1)
Let h(i) be the third derivative of -i**5/80 - i**4/32 + 12*i**2. Solve h(b) = 0 for b.
-1, 0
Suppose 2*k = 4*y - 3*k - 32, -2*y + 22 = -4*k. Find s such that -4*s**2 + y*s**2 + 0 - 12*s - 3*s**2 - 8 = 0.
-2, -1
Let c = 6/157 + 284/785. What is d in 4/5 + 8/5*d**2 - 2*d - c*d**3 = 0?
1, 2
Let b(x) be the third derivative of -x**9/30240 + x**8/10080 - x**5/20 - 3*x**2. Let a(i) be the third derivative of b(i). Suppose a(h) = 0. Calculate h.
0, 1
Let v = -1276 + 1279. Let -1/4*t**v + t**2 + 0 + 0*t = 0. What is t?
0, 4
Let q(n) be the second derivative of 1/15*n**6 + 1/3*n**3 - 1/6*n**4 + n + 0*n**2 - 1/10*n**5 + 0. Suppose q(p) = 0. Calculate p.
-1, 0, 1
Let j(r) be the first derivative of -2/15*r**3 - 2/5*r - 2/5*r**2 - 1. Factor j(h).
-2*(h + 1)**2/5
Let q be 2 - (1/(-1) + 2). Let p = q + 1. Factor -p*y + 0 - 2*y**4 + 4*y**3 - 2*y + 2 + 0.
-2*(y - 1)**3*(y + 1)
Let t(p) = 3*p**2 - 6*p + 3. Let r(n) = 48*n**2 - 96*n + 48. Let y = -11 + 13. Let g(m) = y*r(m) - 33*t(m). Suppose g(s) = 0. What is s?
1
Let x(b) be the first derivative of b**4/4 - 2*b**3/3 - b**2/2 + 2*b - 11. Factor x(p).
(p - 2)*(p - 1)*(p + 1)
Suppose -3*p = -5*u - 78 + 21, 4*p + 29 = -5*u. Let c be 2 - -5*3/u. Factor 1/3*g**3 - 1/3*g - c + 1/3*g**2.
(g - 1)*(g + 1)**2/3
Let w be ((-1)/(-1) + -3)*-1. Suppose w*t = -2*t + 4. Factor -12 + 2*y**2 - 7 + t - 12*y - 4*y**2.
-2*(y + 3)**2
Determine o, given that 0*o - 3/7*o**4 + 3/7*o**2 - 3/7*o**5 + 0 + 3/7*o**3 = 0.
-1, 0, 1
Suppose -3*q = -u - 6, 2*q - 4*q - 2*u + 12 = 0. Suppose 0 = 3*w - 3 - q. Suppose 10/11*s**4 - 14/11*s**3 + 8/11*s + 0 - 16/11*s**w = 0. Calculate s.
-1, 0, 2/5, 2
Suppose 2*a = -3*a + 5*z + 35, a + z - 11 = 0. Let b = a - 9. Solve 2/3 + 4/3*i - 2/3*i**4 - 4/3*i**3 + b*i**2 = 0.
-1, 1
Suppose -f = 3, 0*u - u = f. Suppose -u*v + 2*i + 4 = -1, -2*v = -3*i. Find g, given that 3*g - 7*g**5 + g - 18*g**3 - v*g**5 + 3*g**2 - 26*g**4 - g**2 = 0.
-1, 0, 2/5
Let a(q) = 0*q - 7*q**2 + 2*q + 2*q + 3*q**3 - 7. Let c(b) = -b + b**3 - b**2 + 3*b - 2*b**2 - 3. Let d(u) = -3*a(u) + 7*c(u). Factor d(v).
-2*v*(v - 1)*(v + 1)
Let l be 742/(-63) + 4/(-18). Let x be 70/24 + 3/l. Factor -x*t - 2*t**2 - 2/3.
-2*(t + 1)*(3*t + 1)/3
Suppose 13 + 12 = 5*n. Let a be (4/6)/(n/15). Find p, given that 0*p - 2/5 + 2/5*p**a = 0.
-1, 1
Suppose 3*j = 2*j + 2. Let i(n) be the first derivative of 0*n**j - n + 1/3*n**3 - 3. Factor i(x).
(x - 1)*(x + 1)
Let o(h) = -2*h**4 - 16*h**3 - 39*h**2 + 57. Let d(f) = -4*f**4 - 32*f**3 - 77*f**2 + 113. Let r(u) = 3*d(u) - 5*o(u). Factor r(j).
-2*(j - 1)*(j + 3)**3
Let n(t) be the third derivative of -t**7/11340 - t**6/1620 - t**5/540 - t**4/4 - 2*t**2. Let o(p) be the second derivative of n(p). Factor o(c).
