 2)**2*(5*l + 2)/5
Let v(z) be the second derivative of 0 + 1/80*z**5 + 1/48*z**4 + 0*z**2 - 1/120*z**6 - 5*z - 1/24*z**3. Factor v(m).
-m*(m - 1)**2*(m + 1)/4
Let j(v) be the second derivative of v**7/840 - v**5/120 - v**3/3 - 2*v. Let y(p) be the second derivative of j(p). Let y(c) = 0. What is c?
-1, 0, 1
Let c(k) be the third derivative of -2*k**8/189 - 8*k**7/189 - 11*k**6/180 - k**5/27 - k**4/108 + 2*k**2. Determine r so that c(r) = 0.
-1, -1/4, 0
Let t(w) = -3*w**2 + 15*w - 21. Suppose 0 = 5*z - 5, 4*z = 4*o - 5 + 1. Let l(m) = m**2 - 4*m + 5. Let v(s) = o*t(s) + 9*l(s). Suppose v(a) = 0. Calculate a.
1
Let l(c) be the first derivative of c**4/34 + 2*c**3/51 - 30. Suppose l(d) = 0. What is d?
-1, 0
Let b = 72 + -287/4. Factor -1/4*w**3 + 0*w - 1/4*w**4 + b*w**2 + 1/4*w**5 + 0.
w**2*(w - 1)**2*(w + 1)/4
Let t(k) = k**2 + 6*k - 5. Let h(s) = s**2 + 3*s - 2. Let q(a) = 5*h(a) - 2*t(a). Factor q(c).
3*c*(c + 1)
Let z(q) be the second derivative of -q**7/147 + q**6/105 - 28*q. Factor z(o).
-2*o**4*(o - 1)/7
Find y such that 0*y**2 + 0 - 3/4*y**3 + 3/4*y = 0.
-1, 0, 1
Let z(w) = -w - 3. Let i be z(-5). Determine s so that 4*s + 4 - 14*s**i + 6*s + s - s = 0.
-2/7, 1
Suppose 0*a + 1/2*a**3 - 2 + 3/2*a**2 = 0. Calculate a.
-2, 1
Let n(p) = 4*p - 56. Let z be n(15). Let g(o) be the first derivative of 0*o + 2 + 6/5*o**5 + 0*o**2 + 0*o**3 - 3/4*o**z - 1/2*o**6. Factor g(b).
-3*b**3*(b - 1)**2
Solve -22/3*n + 22/3*n**2 + 8/3*n**5 + 4/3 + 14/3*n**3 - 26/3*n**4 = 0.
-1, 1/4, 1, 2
Let g(q) be the third derivative of q**7/630 + q**6/180 - q**5/180 - q**4/36 - 39*q**2. Determine d, given that g(d) = 0.
-2, -1, 0, 1
Let p(x) = x**4 + x**2 - 1. Let o(n) = -4*n**4 + 2*n**3 - 12*n**2 - 10*n + 2. Let t(c) = -2*o(c) - 12*p(c). Factor t(f).
-4*(f - 2)*(f + 1)**3
Let o(t) be the second derivative of t**2 + 0 - 4*t - 1/20*t**5 - 5/6*t**3 + 1/3*t**4. Suppose o(s) = 0. Calculate s.
1, 2
Factor 0 - 1/2*n**3 + 0*n + 2*n**2.
-n**2*(n - 4)/2
Let k(j) be the third derivative of -j**5/12 - 5*j**4/3 - 40*j**3/3 + 28*j**2. Solve k(w) = 0 for w.
-4
Let l(g) be the third derivative of g**7/735 - g**5/210 + 11*g**2. Factor l(d).
2*d**2*(d - 1)*(d + 1)/7
Let d be 1/1 + 3 + 1. Suppose 3*p - 1 = -i, 2*i + 4 = -2*p - 2. Solve v**p - 3/5*v**3 - 1/5*v - v**4 + 4/5*v**d + 0 = 0.
-1, 0, 1/4, 1
Let w(g) = g**3 - 6*g**2 + 4*g + 7. Let v be w(5). Factor 2*y + v + 3*y + 4*y**2 + 0 + 0*y**2 + y**3.
(y + 1)**2*(y + 2)
Let r = -44 + 48. Let g(a) be the first derivative of 0*a + 0*a**3 - 1/7*a**2 + 1/14*a**r - 2. Factor g(w).
2*w*(w - 1)*(w + 1)/7
Let x(c) be the third derivative of 0*c**5 + 1/18*c**3 - 1/630*c**7 + 1/180*c**6 + 0 - 1/36*c**4 + 0*c - 2*c**2. Find w such that x(w) = 0.
-1, 1
Let z = 3633/4 - 906. Suppose 1/4*x**2 + z + 3/2*x = 0. Calculate x.
