2/3
Let w(n) be the first derivative of 2*n**7/21 - 3*n**5/5 - 2*n**4/3 + 3*n + 2. Let h(r) be the first derivative of w(r). Let h(a) = 0. What is a?
-1, 0, 2
Let t(u) be the first derivative of -u**4/14 + 8*u**3/21 - 5*u**2/7 + 4*u/7 + 10. Suppose t(g) = 0. What is g?
1, 2
Let q(d) = 24*d**4 + 54*d**3 + 23*d**2 - 7*d - 13. Let i(v) = -4*v**4 - 9*v**3 - 4*v**2 + v + 2. Let p(y) = -39*i(y) - 6*q(y). Factor p(t).
3*t*(t + 1)**2*(4*t + 1)
Let 0 - 25/3*k**4 + 0*k - 4/3*k**2 + 20/3*k**3 = 0. What is k?
0, 2/5
Let v(p) = -18*p**5 + 26*p**4 + 2*p**3 - 10*p**2 - 2*p + 2. Let z(k) = k**4 - k**3 - k**2 + 1. Let l(y) = v(y) - 2*z(y). Suppose l(o) = 0. Calculate o.
-1/3, 0, 1
Suppose -6*k = -21 + 9. Factor 243/2*g**2 - 27*g + k - 729/4*g**3.
-(9*g - 2)**3/4
Let t = 1/2 - -1/4. Determine g, given that -1/4*g**4 + 0*g**3 + 0 + t*g**2 - 1/2*g = 0.
-2, 0, 1
Let b be (3*1)/(24/16). Let f(c) be the third derivative of 0*c**4 + 0*c**3 + 0 + 0*c - 1/330*c**5 + b*c**2. Factor f(k).
-2*k**2/11
Let n(p) = 15*p**4 - 21*p. Let q(k) = 2*k + 5*k**4 - 2*k**4 - 6*k. Let a(g) = -4*n(g) + 21*q(g). Factor a(l).
3*l**4
Let t be (-8)/(-15) - (-14)/(-42). Let -1/5*r**2 + t*r**3 - 1/5*r + 1/5 = 0. Calculate r.
-1, 1
What is q in 25*q**2 + 2*q - 189*q**5 + 5*q**3 + 174*q**5 + 8*q - 25*q**4 = 0?
-1, -2/3, 0, 1
Factor -8/3*c + 1/3*c**2 + 1/3*c**3 - 4.
(c - 3)*(c + 2)**2/3
Let w = -1627/528 - -145/33. Let i(v) be the first derivative of -3 - 17/20*v**5 - w*v**4 + 0*v - 1/4*v**2 - 5/24*v**6 - 11/12*v**3. Solve i(y) = 0 for y.
-1, -2/5, 0
Let x(w) = 5*w**3 + 2*w**2 - 23*w - 5. Let c(v) = -10*v**3 - 4*v**2 + 45*v + 11. Let b(i) = 3*c(i) + 5*x(i). Solve b(s) = 0 for s.
-2, -2/5, 2
Suppose 0 = -6*v + 5*v - 5. Let y = -1 - v. Factor y*z**3 + 2*z**4 + z**3 - 2*z**2 - 6*z**3 + z.
z*(z - 1)*(z + 1)*(2*z - 1)
Let i = 67 + -334/5. Let b(m) be the first derivative of -1 - i*m**2 + 4/15*m**3 + 0*m - 1/10*m**4. Let b(r) = 0. Calculate r.
0, 1
Let g(b) = 25*b**3 - 48*b**2 + 14*b + 6. Let a(f) = 100*f**3 - 190*f**2 + 55*f + 25. Let l(q) = -6*a(q) + 25*g(q). Determine d, given that l(d) = 0.
0, 2/5, 2
Let j(x) = 4*x**5 + 2*x**4 + 6*x**3 - 22*x**2 + 22*x - 12. Let c(y) = 5*y**5 + 2*y**4 + 5*y**3 - 21*y**2 + 22*y - 13. Let p(u) = -6*c(u) + 7*j(u). Factor p(v).
-2*(v - 1)**4*(v + 3)
Let o(c) be the first derivative of -c**4/42 - 4*c**3/63 - c**2/21 - 22. Factor o(p).
-2*p*(p + 1)**2/21
Let s be 14/28 - (-3)/2. Solve g**5 - 2*g**3 + g - 1/2*g**4 - 1/2 + g**s = 0.
-1, 1/2, 1
Let k(u) = u**3 + 7*u**2 - 40*u + 46. Let o be k(-11). Factor -4/7*q**3 + 2/7*q**5 + 0*q - 2/7*q**4 + 0 + 0*q**o.
2*q**3*(q - 2)*(q + 1)/7
Let d(l) be the second derivative of -l**5/150 - l**4/60 - 3*l**2/2 + 2*l. Let h(t) be the first derivative of d(t). Factor h(p).
