*3*(n + 2)/5
Let x(s) be the first derivative of -s**3/5 - 3*s**2/5 - 14. Suppose x(g) = 0. What is g?
-2, 0
Let z(w) be the first derivative of 2*w**3/33 - 2*w**2/11 + 1. Find s such that z(s) = 0.
0, 2
Suppose 83 - 23 = -4*x. Let v = x - -17. Find j, given that -2/7 - 18/7*j**v - 12/7*j = 0.
-1/3
Let u(o) be the first derivative of -o**5/180 - o**4/72 - o**2/2 - 1. Let p(j) be the second derivative of u(j). Factor p(x).
-x*(x + 1)/3
Let c(d) = -2*d. Suppose -3*p - 2 = 3*t + 4, 0 = 3*t + 3. Let b be c(p). Solve -2*z + 2*z**3 - 2*z**4 + 3*z**2 - 4*z**4 + 3*z**b = 0.
-1, 0, 1/3, 1
Suppose 2*y + y = -3*y. Let j(k) be the second derivative of -4/15*k**6 + y*k**2 + 0*k**3 - 1/7*k**7 + 0*k**4 + 0 - 3*k - 1/10*k**5. What is z in j(z) = 0?
-1, -1/3, 0
Let b(c) be the first derivative of -3*c**4/2 + 2*c**3 - 9*c**2/2 - 7*c - 1. Let j(d) = 5*d**3 - 5*d**2 + 8*d + 6. Let a(r) = -6*b(r) - 7*j(r). Factor a(o).
o*(o - 2)*(o + 1)
Let g(j) be the second derivative of -j**4/20 + 4*j**3/5 - 24*j**2/5 - 11*j. Solve g(n) = 0.
4
Let g be 6/(-10) - (-656)/960. Let w(t) be the third derivative of 0 + 3*t**2 + 0*t + 0*t**4 - 1/120*t**5 + g*t**3. Solve w(l) = 0.
-1, 1
Let o(q) = q**2 + 3*q - 1. Let g be o(-5). Find z, given that -g*z**2 + 0 + 2 + 3*z**5 - 16*z + 13*z**4 - 7 + 13*z**3 + 1 = 0.
-2, -1, -1/3, 1
Let l(h) be the third derivative of -h**7/420 - h**6/144 + h**5/90 + h**4/36 - 45*h**2. Factor l(r).
-r*(r - 1)*(r + 2)*(3*r + 2)/6
Solve -3*g**3 + 9*g**4 - 4*g + 18*g**2 - 27*g**2 + g + 6*g**5 = 0 for g.
-1, -1/2, 0, 1
Suppose 5*c + 18 = -v, 5*v + 0*c = c + 14. Let b be (-6)/(-15) - (-13)/5. Find o such that -b + o**2 + o**v + 1 = 0.
-1, 1
Let a(u) be the second derivative of u**7/189 + u**6/27 - 13*u**5/90 + 7*u**4/54 + 10*u. Factor a(c).
2*c**2*(c - 1)**2*(c + 7)/9
Factor 0 - 1/2*r - 1/2*r**3 - r**2.
-r*(r + 1)**2/2
Let v(q) be the first derivative of -3*q**5/5 - 5. Factor v(t).
-3*t**4
Let w(g) = -9*g**3 + 18*g**2 + 57*g - 12. Let r(k) = -18*k**3 + 35*k**2 + 113*k - 25. Let l(z) = -6*r(z) + 11*w(z). Determine y so that l(y) = 0.
-2, 1/3, 3
Let m(f) = -f - 3. Let g be m(-5). Suppose 0 = 4*b - 4*z - 4, 3*b = g*z - 3*z + 7. Factor 3*u**2 + 0*u**b + 0*u + u - 2*u**2.
u*(u + 1)
Suppose q = 3*k - 9, 5*q + k - 6 + 3 = 0. Let u(y) be the second derivative of 0*y**2 + q + 1/54*y**4 + y + 1/90*y**5 + 0*y**3. Determine x so that u(x) = 0.
-1, 0
Let v be 3/4 - (-63)/28. Let t(m) = 5*m**2 - 6*m + 1. Let c(k) = k - 1. Suppose -4*n + 9 = r, -2*n + r = 3*n. Let p(w) = n*t(w) + v*c(w). Factor p(z).
(z - 1)*(5*z + 2)
Let u(q) be the third derivative of -1/165*q**5 + 1/132*q**4 + 0*q + 0 + 2*q**2 + 1/660*q**6 + 0*q**3. Factor u(h).
2*h*(h - 1)**2/11
Let p(s) be the third derivative of s**8/110880 - s**7/6930 + s**6/990 - s**5/20 + 4*s**2. Let o(b) be the third derivative of p(b). Factor o(i).
