ctor u(n).
2*(n - 1)**3*(n + 1)/5
Find m, given that 8/11 + 2/11*m**4 + 8/11*m + 2/11*m**5 - 10/11*m**2 - 10/11*m**3 = 0.
-2, -1, 1, 2
Let c(h) be the third derivative of 1/6*h**3 - 1/120*h**6 - h**2 + 0 + 1/20*h**5 - 1/8*h**4 + 0*h. Suppose c(i) = 0. What is i?
1
Suppose -3*n = -2*n - 3. Suppose n = 3*z, 2*z + 2*z = -2*c + 8. Factor 2*a**3 + a**3 - 10*a**2 + 8*a**2 + 5*a**c.
3*a**2*(a + 1)
Let h(m) be the second derivative of -1/3*m**4 + 1/15*m**6 - 4*m - 2/3*m**3 + 2/5*m**5 - 2/21*m**7 + m**2 + 0. Solve h(y) = 0 for y.
-1, 1/2, 1
Let h(c) be the third derivative of -c**6/40 - c**5/20 + c**4/8 + c**3/2 - 3*c**2. Find b, given that h(b) = 0.
-1, 1
Suppose 0*i + 0*i**2 + 1/4*i**5 - i**4 + 0 + 3/4*i**3 = 0. What is i?
0, 1, 3
Let d = -739 - -739. Determine q, given that d*q + 19/2*q**2 + 15/2*q**3 - 2 = 0.
-1, -2/3, 2/5
Let r(n) = -n**3 - n**2 - n + 1. Let z(f) = -36*f**4 - 155*f**3 - 72*f**2 + 209*f - 65. Let j(d) = -r(d) - z(d). Factor j(i).
(2*i - 1)**2*(3*i + 8)**2
Let b(u) = -39*u**4 - 45*u**3 + 60*u**2 + 24*u - 24. Let h(v) = -8*v**4 - 9*v**3 + 12*v**2 + 5*v - 5. Let c(a) = -5*b(a) + 24*h(a). Factor c(i).
3*i**2*(i - 1)*(i + 4)
Let g(k) be the third derivative of -1/40*k**6 + 0*k**3 - 1/8*k**4 - 1/10*k**5 + 0 + 2*k**2 + 0*k. Let g(r) = 0. Calculate r.
-1, 0
Determine m so that 0 + 0*m + 0*m**3 + 0*m**2 - 2/7*m**5 + 2/7*m**4 = 0.
0, 1
Factor 1/2*y**3 + 0 - 2*y + 0*y**2.
y*(y - 2)*(y + 2)/2
Let w = -19 + 39/2. Let -w*t**2 - 1/2 - t = 0. What is t?
-1
Let q be 4/(-22) - (-240)/110. Solve 2 - 2*f**3 - 4*f**2 - 1 + f**q = 0.
-1, 1/2
Let y(d) be the first derivative of -d**3/9 + 2*d**2/3 + 4*d - 19. Find j such that y(j) = 0.
-2, 6
Let s(p) be the first derivative of -2*p**3/21 + 7. Factor s(j).
-2*j**2/7
Factor 12/7*f + 1/7*f**3 - 6/7*f**2 - 8/7.
(f - 2)**3/7
Let p be (4 - 69/18)*3. Let x(t) be the first derivative of -p*t - 1/6*t**3 + 1/2*t**2 - 1. What is g in x(g) = 0?
1
Let u(g) be the first derivative of 3*g**4/4 + 5*g**3 + 21*g**2/2 + 9*g - 5. Determine d, given that u(d) = 0.
-3, -1
Let k(p) be the third derivative of 1/84*p**4 + 0*p**5 + 2*p**2 + 0 - 1/420*p**6 + 0*p**3 + 0*p. Find o such that k(o) = 0.
-1, 0, 1
Let y be 1/(-15) + 30/75. Let o(d) be the second derivative of 1/36*d**4 - 1/18*d**3 - y*d**2 - d + 0. Solve o(c) = 0.
-1, 2
Let r(i) be the second derivative of i**9/3024 + i**8/840 + i**7/840 + i**3/2 - 3*i. Let y(k) be the second derivative of r(k). Factor y(u).
u**3*(u + 1)**2
Let l(q) be the second derivative of q**5/110 + q**4/33 - q**3/33 - 2*q**2/11 + 2*q. What is z in l(z) = 0?
-2, -1, 1
Let s(b) be the first derivative of 1/6*b**3 + 0*b**2 - 9/20*b**5 + 7/16*b**4 + 0*b + 5. Factor s(h).
-h**2*(h - 1)*(9*h + 2)/4
Let b be ((-8)/10)/((-6)/15). Determine y, given that 24 + b*y**4 - 6*y**2 - 2*y**3 - 19*y - 20*y**4 + 55*y - 3*y**5 - 31*y**3 = 0.