-2*p*(p + 1)/5
Let b(j) = j**2 + 14*j. Let o be b(-14). Find h, given that -2/7*h**2 + 2/7*h + o = 0.
0, 1
Let l(x) = 4*x**2 + 4. Let s(f) = f**2. Let p(v) = l(v) - 5*s(v). Let p(d) = 0. Calculate d.
-2, 2
Let d(y) be the third derivative of -1/168*y**8 - 1/10*y**6 - 4/105*y**7 - 2/15*y**5 + 0 + 0*y + 0*y**3 - 1/12*y**4 - 4*y**2. Factor d(s).
-2*s*(s + 1)**4
Let y be (-48)/27*2/(-4). Suppose 0 = -10*m + 39 + 1. Find o, given that 0 - 8/9*o**m + 2/9*o + y*o**2 - 2/3*o**5 + 4/9*o**3 = 0.
-1, -1/3, 0, 1
Factor -5*p**3 - 94*p + 20*p**2 - 88*p + 162*p.
-5*p*(p - 2)**2
Let y be (-57)/76*16/(-21). Find s such that 10/7*s**3 - 10/7*s + 4/7*s**2 - y = 0.
-1, -2/5, 1
Let w(j) = -j**2 + 8*j - 9. Let b be w(6). Let k**b + k**3 + 2*k + 0*k - 4*k**2 = 0. What is k?
0, 1
Let k(r) be the third derivative of -r**2 + 0*r**3 + 1/168*r**8 + 0*r**6 + 0*r**4 + 0 + 0*r**5 + 0*r**7 + 0*r. Suppose k(j) = 0. What is j?
0
Let h(p) be the first derivative of -p**7/15 - 16*p**6/75 - 11*p**5/50 - p**4/15 + p - 2. Let u(d) be the first derivative of h(d). Solve u(r) = 0 for r.
-1, -2/7, 0
Let f(h) = 3*h**4 + 11*h**3 - h**2 - 19*h + 16. Let t(q) = 2*q**4 + 6*q**3 - q**2 - 9*q + 8. Let b(p) = -3*f(p) + 5*t(p). Find y, given that b(y) = 0.
-2, 1, 2
Let m be (1/(-16))/((50/15)/(-10)). Let g(o) be the first derivative of 1/8*o**2 - 1/12*o**6 + 1 + 1/4*o**5 - m*o**4 + 0*o - 1/12*o**3. Factor g(i).
-i*(i - 1)**3*(2*i + 1)/4
Let t(w) = -w**2 - w - 1. Let r(b) = 9*b**2 + 12*b - 18. Let l(m) = r(m) + 6*t(m). Factor l(o).
3*(o - 2)*(o + 4)
Find b such that 4/9 - 10/9*b - 14/9*b**2 = 0.
-1, 2/7
Let w(s) = 3*s + 30. Suppose 0 = -0*g + g + 4*t + 13, 5*g = -3*t - 48. Let b be w(g). Solve 0 + 0*p - 1/2*p**2 + 1/4*p**b = 0.
0, 2
Suppose 2*u - j = 2*j - 19, 3*u = 5*j - 31. Let c = u + 2. Factor 0 + 0*i + 1/3*i**3 + c*i**2.
i**3/3
Let m(b) be the third derivative of 4*b**2 - 1/20*b**5 - 1/3*b**3 + 0 + 7/24*b**4 + 0*b + 1/42*b**7 - 7/120*b**6. Factor m(t).
(t - 1)**2*(t + 1)*(5*t - 2)
Let f(t) be the second derivative of 1/63*t**7 + 2*t + 0 - 4/45*t**6 + 1/5*t**5 + 0*t**2 + 1/9*t**3 - 2/9*t**4. Factor f(y).
2*y*(y - 1)**4/3
Suppose 43*f + 8 = 45*f. Factor 9/2*j**2 - 3/2*j + 0 + 3/2*j**f - 9/2*j**3.
3*j*(j - 1)**3/2
Let q(p) = -p**2 + 7*p - 6. Let k be (-1 - -3)*9/3. Let a be q(k). Let 4/9*c**2 + 2/9*c**3 + a - 2/9*c**4 + 0*c = 0. What is c?
-1, 0, 2
Let y(s) be the second derivative of -s**5/6 - 2*s**4/3 - s**3 - 2*s**2/3 + 11*s. What is b in y(b) = 0?
-1, -2/5
Let w(z) = z**3 + 7*z**2 + 7*z + 6. Let g be w(-6). What is v in 0*v + 1/4*v**2 + g = 0?
0
Let d(r) be the second derivative of -r**5/70 - 2*r**4/21 - 5*r**3/21 - 2*r**2/7 - 5*r. Let d(c) = 0. What is c?
