/2
Let y(i) be the second derivative of -i**4/4 - i**3 - 6*i. Solve y(g) = 0 for g.
-2, 0
Solve -3/7*c**4 + 12/7*c - 6/7*c**3 + 9/7*c**2 - 12/7 = 0.
-2, 1
Suppose -2*l - 3*l = 30. Let n be (-8)/l*2/4. Find d such that n*d**2 + 2/3 + 4/3*d = 0.
-1
Let p(b) be the second derivative of -b**5/30 - b**4/6 - b**3/3 - 4*b**2 - 3*b. Let k(g) be the first derivative of p(g). Determine a so that k(a) = 0.
-1
Suppose -2*w + 7 = 3. Factor 4*x**2 - 4*x**3 - 2*x**2 + 2*x - w*x**4 + 2*x**3.
-2*x*(x - 1)*(x + 1)**2
Let c(h) be the first derivative of 0*h**3 + h**2 + 1/90*h**5 + 1 + 1/18*h**4 + 0*h. Let l(m) be the second derivative of c(m). Find q, given that l(q) = 0.
-2, 0
Let u(c) be the first derivative of -2*c**5/105 + 2*c**4/21 - 2*c**3/21 - 4*c**2/21 + 8*c/21 + 1. Suppose u(r) = 0. What is r?
-1, 1, 2
Let l be 6 + (-4)/(-2) + -2. Let d(t) = t - 4. Let w be d(l). Factor -4*f**3 + 2*f**5 + 3*f**3 - 3*f**3 + w*f**3.
2*f**3*(f - 1)*(f + 1)
Let v = -13 + 21. Let w = v + -6. Solve -4*n**2 + 6*n**4 + w*n**5 + 2*n - 2*n**4 - 4*n = 0.
-1, 0, 1
Let j be -1*7*48/(-7). Let j - 3*b + 3*b**2 + 7*b + 20*b = 0. What is b?
-4
Let u(a) = a**4 + a**3 + 1. Let h(s) = 15*s**5 - 52*s**4 + 62*s**3 - 33*s**2 + 6*s - 1. Let k(n) = -h(n) - u(n). Let k(r) = 0. Calculate r.
0, 2/5, 1
Let h = 1 - 1. Let n(u) = -u**2 + 6*u + 9. Let p be n(7). Find g, given that -2*g**5 + p*g**4 + h*g**4 + 4*g**5 = 0.
-1, 0
Let d(t) = 60*t**3 - 67*t**2 + 5*t + 6. Let j(b) = -120*b**3 + 133*b**2 - 11*b - 12. Let f(q) = 5*d(q) + 2*j(q). Factor f(i).
3*(i - 1)*(4*i + 1)*(5*i - 2)
Suppose 0*b - 5*b = 20. Let r be 0/b + (-4)/(-10). Factor 0 + 2/5*f**2 - 2/5*f**4 + 2/5*f - r*f**3.
-2*f*(f - 1)*(f + 1)**2/5
Suppose -6*h + 10 = -h. Let n(w) = -w**3 + 4*w**2 - w - 4. Let v be n(h). Factor 0 + 1/4*f - f**4 - 3/2*f**v + 9/4*f**3.
-f*(f - 1)**2*(4*f - 1)/4
Let c = -752 - -15800/21. Let n(f) be the first derivative of -2 - 22/5*f**5 + 16/7*f**4 + 0*f**2 + 0*f - c*f**3 + 7/3*f**6. Factor n(a).
2*a**2*(a - 1)*(7*a - 2)**2/7
Let j(z) = -15*z**2 + 24*z - 9. Let x(i) = -7*i**2 + 12*i - 5. Let f(y) = -3*j(y) + 7*x(y). Factor f(b).
-4*(b - 2)*(b - 1)
Let u(z) be the second derivative of 3*z**5/20 + 3*z**4/4 + 3*z**3/2 + 3*z**2/2 - z. Factor u(g).
3*(g + 1)**3
Let p(m) be the first derivative of m**7/1680 - m**5/240 - m**3 - 4. Let f(t) be the third derivative of p(t). Let f(d) = 0. Calculate d.
-1, 0, 1
Suppose 0 = 4*a - 12 + 4. Suppose f + 0*p + 2*p = 2, 2*p = -4*f + 20. Suppose f*q**4 - 2*q - 4*q**4 + 2*q**3 - 2*q**a + 0*q = 0. Calculate q.
-1, 0, 1
Let p(c) be the first derivative of 5 + 0*c - 2/15*c**3 - 1/10*c**4 + 1/5*c**2 + 2/25*c**5. Find d such that p(d) = 0.
-1, 0, 1
Factor -16*r**2 + 8*r**2 + 14*r**2 - 4*r + 6*r**2.