-2*(c + 1)**2/9
Let j(t) be the first derivative of 2/5*t**5 + 6 + 0*t + t**2 + 3/2*t**4 + 2*t**3. Factor j(d).
2*d*(d + 1)**3
Factor 6/11*l**3 + 48/11 + 72/11*l + 36/11*l**2.
6*(l + 2)**3/11
Suppose 0 = 3*k - h + 9, 5*h + 2 - 23 = 3*k. Let s be (k/((-12)/(-9)))/(-6). Factor -s - 1/2*m**3 + 1/2*m + 1/4*m**4 + 0*m**2.
(m - 1)**3*(m + 1)/4
Let u(n) be the second derivative of -n**9/75600 - n**8/33600 + n**7/12600 + n**6/3600 + n**4/12 + 3*n. Let q(f) be the third derivative of u(f). Factor q(m).
-m*(m - 1)*(m + 1)**2/5
Let q(v) be the third derivative of -v**8/84 + v**6/10 - 2*v**5/15 - 27*v**2. Factor q(u).
-4*u**2*(u - 1)**2*(u + 2)
Let t(h) be the first derivative of h**6/30 - h**4/12 + h - 4. Let j(z) be the first derivative of t(z). Let j(l) = 0. What is l?
-1, 0, 1
Let f(t) be the second derivative of -t**7/126 + t**5/30 - t**3/18 + 18*t. Solve f(a) = 0 for a.
-1, 0, 1
Let g = 6 + -13. Let n(c) = -c**2 - 8*c - 7. Let x be n(g). Solve -6/5*w**4 - 2/5*w**5 + x + 0*w - 2/5*w**2 - 6/5*w**3 = 0.
-1, 0
Let c(f) be the first derivative of -f**5/5 - 5*f**4/4 - f**3 + 5*f**2/2 + 4*f - 7. Solve c(k) = 0.
-4, -1, 1
Let q(w) be the first derivative of -w**4/16 + w**3/6 - 30. Factor q(r).
-r**2*(r - 2)/4
Let z(c) be the first derivative of -3*c**4/14 - 10*c**3/21 - 2*c**2/7 + 46. Find l, given that z(l) = 0.
-1, -2/3, 0
Suppose -6*d + 10 = -d. What is p in -8*p**d + p**3 - 6*p + 7*p**2 + 2*p + p**4 + 3*p = 0?
-1, 0, 1
Let w = 2226/5 + -444. Factor -w*b - 3/5*b**2 + 9/5.
-3*(b - 1)*(b + 3)/5
Let y = -417 + 422. Factor 1/5*v**y + 0*v**3 + 0 + 0*v + 0*v**2 + 0*v**4.
v**5/5
Let l = 2 + 4. Suppose 0 = l*r + 6 - 18. Let 2/3*v**r + 1/3*v**3 + 0 + 0*v = 0. What is v?
-2, 0
Let x(v) be the first derivative of -v**4/16 - v**3/6 + 5*v**2/8 + 3*v/2 + 15. What is i in x(i) = 0?
-3, -1, 2
Let x(f) be the third derivative of -f**5/150 + f**4/15 + 2*f**2 + 20. Factor x(y).
-2*y*(y - 4)/5
Let r(q) be the third derivative of q**8/420 + q**7/1050 - q**6/150 - q**5/300 + 20*q**2. Determine a so that r(a) = 0.
-1, -1/4, 0, 1
Let f(u) be the third derivative of u**7/1260 + u**6/180 + u**4/12 - 2*u**2. Let j(z) be the second derivative of f(z). Determine h so that j(h) = 0.
-2, 0
Let i(t) = -4*t - 34. Let x be i(-9). Suppose -32/11*z**4 - 14/11*z**5 + 0 - 4/11*z**2 - x*z**3 + 0*z = 0. Calculate z.
-1, -2/7, 0
Let s be ((-3)/7)/((-1)/1). Factor s*c + 0 + 12/7*c**4 + 27/7*c**3 + 18/7*c**2.
3*c*(c + 1)**2*(4*c + 1)/7
Let v be 29/28 + (-1)/(14/4). Let 3/4*i + 1/4*i**3 + 1/4 + v*i**2 = 0. What is i?
-1
What is q in -84*q**4 + 9/2 + 27/2*q**3 + 159/2*q**2 - 75/2*q + 24*q**5 = 0?
-1, 1/4, 1, 3
Let m be ((-4)/10)/(56/(-70)). Factor m*p - 1/2 + 9/2*p**2 + 11/2*p**3 + 2*p**4.
(p + 1)**3*(4*p - 1)/2
Suppose -2*z**5 - 2*z - 10*z**2 + 2*z**4 - 4*z**3 + 6*z + 10*z**3 = 0. What is z?