2*(i - 2)**2/11
Factor 79*u**2 - 38*u**4 + 21*u**3 - 48*u - 129*u**3 - 239*u**2 + 18*u**4.
-4*u*(u + 2)*(u + 3)*(5*u + 2)
Let g(r) be the second derivative of -r**5/70 - 2*r**4/21 + 4*r**3/7 + r - 3. Determine b so that g(b) = 0.
-6, 0, 2
Factor 7*w**2 - 2*w - 19*w**2 + 14*w**2 - 4.
2*(w - 2)*(w + 1)
Let q(s) = 2*s - 21. Let g be q(8). Let m be g/(-3) - (5 - 4). Let -m*x**4 + 2/3*x**3 + 0 + 4/3*x**2 + 0*x = 0. What is x?
-1, 0, 2
Let w(r) be the third derivative of -r**8/504 + r**7/105 - r**6/60 + r**5/90 - 8*r**2. Determine h, given that w(h) = 0.
0, 1
Suppose 4 = 4*u, 4*u - 5 = -3*x + 20. Factor 11*w**3 + 9*w**4 + x*w**4 + 2 + 2*w**2 - 2 + 7*w**5.
w**2*(w + 1)**2*(7*w + 2)
Let m(j) be the third derivative of -2/15*j**3 + 1/15*j**4 - 1/75*j**6 + 0*j**5 + 4*j**2 + 0*j + 2/525*j**7 + 0. Factor m(w).
4*(w - 1)**3*(w + 1)/5
Let c = 2 + 0. Suppose -x = 3*b + b - c, 3*b = -x + 2. Solve -x*r + 5*r**3 + 4*r - 7*r**3 = 0.
-1, 0, 1
Let p(q) be the second derivative of -q**4/108 + q**3/27 - q**2/18 - 5*q. Determine g so that p(g) = 0.
1
Let w(h) be the first derivative of h**6/8 - 9*h**4/8 - 2*h**3 - 9*h**2/8 - 38. Factor w(c).
3*c*(c - 3)*(c + 1)**3/4
Determine l, given that -4*l**4 - 32/5*l + 4/5*l**5 + 28/5*l**3 + 4/5*l**2 + 16/5 = 0.
-1, 1, 2
Let c(f) be the third derivative of 3*f**2 - 1/840*f**7 + 1/1344*f**8 - 1/240*f**6 + 1/120*f**5 + 0*f - 1/24*f**3 + 1/96*f**4 + 0. Factor c(v).
(v - 1)**3*(v + 1)**2/4
Suppose -49*i + 2 = -47*i. Let a(y) be the first derivative of 2/9*y**3 - 1/15*y**5 + i + 1/6*y**2 - 1/6*y**4 + 1/18*y**6 - 1/3*y. What is d in a(d) = 0?
-1, 1
Let t(a) be the second derivative of 3*a - 1/12*a**3 + 0 + 0*a**2 + 1/16*a**4 + 1/16*a**5. Let t(n) = 0. What is n?
-1, 0, 2/5
Let b(v) be the second derivative of 5*v**7/189 + v**6/45 - v**5/45 + 4*v. Determine w, given that b(w) = 0.
-1, 0, 2/5
Suppose -3*j - 5*n = 19, 0*n + n + 1 = -2*j. Let r be (-3)/(-6)*j/5. Factor -7/5*l**2 - 13/5*l**4 - 3*l**3 - r*l + 0 - 4/5*l**5.
-l*(l + 1)**3*(4*l + 1)/5
Factor 20*m**3 - 6/7*m**2 + 8/7 - 40/7*m + 14*m**4.
2*(m + 1)**2*(7*m - 2)**2/7
Let m be (16/(-10))/(2/(-5)). Let d(k) be the second derivative of 4/5*k**6 - 2*k - 1/3*k**m + 3/10*k**5 + 0*k**3 + 0*k**2 + 1/3*k**7 + 0. Factor d(w).
2*w**2*(w + 1)**2*(7*w - 2)
Let g(k) = k**4 + k**3 + k - 1. Let l(w) = -3*w**4 + 3*w**2 - 6*w - 2. Let c(m) = -2*g(m) - l(m). Suppose c(d) = 0. Calculate d.
-1, 2
Suppose -j - 4*j = 0, h = -3*j. Suppose h = -2*v + 7*v. Let -s**5 - 4*s**4 + 3*s**4 + s**2 + s**3 + v*s**2 = 0. Calculate s.
-1, 0, 1
Let b(a) be the second derivative of a**5/24 + 7*a**4/72 - 2*a**3/9 - a**2/3 - 23*a. Factor b(u).
(u - 1)*(u + 2)*(5*u + 2)/6
Let a(s) be the second derivative of 3*s**5/35 + 10*s**4/21 + 6*s**3/7 + 4*s**2/7 + 5*s. Let a(r) = 0. Calculate r.