4*r*(3*r - 1)
Let w(l) be the first derivative of l**5 - 15*l**4/4 - 10*l**3/3 + 30*l**2 - 40*l - 37. Determine m, given that w(m) = 0.
-2, 1, 2
Let k(v) be the third derivative of -v**8/8400 + v**6/1800 - v**3/2 - 5*v**2. Let p(h) be the first derivative of k(h). Factor p(l).
-l**2*(l - 1)*(l + 1)/5
Suppose -2*u + 0 = -6. Let s(z) = z**4 + 5*z**3 + z**2 - z. Let r(h) = -h**4 - 6*h**3 + 2*h. Let c(q) = u*s(q) + 2*r(q). Suppose c(o) = 0. Calculate o.
-1, 0
Let u be (-4)/((-5)/(15/42)). Let t = u - -1/21. Factor t + 1/3*p**2 + 2/3*p.
(p + 1)**2/3
Let d = 0 - -3. Factor -o - d*o**2 + 5*o**2 - o**2.
o*(o - 1)
Let s(v) be the third derivative of -1/150*v**5 + 0*v**3 - 1/30*v**4 + 0 + 0*v - v**2. Find c such that s(c) = 0.
-2, 0
Let r be 22/(-12)*-1 + 1/(-3). Determine u, given that 3/2*u**2 + 0*u**3 + 3/4*u - 3/4*u**5 - r*u**4 + 0 = 0.
-1, 0, 1
Let s(q) be the second derivative of q**6/6 - 3*q**5/4 - 5*q**4/12 + 5*q**3/2 - 12*q. Factor s(k).
5*k*(k - 3)*(k - 1)*(k + 1)
Let y(w) = w**2 - w + 1. Let a(g) = -3*g**3 + 11*g**2 - 2*g - 1. Let j(i) = -a(i) + 5*y(i). Find v such that j(v) = 0.
-1, 1, 2
Let q(j) = 3*j**2 - 3*j. Let n(g) = -g - 6. Let w be n(-3). Let t(i) = -3*i**2 + 2*i + 1. Let d(h) = w*t(h) - 4*q(h). Suppose d(m) = 0. What is m?
1
Factor g - g**5 + 2*g**4 - g**2 + 2*g**2 + 0*g - 3*g**2.
-g*(g - 1)**3*(g + 1)
Suppose -40 + 7*w**3 - 20*w + 7*w**3 - 13*w**3 + 10*w**2 + 4*w**3 = 0. What is w?
-2, 2
Let b be 5/(-1050)*-4*10. Let a(i) be the second derivative of 0 + 1/7*i**2 + 2/35*i**5 - b*i**3 - i - 1/42*i**4. Suppose a(n) = 0. What is n?
-1, 1/4, 1
Let p(k) be the third derivative of -k**5/90 - 7*k**4/36 - 10*k**3/9 + k**2 - 21. Factor p(c).
-2*(c + 2)*(c + 5)/3
Find q, given that -4/7 + 10/7*q - 8/7*q**2 + 2/7*q**3 = 0.
1, 2
Let s = 3 + -1. Suppose o = -5*t + 16 + 11, 3*o - 16 = -2*t. Determine b, given that -2 - o*b - 4*b**2 + 4 + s*b**3 + 2*b**2 = 0.
-1, 1
Let s(i) = -i**2 + 5*i + 12. Let k(l) = -4*l**2 + 24*l + 60. Let x(r) = 3*k(r) - 16*s(r). Factor x(g).
4*(g - 3)*(g + 1)
Let t(v) be the first derivative of v + 1/80*v**5 + 1/24*v**3 - 1 + 0*v**2 + 1/24*v**4. Let j(b) be the first derivative of t(b). Let j(s) = 0. Calculate s.
-1, 0
Let b(r) be the third derivative of r**8/560 - r**7/350 - r**6/100 + r**5/50 + r**4/40 - r**3/10 - 49*r**2. What is d in b(d) = 0?
-1, 1
Factor -20*b**3 + 6*b - 6*b - 27*b**2 - b**3 - 6*b.
-3*b*(b + 1)*(7*b + 2)
Let u(b) be the third derivative of -b**8/2184 + b**7/273 - 3*b**6/260 + 7*b**5/390 - b**4/78 + 6*b**2. Let u(t) = 0. What is t?
0, 1, 2
Let r = -60/11 - -153/22. Factor -r*u**2 - 1/2 - 2*u.
-(u + 1)*(3*u + 1)/2
Let h(r) be the third derivative of -r**7/70 + 9*r**6/40 - 21*r**5/20 + 19*r**4/8 - 3*r**3 - 22*r**2. Factor h(x).
-3*(x - 6)*(x - 1)**3
Let p be 106/6 - 5/(-15). Determine o, given that -98*o**5 - 11*o**2 - 722*o**3 + 16 + 0*o**5 - 152*o + p*o**4 + 430*o**4 + 519*o**2 = 0.