-3
Let t(u) be the second derivative of 3*u**5/20 - u**3/2 + 28*u. Factor t(o).
3*o*(o - 1)*(o + 1)
Let d = 11/51 - -2/17. Let s(z) be the first derivative of d*z**3 + z - 3 - z**2. Find j such that s(j) = 0.
1
Let r(p) = 21*p**3 - 13*p**2 - 5*p - 5. Let h(l) = -32*l**3 + 20*l**2 + 8*l + 8. Let f(n) = -5*h(n) - 8*r(n). Determine m so that f(m) = 0.
0, 1/2
Let j(v) be the third derivative of 1/18*v**3 + 0*v + 1/180*v**5 + 0 - 1/36*v**4 - v**2. Factor j(k).
(k - 1)**2/3
Let g(b) be the third derivative of -b**8/168 + b**7/105 + b**6/5 - 14*b**5/15 + 4*b**4/3 + 41*b**2. Suppose g(w) = 0. What is w?
-4, 0, 1, 2
Suppose 61*m**3 + 7*m - 69*m**3 - 55*m - 36*m**2 - 16 = 0. What is m?
-2, -1/2
Suppose -8 = -2*o - 2*h, 4*o + 3*h = h + 14. Factor -2/11*n + 2/11*n**o + 4/11 - 4/11*n**2.
2*(n - 2)*(n - 1)*(n + 1)/11
Let n be 56/120 + 1/5. Let s = -6/29 + 76/87. Factor -n*h**3 + 2/3*h + 0 - 2/3*h**2 + s*h**4.
2*h*(h - 1)**2*(h + 1)/3
Let u(a) be the second derivative of 0 - 2*a + 0*a**2 - 1/20*a**5 - 1/6*a**4 - 1/6*a**3. Factor u(k).
-k*(k + 1)**2
Let n(u) be the second derivative of -u**7/14 + 2*u**6/5 + 3*u**5/10 - 3*u**4 - 9*u**3/2 + 7*u. Solve n(v) = 0.
-1, 0, 3
Let g(l) be the first derivative of l**4/16 - l**3/4 + 3*l**2/8 - l/4 - 4. What is c in g(c) = 0?
1
Let i be ((-128)/224)/((-78)/21). Factor 0*z + 2/13*z**4 + 0 - i*z**2 + 0*z**3.
2*z**2*(z - 1)*(z + 1)/13
Suppose -2*k + 12 = 2*k. Suppose -r + k = 1. Factor 0*t**2 - t**3 + 3*t**3 + 2*t**r.
2*t**2*(t + 1)
Let i = -1/49 - -67/882. Let b(d) be the third derivative of d**2 + i*d**4 + 1/180*d**5 + 0*d + 0 + 2/9*d**3. Factor b(y).
(y + 2)**2/3
Solve 16/7 - 2/7*l**2 - 2*l = 0.
-8, 1
Let z = -4 - -5. Let v be z*(0 - 6/(-3)). Factor -4*x**3 + v*x**2 + 2*x**4 - 3*x**3 + 3*x**3.
2*x**2*(x - 1)**2
Let n(q) = q**4 + q + 1. Let u(w) = 16*w**4 - 6*w**3 + 2*w**2 + 24*w + 18. Let v(a) = -36*n(a) + 2*u(a). Let v(o) = 0. Calculate o.
-3, -1, 0, 1
Let q be (-1)/(1/((-1)/1)). Suppose -2*x + q = -3*k, -3*x + 9 = 4*k - k. Factor h**x - 4*h - 3*h**2 + 6*h.
-2*h*(h - 1)
Let h(k) be the second derivative of k**4/6 - 16*k**3/3 + 64*k**2 - 42*k. What is b in h(b) = 0?
8
Let b(c) = -13*c**4 + 63*c**3 - 61*c**2 + 12*c + 11. Let d(k) = -k**4 - k**3 - k**2 - 1. Let q(f) = -b(f) - 3*d(f). Find r such that q(r) = 0.
-1/4, 1, 2
Suppose 5*d = -2*c - 8, 0*d - 5 = d - 3*c. Let m = 4 + d. Solve 0*l**m + 2*l**4 + l**2 - 2 - l**2 + 4*l - 4*l**3 = 0.
-1, 1
Suppose 3*c - 7*q = -2*q - 6, -5 = -c + 4*q. Let j be c/21*(-1 + 1). Factor -3/5*k**3 + 0*k + j*k**2 + 0.
-3*k**3/5
Let z = 50/27 + -41/27. Factor -1/3*l + z - 2/3*l**2 - 1/3*l**5 + 2/3*l**3 + 1/3*l**4.
-(l - 1)**3*(l + 1)**2/3
Let y be -3 + (-87)/(-33) + 1. Let w = -3/22 + y. Factor o + w*o**2 + 1/2.
