 1. Suppose w(h) = 0. Calculate h.
-1/3, 0
Let n(y) be the first derivative of -y**5/20 + y**4/4 - y**3/4 - y**2/2 + y - 13. What is t in n(t) = 0?
-1, 1, 2
Suppose -3*r = -15 - 9. Find j such that -16*j**3 - r + 8 + 28*j**2 + 7*j - 15*j - 16*j**4 = 0.
-2, 0, 1/2
Suppose 0 = -8*b + 3*b. Suppose b - 1/2*s**3 + 0*s - s**2 = 0. Calculate s.
-2, 0
Let f(p) be the first derivative of 2/9*p**3 + 0*p + 0*p**2 - 5/6*p**4 - 3. Let f(j) = 0. Calculate j.
0, 1/5
Let f(z) be the third derivative of 0*z**5 + 0*z**3 + 1/156*z**4 + 3*z**2 + 0*z + 0 - 1/780*z**6. Solve f(s) = 0.
-1, 0, 1
Let d(i) = 5*i**2 - 65*i + 145. Let p(g) = g**2 - 11*g + 24. Let x(c) = -6*d(c) + 35*p(c). Factor x(f).
5*(f - 2)*(f + 3)
Suppose -a - 5 + 9 = 0. Factor 0*s**2 + 2/5*s**5 + 2/5*s**3 + 0*s - 4/5*s**a + 0.
2*s**3*(s - 1)**2/5
Let m(t) be the second derivative of -t**4/4 + t**3/2 + 3*t. Factor m(k).
-3*k*(k - 1)
Suppose 2*l + 4*r = 3*l + 7, l + 5 = 3*r. Let i be l - ((-125)/15 + 0). Find x, given that 8/3*x**3 + 2*x - 14/3*x**5 + i*x**2 - 4/3 - 8*x**4 = 0.
-1, 2/7, 1
Suppose -3*q + 4 = -q. Factor -4 + 0*w**2 + 5*w**3 - 12*w + w**q - 4*w**2.
(w - 2)*(w + 1)*(5*w + 2)
Let i = 2/163 + -557/58680. Let u(r) be the third derivative of 0 - r**2 - 1/36*r**3 - i*r**5 - 1/72*r**4 + 0*r. Let u(q) = 0. What is q?
-1
Let k = 35 - 33. Let l(y) be the second derivative of -2/3*y**3 + 1/15*y**6 + 0 + y - y**k + 0*y**4 + 1/5*y**5. Factor l(x).
2*(x - 1)*(x + 1)**3
Suppose d - z + 35 = 5*d, 2*z = -3*d + 25. Factor -5*b**2 - 9 - 3*b**4 - 31*b**2 - d*b**3 - 30*b - 9*b**3.
-3*(b + 1)**3*(b + 3)
Determine o so that 1057*o**2 + 36 - 526*o**2 + 12*o - 530*o**2 = 0.
-6
Let r(o) be the third derivative of -o**8/84 - 4*o**7/105 - o**6/30 - 24*o**2. Factor r(g).
-4*g**3*(g + 1)**2
Let r(j) = -j**3 + 8*j**2 - 7*j + 3. Let b be r(7). Suppose -q + b + 0 = 0. Factor 4 - 4 - 2*m**2 - m**q.
-m**2*(m + 2)
Let g(b) be the second derivative of -3*b + 0 + 1/24*b**4 - 1/6*b**3 - 1/240*b**5 - b**2. Let q(a) be the first derivative of g(a). Solve q(t) = 0 for t.
2
Let s = 899 + -4512/5. Let c = -3 - s. Determine u so that 2/5*u**4 + 0 - 2/5*u**2 - 2/5*u**3 + c*u = 0.
-1, 0, 1
Factor 12*o**2 - o**3 - 2*o**2 - 4*o**3.
-5*o**2*(o - 2)
Let b(q) be the second derivative of q**5/70 + q**4/14 + 64*q. Factor b(c).
2*c**2*(c + 3)/7
Suppose 3*p + 3 = 4*p. Factor -2*y**2 - 3*y**p + y**4 - 4*y**4 + y**2 - y**5.