2/7, 1, 2
Factor 24/7*b**2 - 3/7*b**4 + 0*b**3 - 48/7 + 0*b.
-3*(b - 2)**2*(b + 2)**2/7
Let d = -20 + 20. Determine s, given that 7*s**3 - 6 + 9*s**2 + d - 4*s**3 - 6 = 0.
-2, 1
Factor 4*f**3 + 9/4*f - 6*f**2 - 1/4.
(f - 1)*(4*f - 1)**2/4
Let i(s) = -s**3 + 5*s**2 + s - 1. Let m be i(3). Let a be m/(-12)*6/(-2). Solve -2/7*d + 8/7*d**3 - 4/7 - 8/7*d**4 + 12/7*d**2 - 6/7*d**a = 0 for d.
-1, 2/3, 1
Suppose 0 = n + n - 52. Let r(k) = 24*k**2 - n*k + 351 + 15*k**2 - 208*k. Let d(s) = 3*s**2 - 18*s + 27. Let g(i) = 27*d(i) - 2*r(i). What is u in g(u) = 0?
3
Factor 8/7*m**2 + 0*m - 20/7*m**3 - 4*m**4 + 0.
-4*m**2*(m + 1)*(7*m - 2)/7
Factor 9/2*r**2 - 5/2*r**3 + 1 - 7/2*r + 1/2*r**4.
(r - 2)*(r - 1)**3/2
Let y = -4/409 + 1255/2863. Find m, given that 3/7*m**4 + 0 - y*m**2 - 3/7*m + 3/7*m**3 = 0.
-1, 0, 1
Let a be -2 - -1*(-72)/(-30). Let 0*z + a*z**2 + 0 - 2/5*z**3 = 0. Calculate z.
0, 1
Suppose 0 = -0*r - r. Let v = 9 + -7. Determine n, given that -14/5*n**v - 2*n**3 - 4/5*n + r = 0.
-1, -2/5, 0
Suppose 19 = 8*p + 3. Let y(r) be the first derivative of 1/3*r**3 - p + 1/2*r**2 - 2*r. Factor y(d).
(d - 1)*(d + 2)
Let n be (-9 + (-6)/(-2))/(21/(-2)). Factor 4/7*l**4 + 2/7*l + 0 + 0*l**3 - 2/7*l**5 - n*l**2.
-2*l*(l - 1)**3*(l + 1)/7
Let y(i) = -i - 4. Let d be y(-4). Determine f so that 0*f**4 + d + 2*f + 6*f**2 + 2*f**4 - 2*f**3 - 4 - 4*f**4 = 0.
-2, -1, 1
Let y(i) = 3*i**5 - 17*i**4 + 3*i**3 + 9*i**2 + 2*i. Let c(m) = m**5 - 6*m**4 + m**3 + 3*m**2 + m. Let u(r) = -8*c(r) + 3*y(r). Factor u(k).
k*(k - 2)*(k - 1)**2*(k + 1)
Factor 20*c - 5*c**2 + 17*c**2 + 15 - 7*c**2.
5*(c + 1)*(c + 3)
Let g(m) = -m + 7. Let l be ((-4)/6)/((-8)/36). Let a be g(l). Determine d, given that -a*d**4 - 2*d**2 - 3*d**3 - d**5 + 3*d**2 + 0*d**5 + 7*d**4 = 0.
0, 1
Let d(p) be the second derivative of 1/15*p**6 + 1/18*p**4 + 0*p**2 - 1/63*p**7 - 1/10*p**5 - 3*p + 0 + 0*p**3. Find l, given that d(l) = 0.
0, 1
Let m(h) be the second derivative of h**6/360 + h**5/40 + h**4/12 + h**3/2 + 4*h. Let a(i) be the second derivative of m(i). Suppose a(k) = 0. Calculate k.
-2, -1
Let f be (-3)/9 + (-5)/(-6). Suppose -3*g - y + 13 = 2*g, -3*y = -9. Factor f - 3/4*w + 1/4*w**g.
(w - 2)*(w - 1)/4
Suppose 3*p + 4*k - 7 = 8, -2*k - 5 = -p. Suppose 0 = -q + p*q. Factor 4/3*j**2 - 2/3*j + q.
2*j*(2*j - 1)/3
Let j(b) be the third derivative of 0*b - 17/120*b**6 - 2*b**2 + 1/3*b**3 - 11/24*b**4 + 1/42*b**7 + 0 + 7/20*b**5. Factor j(v).
(v - 1)**3*(5*v - 2)
Let b be (1 + 1)/((-24)/(-60)). Let j be -5*(-4 - (-18)/b). Factor -s**5 + 0*s**j - 1/3*s**4 + 0 + 0*s + 0*s**3.
-s**4*(3*s + 1)/3
Let b(v) be the second derivative of -v*