-2, -1, 1
Let p(s) = -3*s**2 - 27*s - 19. Let k(n) = -4*n**2 - 40*n - 28. Let d(u) = -5*k(u) + 8*p(u). Determine h, given that d(h) = 0.
-3, -1
Suppose 12 = 4*q, 4*z - 4*q + 7 = q. Factor -c - c**5 + c**4 + 2*c**2 + 0*c**2 + z*c**3 - 1 - 2*c**4.
-(c - 1)**2*(c + 1)**3
Let m = -25 + 29. Let l be 4 + (-30)/9 + m. Determine z so that 10/3*z + 4/3 - l*z**2 = 0.
-2/7, 1
Let q(g) be the second derivative of g**7/63 - 2*g**6/9 + 4*g**5/3 - 40*g**4/9 + 80*g**3/9 - 32*g**2/3 + 2*g. Factor q(f).
2*(f - 2)**5/3
Suppose -2*g + 20 = 3*g. Let v(y) be the first derivative of 7/4*y**4 - g*y + 1 - 6*y**2 + 3*y**3. Factor v(l).
(l - 1)*(l + 2)*(7*l + 2)
Let w(m) be the third derivative of -m**8/420 + 8*m**7/525 + 3*m**6/25 + 4*m**5/15 + 7*m**4/30 + 39*m**2. Suppose w(c) = 0. Calculate c.
-1, 0, 7
Let q(l) be the third derivative of -1/12*l**4 + 2*l**2 + 1/15*l**5 + 0 - 1/60*l**6 + 0*l**3 + 0*l. Factor q(p).
-2*p*(p - 1)**2
Let s(c) = 8*c**2 - 11*c + 9. Let l(x) = 17*x**2 - 23*x + 19. Let w(a) = 6*l(a) - 13*s(a). Suppose w(g) = 0. Calculate g.
1, 3/2
Suppose w + 3*d = -4, 4*d + 14 = -0*w + 3*w. Determine k so that 0*k - 1/2*k**w + 1/2 = 0.
-1, 1
Let c(v) be the second derivative of -7/120*v**6 + 7/48*v**4 + 0*v**2 + 3*v + 0 - 1/40*v**5 + 1/12*v**3. Find z such that c(z) = 0.
-1, -2/7, 0, 1
Let r be 1/(-6) - (-140)/(-24). Let q be r/3*2/(-8). Factor -3/2*l**3 - q*l + 1/2*l**4 + 3/2*l**2 + 0.
l*(l - 1)**3/2
Let l(j) be the third derivative of j**8/1176 + 2*j**7/735 - j**6/210 - 4*j**5/105 - j**4/12 - 2*j**3/21 - j**2. Factor l(h).
2*(h - 2)*(h + 1)**4/7
Let f(l) be the second derivative of -l**4/48 + l**3/8 - l**2/4 + 4*l. Factor f(t).
-(t - 2)*(t - 1)/4
Let x(v) = -4*v**4 - 6*v**3 + 18*v**2 - 14*v. Let o(g) = 4*g**4 + 5*g**3 - 17*g**2 + 13*g. Let s(l) = -6*o(l) - 5*x(l). Factor s(w).
-4*w*(w - 1)**2*(w + 2)
Suppose z + 1 - 5 = 0. Suppose 2*k - 6 = -4*j - 0*k, z*j + 3*k = 5. Factor j*v**2 + 0*v**4 + v**4 - 3*v**4.
-2*v**2*(v - 1)*(v + 1)
Let s(g) be the first derivative of 3*g**4/8 + 9*g**3/2 + 81*g**2/4 + 81*g/2 + 1. Determine o so that s(o) = 0.
-3
Factor -4/3*j**3 + 19/3*j**2 + 0 + 5/3*j.
-j*(j - 5)*(4*j + 1)/3
Suppose 0*u + u = -u. Let k(n) be the third derivative of 8/105*n**7 + 0*n**4 + 1/60*n**5 + 0*n**3 + u + 0*n - 1/15*n**6 + 3*n**2. Factor k(b).
b**2*(4*b - 1)**2
Let h = -66267/7 + 9315. Let q = 152 + h. Suppose -2/7*i + 0 + q*i**2 = 0. What is i?
0, 1
Factor u**2 - 1/4*u**4 - 3/2*u**3 + 0 + 2*u + 1/4*u**5.
u*(u - 2)**2*(u + 1)*(u + 2)/4
Let n(o) be the first derivative of -2/27*o**3 - 8/9*o**2 - 8/9*o + 1/6*o**4 - 2. Determine q so that n(q) = 0.
-1, -2/3, 2
Let q = -68/3 + 23. Let x = q - 1/12. Factor -w - w**3 - 1/4 - 3/2*w**2 - x*w**4.