-2, -1
Let p(t) = t - 6. Let l(r) = -1. Let q(w) = 3*l(w) - p(w). Let i be q(0). Find o such that 0*o - 1/2*o**i + 1/2*o**2 + 0 = 0.
0, 1
Let f(a) be the first derivative of a**9/1512 - a**7/420 - a**3/3 + 2. Let q(y) be the third derivative of f(y). Factor q(b).
2*b**3*(b - 1)*(b + 1)
Let n(x) be the first derivative of x**4/42 - x**3/21 + 3*x - 1. Let s(p) be the first derivative of n(p). Let s(h) = 0. What is h?
0, 1
Suppose -o + 2*o - 5 = 0. Suppose -12 = 4*t, -2*t + 21 = o*q - 4*t. Solve -4/7*b**2 + 2/7*b + 2/7*b**q + 0 = 0 for b.
0, 1
Find c such that -3 + 54*c**4 - 2*c + 11*c - 54*c**3 + 2*c**3 - 29*c**3 + 21*c**2 = 0.
-1/3, 1/3, 1/2, 1
Let c(b) = -b**2 - 7*b - 6. Let k be c(-4). Suppose -m + 4*m = k. Factor -a**5 + 3*a**3 - a + a - m*a**2.
-a**2*(a - 1)**2*(a + 2)
Let h(v) be the first derivative of v**6/120 - v**5/30 + v**4/24 + 3*v**2/2 - 1. Let f(r) be the second derivative of h(r). Factor f(g).
g*(g - 1)**2
Let d(i) be the third derivative of 1/6*i**3 - 2*i**2 + 0*i + 1/336*i**8 + 0 + 1/24*i**4 - 1/60*i**6 + 1/210*i**7 - 1/30*i**5. Suppose d(p) = 0. Calculate p.
-1, 1
Let n be 5/15*(17 + 1). Suppose 0 = 5*x - n*x. Let 8/5*a**2 + x*a - 6/5*a**4 + 0 - 2/5*a**5 + 0*a**3 = 0. Calculate a.
-2, 0, 1
Let g(w) be the third derivative of -w**6/660 - w**5/330 + w**4/66 - 11*w**2. Determine y so that g(y) = 0.
-2, 0, 1
Let f(v) = v**4 - v**3 - v - 1. Let j(x) = 2*x**4 - 16*x**3 + 10*x**2 - 8*x - 12. Suppose 29 = -4*s - 19. Let g(p) = s*f(p) + j(p). Suppose g(m) = 0. What is m?
-1, -2/5, 0, 1
Let a(o) = -o**3 + 5*o**2 + 6*o + 7. Let m be a(6). Let b = -5 + m. Find g such that 0 + 2*g**b - 4/3*g = 0.
0, 2/3
Let j be (-2)/5*(-5)/12. Let b(k) be the third derivative of 1/30*k**5 + j*k**4 + 0 + 1/3*k**3 + 0*k - k**2. Factor b(v).
2*(v + 1)**2
Let h be 0 - (-2)/(8/12). Factor 4*k + 2*k**4 - 2*k**h - 2 + k**3 - 3*k**3.
2*(k - 1)**3*(k + 1)
Let l(b) be the third derivative of b**7/6300 + b**6/1800 - b**4/24 - 3*b**2. Let p(w) be the second derivative of l(w). Suppose p(j) = 0. What is j?
-1, 0
Suppose 15*w = 10*w + 10. Let o(d) be the first derivative of -1 + 1/16*d**4 + 1/12*d**3 + 0*d**w + 0*d. Find q, given that o(q) = 0.
-1, 0
Let q be (-42)/(-9) - 5 - -1. Factor 2/3*j**2 - q*j - 4/3.
2*(j - 2)*(j + 1)/3
Let b(r) = -2*r**2 + 25*r + 27. Let f(n) = -n**2 + 8*n + 9. Let c(w) = -4*b(w) + 11*f(w). Suppose c(x) = 0. What is x?
-3, -1
Let k = -5 + 7. Let 1 - 9 + 0*s**2 + 6*s**k - 2*s**3 = 0. Calculate s.
-1, 2
Suppose -5*c = -c. Suppose -5*y + 2*y + 6 = c. Factor 1/2*q - 1/2*q**y + 0.
-q*(q - 1)/2
Let a(j) = -5*j**5 - 14*j**4 - 2*j**3 + 12*j**2 + 9*j + 2. Let c(s) = s**5 - s**4 + s**3 + s**2. Let t(o) = a(o) - c(o). Suppose t(m) = 0. Calculate m.
-1, -2/3, -1/2, 1
Suppose 4/3*w + 0 - 2/3*w**3 + 2/3*w**2 = 0. What is w?
-1, 0, 2
Solve 6/5*g**3 + 4/5 - 2/5*g**2 - 2/5*g*