-2, -1, -1/3
Let g(z) be the third derivative of z**5/30 - z**4/4 - 10*z**3/3 + 7*z**2 + 3. Factor g(r).
2*(r - 5)*(r + 2)
Determine u, given that -5*u**3 + u - 8*u**4 + 3*u - 8 + 18*u**2 + 0*u + 3*u**5 = 0.
-1, 2/3, 2
Factor 1/2*k**4 + 3/2*k**2 - 3/2*k**3 + 0 - 1/2*k.
k*(k - 1)**3/2
Let w be ((-1)/8)/((-13)/(1404/9)). Factor -w*o**2 + 3/2*o**4 + 3/4*o - 3/4*o**5 + 0 + 0*o**3.
-3*o*(o - 1)**3*(o + 1)/4
Factor 0*j - 2/5*j**3 - 1/5*j**2 - 1/5*j**4 + 0.
-j**2*(j + 1)**2/5
Let g(d) = d + 1. Let z(x) = -15*x**5 - 34*x**4 + 11*x**3 + 42*x**2 - 3*x - 15. Let t(a) = 21*g(a) + 3*z(a). Find u such that t(u) = 0.
-2, -1, -2/3, 2/5, 1
Let z = 6 - 8. Let s be -3*((-42)/(-27) + z). Determine f so that 4/3 - s*f + 1/3*f**2 = 0.
2
Let q be (1/3)/((-1)/(-12)). Let f = q + -2. Solve 2*c**4 - 4*c**4 + 5*c**3 - 2*c - 3*c**3 + f*c**2 = 0 for c.
-1, 0, 1
Let m(d) be the second derivative of -1/30*d**5 + 0*d**2 + 0*d**4 + 0 - 1/63*d**7 + 2/45*d**6 + 0*d**3 - 2*d. Factor m(x).
-2*x**3*(x - 1)**2/3
Let d(f) be the second derivative of 5*f**4/12 - 5*f**3/3 - 15*f**2/2 - 2*f. Factor d(y).
5*(y - 3)*(y + 1)
Let k = 37 - 35. Let q(t) be the second derivative of 1/135*t**6 + 1/90*t**5 + 0*t**3 - 1/189*t**7 - 1/54*t**4 + 3*t + 0 + 0*t**k. Factor q(c).
-2*c**2*(c - 1)**2*(c + 1)/9
Let x(h) = -h**3 + 3*h + 1. Let z be x(-2). Suppose z*i + 0*i = 30. Factor -i*d**3 - 2*d**3 - 2*d**2 - d**2.
-3*d**2*(4*d + 1)
Let q(x) = -10*x**3 + 10*x - 6. Let o(k) = -k**3 + k - 1. Suppose 0 = 5*u - 37 + 7. Let z(h) = u*o(h) - q(h). Factor z(w).
4*w*(w - 1)*(w + 1)
Find l such that 0*l**2 + 1/2*l**3 - 1/4*l**4 - 1/2*l + 1/4 = 0.
-1, 1
Suppose 1 = 4*g - 3. Let a be (4/6)/(g/3). Solve -2/5*m**5 - 2/5*m**3 + 0*m**a + 0*m + 4/5*m**4 + 0 = 0 for m.
0, 1
Suppose 2*q = -2*x, -4*x = q + q + 10. Let r(v) be the third derivative of 1/90*v**q + 1/18*v**4 + 0 + 1/9*v**3 + 3*v**2 + 0*v. What is k in r(k) = 0?
-1
Let x(i) = -i**3. Let j(c) = -6*c**3 + 2*c**2 + 2*c - 2. Let s(f) = j(f) - 4*x(f). Factor s(u).
-2*(u - 1)**2*(u + 1)
Let z be (1 - 6) + (-9036)/(-1800). Let i(r) be the second derivative of -z*r**6 + 0*r**2 + 0 + 0*r**3 - 1/60*r**4 - 3/100*r**5 - 1/210*r**7 + 2*r. Factor i(k).
-k**2*(k + 1)**3/5
Let r be 2/4 + (-356)/720. Let b(v) be the third derivative of 0 - 1/108*v**4 + 0*v**3 - 1/945*v**7 + 3*v**2 - r*v**6 + 0*v - 1/90*v**5. Factor b(p).
-2*p*(p + 1)**3/9
Let z be 2*(-14)/(-8)*2. Let -z + 30*v - 11 - 2*v**2 - 18*v = 0. What is v?
3
Let g be 1/(-5) + (-63)/(-15). Let y(d) be the third derivative of 0*d**3 + 1/60*d**6 + 0*d**g + 0 + 0*d + 1/30*d**5 - d**2. Factor y(h).
2*h**2*(h + 1)
Find u, given that 8/9*u + 0 + 98/9*u**3 - 56/9*u