-2, 0, 1
Let w(p) = 2*p**3 - 7*p**2 + 3*p + 5. Let d be w(4). Let 2 + 6 + 1 + d*m**4 + 45*m**5 + 3 + 48*m - 129*m**3 - 9*m**2 = 0. Calculate m.
-2, -2/5, -1/3, 1
Let c(q) = q**2 + 9*q - 6. Let r be c(-10). Let m(k) be the second derivative of -2/27*k**3 - k + 0 + 1/10*k**5 + 0*k**2 + 7/54*k**r. Solve m(d) = 0 for d.
-1, 0, 2/9
Let m(o) be the first derivative of 4*o**5/55 + 5*o**4/22 + 8*o**3/33 + o**2/11 - 12. Suppose m(x) = 0. Calculate x.
-1, -1/2, 0
Suppose -1/3 - 1/6*h**2 - 1/2*h = 0. Calculate h.
-2, -1
Let z(p) = -p**3 + 4*p**2 - 2*p - 1. Let g be z(2). Factor 3*t**3 + 0*t**3 + t**g - 10*t**5 + 3*t**4 + 3*t**4.
-2*t**3*(t - 1)*(5*t + 2)
Let a(f) be the first derivative of f**6/180 - f**5/40 + f**4/36 + 2*f - 9. Let m(c) be the first derivative of a(c). Factor m(z).
z**2*(z - 2)*(z - 1)/6
Let y be (-87)/(-27) + (-2)/9. Let z be 0 - (-3 + (2 - 1)). Factor z*d - d**2 + y*d**2 + 2*d.
2*d*(d + 2)
Let o = -20 + 46. Factor 15*q**4 + 42*q**3 + 21*q**4 - 17*q**4 + o*q**4 + 9*q**2.
3*q**2*(3*q + 1)*(5*q + 3)
Let p(n) = -5*n**3 - 9*n**2 + 45*n + 21. Let g(f) = -7*f**3 - 14*f**2 + 68*f + 32. Let o(i) = 5*g(i) - 8*p(i). Factor o(t).
(t - 2)*(t + 2)*(5*t + 2)
Let b(s) be the first derivative of -s**8/560 - s**7/70 - s**6/24 - s**5/20 - 2*s**3 - 5. Let g(h) be the third derivative of b(h). Find l, given that g(l) = 0.
-2, -1, 0
Let u(j) = j**3 + 7*j**2 - j - 5. Let i be u(-7). Let v be (i - 0)*(-4 + 5). Factor 0*m + 0 - 1/3*m**v.
-m**2/3
Let j(k) be the third derivative of -k**5/540 - 5*k**4/108 - 25*k**3/54 + 17*k**2. Solve j(n) = 0 for n.
-5
Suppose 0 = -4*z - 81 - 39. Let m = -25 - z. Factor 2/9*o**3 - 2/9*o**4 + 2/9*o**2 + 0 + 0*o - 2/9*o**m.
-2*o**2*(o - 1)*(o + 1)**2/9
Suppose 5*m = -5*d - 10, 2*d + 3*d - m - 14 = 0. Suppose -6/5*o + 2/5*o**d + 4/5 = 0. Calculate o.
1, 2
Let j(m) = 25*m**3 + 40*m**2 + 5*m - 6. Let x(z) = 99*z**3 + 159*z**2 + 21*z - 24. Let v(y) = 15*j(y) - 4*x(y). Let v(b) = 0. Calculate b.
-1, 2/7
Let y = -8 + 1. Let f(d) = -d**2 - 5*d + 17. Let t be f(y). Factor 0*w + 0*w**2 + 0 - 1/3*w**t.
-w**3/3
Let d(r) be the second derivative of -2*r + 0*r**3 + 1/12*r**4 + 0 + 0*r**2 + 1/42*r**7 - 1/20*r**5 - 1/30*r**6. Determine y so that d(y) = 0.
-1, 0, 1
Let a be 9 - 5 - (-91)/(-28). Let -a + 3/4*l**2 + 3/4*l**3 - 3/4*l = 0. What is l?
-1, 1
Let a(q) be the third derivative of -q**7/105 - q**6/60 + q**5/10 + q**4/12 - 2*q**3/3 + q**2. Find x, given that a(x) = 0.
-2, -1, 1
Let d be (-465)/(-10) - 2/(-4). Suppose -8*s**4 - 2*s + 8*s**2 + 49*s**3 - d*s**3 + 0*s = 0. Calculate s.
-1, 0, 1/4, 1
Determine c, given that 0 + 0*c**3 + 4/9*c**2 + 0*c - 4/9*c**4 = 0.
-1, 0, 1
Let a(k) be the third derivative of k**6/600 - k**5/50 + k**4/10 - 4*k**3/15 + 6*k**2. Fact