-y**2*(y + 1)**3
Factor -8*p**3 + p**5 + 3*p**3 + 4*p**5.
5*p**3*(p - 1)*(p + 1)
Let m(p) be the first derivative of -3*p**4/16 - p**3/4 + 3*p**2/4 + 2. Solve m(u) = 0 for u.
-2, 0, 1
Let h(n) be the second derivative of n**7/1260 + n**6/540 - n**5/180 - n**4/6 - 3*n. Let w(q) be the third derivative of h(q). Factor w(x).
2*(x + 1)*(3*x - 1)/3
Let b(x) be the third derivative of -x**5/12 + 115*x**4/72 - 35*x**3/9 - 2*x**2 + 8. Solve b(j) = 0.
2/3, 7
Suppose 12*t = t + 77. Let g(v) be the third derivative of 0*v + 0 + 1/160*v**6 + 0*v**3 - 1/80*v**5 + 1/96*v**4 + 2*v**2 - 1/840*v**t. Factor g(i).
-i*(i - 1)**3/4
Let j(b) be the third derivative of b**5/20 + b**4/24 - 2*b**2. Factor j(h).
h*(3*h + 1)
Let f(h) = h**2 + 1. Let a(l) be the first derivative of -3*l**4/2 + 7*l**3 - 6*l**2 + 9*l - 1. Let w(r) = -a(r) + 6*f(r). Determine q, given that w(q) = 0.
1/2, 1
Suppose -5*h + 85 - 75 = 0. What is t in 2*t + 4*t**h + 4*t**3 + 2/5*t**5 + 2/5 + 2*t**4 = 0?
-1
Let c(t) = -t**4 - t**3 + t**2 + t - 1. Let b(p) = p**4 - 11*p**3 + 9*p**2 + p - 1. Let o(n) = -b(n) + c(n). Let o(s) = 0. What is s?
0, 1, 4
Let v(g) be the first derivative of 7*g**4/3 - 4*g**3/3 - 8*g**2/3 + 10. Factor v(x).
4*x*(x - 1)*(7*x + 4)/3
Let t = 2 - -1. Suppose -t*x + 2*x = 0. Solve -2*g**2 + 0*g**4 + 2*g**4 + x*g**2 = 0 for g.
-1, 0, 1
Suppose 5*l = -12 + 37. Let u(f) be the third derivative of 0*f - f**2 - 1/3*f**3 + 0 - 1/30*f**l + 1/6*f**4. Factor u(g).
-2*(g - 1)**2
Let y = -5/873 - 131798/4365. Let v = -30 - y. Factor -1/5*l + 1/5 + 1/5*l**3 - v*l**2.
(l - 1)**2*(l + 1)/5
Let g(a) be the third derivative of -a**5/60 - 3*a**2. Let f(z) = -8*z**2 + 27*z - 6. Let y(b) = f(b) + 4*g(b). Find c such that y(c) = 0.
1/4, 2
Find w such that -2*w**4 + 2*w**2 - 2*w**3 + 0*w**4 - 12*w**5 + 14*w**5 = 0.
-1, 0, 1
Let n(z) = -z**2 + 2*z - 3. Let w(l) = 2*l**2 - 296 - 2*l + 301 - l. Let s be -4 + (1 - 1) + -1. Let t(j) = s*n(j) - 3*w(j). Suppose t(c) = 0. What is c?
-1, 0
Let d(a) = 1 + a**2 - 7 - 2*a - 5*a + 0. Let r be d(8). Factor 2/7*v**r - 2/7*v + 0.
2*v*(v - 1)/7
Let i = -18 + 20. Let j = 251/3 + -83. Factor j*x**3 - 2/3*x + 1/3*x**4 - 1/3 + 0*x**i.
(x - 1)*(x + 1)**3/3
Suppose 6*d + 1 = 25. Determine s, given that 1/2*s**2 + 0 + s**3 + 0*s + 1/2*s**d = 0.
-1, 0
Suppose -3*p = -v