-(w + 1)**4/4
Let h(l) be the second derivative of l**8/112 + l**7/35 + l**6/40 + l**2 - 4*l. Let p(r) be the first derivative of h(r). Factor p(i).
3*i**3*(i + 1)**2
Let z = 14 - 6. Suppose 0 = -f, 3 = w + 5*f - 0*f. Suppose -z*d**2 - 7*d**w - 4/3*d + 49/3*d**4 + 0 = 0. What is d?
-2/7, 0, 1
Let -3/4*p**2 - 15/4*p - 3 = 0. What is p?
-4, -1
Suppose -4*m - 9 + 33 = 0. Let g = 11 - 18. Let s(q) = 8*q**3 - 2*q**2 + 2*q. Let w(b) = 9*b**3 - 3*b**2 + 2*b. Let n(z) = g*s(z) + m*w(z). Factor n(d).
-2*d*(d + 1)**2
Let y(s) = -s**5 + s**4. Let d(a) = 7*a**5 - 6*a**4 - 4*a**3 - 2*a**2 + 3*a + 2. Let x(i) = d(i) + 6*y(i). Factor x(f).
(f - 2)*(f - 1)*(f + 1)**3
Let y = -14 - -19. Suppose -588*g**y + 12*g**2 + 74*g**4 - 132*g**3 + 409*g**4 + 4*g - 4*g = 0. Calculate g.
0, 1/4, 2/7
Let a(d) be the first derivative of -d**3/3 - 5*d**2/2 + 6*d - 9. Solve a(s) = 0 for s.
-6, 1
Suppose 4*l + l = 20. Suppose z + 5*f - 8 = 20, 0 = z - l*f + 17. Let -5*o**4 + 6*o**2 - 5*o**5 + 3*o**5 - o**4 + 5*o**5 - 3*o**z = 0. What is o?
-1, 0, 1, 2
Let d = -1077/70 - -77/5. Let q(p) be the second derivative of 0*p**2 + d*p**5 + 0 - 1/42*p**4 + 2*p + 0*p**3. Factor q(b).
2*b**2*(b - 1)/7
Let b = 103 + -203/2. Factor 3*l**2 + 0 - b*l - 3/2*l**3.
-3*l*(l - 1)**2/2
Let a = -85 - -37. Let r be (40/a)/((-15)/9). Solve j + r*j**2 + 1/2 = 0 for j.
-1
Let f(j) = j**3 + 1. Let g be f(-1). Let p(z) be the third derivative of -3*z**2 - 1/20*z**5 + 0*z + 0*z**3 + 0 + g*z**4 + 0*z**6 + 1/70*z**7. Factor p(x).
3*x**2*(x - 1)*(x + 1)
Let z(h) be the second derivative of -h**4/60 + h**3/10 - h**2/5 + 9*h. What is t in z(t) = 0?
1, 2
Let t be 0/(2/(-3)*-3). Let w = -413/4 - -104. Determine j, given that -1/2 + w*j**5 + 5/2*j**3 + 5/2*j**4 + t*j**2 - 5/4*j = 0.
-1, 2/3
Let i be 1 + 1 + 8/(-4). Suppose -2*o**3 + 2 + 6*o**2 + i*o**3 + 2*o - 8*o = 0. Calculate o.
1
Suppose 5 + 7 = 6*w. Let b(p) be the third derivative of -w*p**2 + 7/24*p**4 + 0 + 0*p + 1/12*p**5 + 1/3*p**3. Factor b(x).
(x + 1)*(5*x + 2)
Factor -2/3*l + 2/3*l**3 + 0*l**2 + 1/3*l**4 - 1/3.
(l - 1)*(l + 1)**3/3
Let z(n) be the first derivative of -5*n**6/12 + n**5 - 5*n**3/3 + 5*n**2/4 - 23. Determine u so that z(u) = 0.
-1, 0, 1
Let a be 5 - (-1 - -4) - -2. What is f in 1 - a + 15*f**2 + 24*f - 9 = 0?
-2, 2/5
Factor 19*a**3 - 7*a**3 + 3 + 2*a**4 + 12*a + a**4 + 18*a**2.
3*(a + 1)**4
Let j be (-20)/(-3) - (-9)/27. Factor 3 + 2*f**4 + 1 + 3*f**2 - 2 - j*f**2.
2*(f - 1)**2*(f + 1)**2
Let w(d) = -d - 5. Let o be w(-9). Suppose 0 = -o*m - 4, 4*m - 3 = -4*b + 1. Factor v**3 + 0*v + 1/2*v**4 + 0 + 1/2*v**b.
v**2*(v + 1)**2/2
Let j(d) be the first derivative of 10*d**6 + 9*d**5/5 - 33*d**4/2 - 3*d**3 + 3*d**2 + 8. Suppose j(x) = 0. What is x?
-1, 