(o + 1)**2/2
Let r(c) be the second derivative of 8*c + 13/20*c**5 + 1/4*c**4 + 0*c**2 + 0*c**3 + 0 + 2/15*c**6. Factor r(p).
p**2*(p + 3)*(4*p + 1)
Suppose -3*g + 39 = 5*u, -3*u = g - 0*g - 21. Let l be 3 - 12/(-2 + u). Factor 4/3*a**3 + 0*a**2 - 14/3*a**4 + l + 0*a + 10/3*a**5.
2*a**3*(a - 1)*(5*a - 2)/3
Suppose 6*q = 9*q. Let d(o) be the first derivative of 0*o + 0*o**3 - 2 + q*o**2 + 2/5*o**5 + 1/2*o**4. Let d(p) = 0. Calculate p.
-1, 0
Let d(n) = -4*n**2 + 16*n + 4. Let i(w) = 1. Let a(m) = d(m) - 4*i(m). Solve a(g) = 0 for g.
0, 4
Let u(s) = s**2 - 9*s + 6. Let w be u(8). Let g(d) = d**2 - d. Let k(i) = i**3 + 9*i**2 - 6*i. Let q(f) = w*k(f) + 14*g(f). Factor q(y).
-2*y*(y + 1)**2
Let v(p) be the second derivative of 5*p**7/84 - p**6/6 + p**5/8 - 3*p - 3. Determine n, given that v(n) = 0.
0, 1
Suppose -p - 7 + 17 = 0. Factor -9*v - v**2 + 2*v + p*v**2 + v.
3*v*(3*v - 2)
Let q(p) be the first derivative of p**6/720 + p**5/120 + 2*p**3/3 + 2. Let u(w) be the third derivative of q(w). Factor u(t).
t*(t + 2)/2
Let m(v) be the third derivative of -v**8/30240 - v**7/1890 - v**6/270 - v**5/60 + v**2. Let x(u) be the third derivative of m(u). Factor x(i).
-2*(i + 2)**2/3
Let -3*w - 2/3 - 4/3*w**2 = 0. Calculate w.
-2, -1/4
Let f(i) = 0 + 2 + 4 + 3 - 5*i**2 + 11*i - 2*i**3. Let r(o) = -3*o**3 - 8*o**2 + 17*o + 14. Let u(v) = 8*f(v) - 5*r(v). Factor u(p).
-(p - 2)*(p + 1)**2
Let t(z) be the second derivative of 1/7*z**2 + 4*z + 0 + 0*z**3 - 1/42*z**4. Find y such that t(y) = 0.
-1, 1
Let w(f) be the third derivative of f**10/40320 + f**9/10080 + f**8/8960 + f**4/12 + 3*f**2. Let q(z) be the second derivative of w(z). Factor q(m).
3*m**3*(m + 1)**2/4
Let l(z) be the first derivative of 2*z**3/21 - 4*z**2/7 + 8*z/7 - 15. Factor l(f).
2*(f - 2)**2/7
Suppose 4*o = -4 + 20. Suppose 2/9*z + 0 + 0*z**3 - 4/9*z**2 + 4/9*z**o - 2/9*z**5 = 0. Calculate z.
-1, 0, 1
Let n(u) be the second derivative of 0*u**2 - u**4 + 0 + 0*u**3 + 19/10*u**6 - 6/5*u**5 - 1/2*u**7 + 5*u. Suppose n(a) = 0. What is a?
-2/7, 0, 1, 2
Let f = 68 - 46. Let g = f + -19. Factor 1/3*n**5 + n**g - n**4 - 1/3*n**2 + 0*n + 0.
n**2*(n - 1)**3/3
Let h(r) = -r**2 + 7*r - 6. Let j be h(6). Find t such that 2/11*t**2 + 0 + j*t = 0.
0
Let s(q) = -q**3 + 46*q**2 - 44*q - 44. Let x be s(45). Suppose x - 1/4*k**3 + 5/4*k**2 - 2*k = 0. Calculate k.
1, 2
Let l(b) be the second derivative of b**6/105 + 3*b**5/70 + b**4/21 - 2*b. Factor l(m).
2*m**2*(m + 1)*(m + 2)/7
Determine f, given that -1/2*f**2 + 0*f + 2 = 0.
-2, 2
Factor 3/2*y**3 - 3/2*y**2 + 0*y + 0.
3*y**2*(y - 1)/2
Let k = 36 - 71. Let j = k + 178/5. Solve -1/5 + j*d**2 + 0*d + 2/5*d**3 = 0 for d.
-1, 1/2
Suppose -5*d - 3*m + 28 = 0, 5*d + 2*m - 24 = 3. Let p(u) be the thi