/3
Let o = 16 - 18. Let f be (o/5)/(3/(-15)). Find x, given that 2*x**3 + 5*x - 3*x + 4*x**f + 0*x**3 = 0.
-1, 0
Let p be (0 + (-3 - -2))*-41. Suppose -31*l + l**2 + p*l + 8 + 0*l**2 + l**2 = 0. Calculate l.
-4, -1
Factor -2/15*y**2 - 64/15 - 8/5*y.
-2*(y + 4)*(y + 8)/15
Suppose -5*j + 42 = 11*j + 42. Factor -16/5*x**2 - 32/5*x + j - 2/5*x**3.
-2*x*(x + 4)**2/5
Suppose 14 = 11*x - 4*x. Let g be (-7)/(-4) - 1/(-4). Factor -x*i - 2 - 1/2*i**g.
-(i + 2)**2/2
Let k(x) be the second derivative of x**6/165 - 3*x**5/55 + 4*x**4/33 + 2*x**3/11 - 9*x**2/11 + 78*x + 1. Determine w, given that k(w) = 0.
-1, 1, 3
Let q(s) be the second derivative of -2/3*s**6 - 3/2*s**5 - 5/3*s**4 + 0*s**2 - 5/6*s**3 + 0 - 5/42*s**7 + 10*s. Suppose q(z) = 0. What is z?
-1, 0
Let b(n) be the first derivative of 3*n**5/5 + 3*n**4/2 - 3*n**3 + 524. Factor b(w).
3*w**2*(w - 1)*(w + 3)
Suppose 2 = 2*l + 2*a, 2 = -2*l - 4*a + 6*a. Let u(g) be the second derivative of l - g + 0*g**2 - 3/80*g**5 - 1/8*g**4 + 0*g**3. Let u(h) = 0. Calculate h.
-2, 0
Suppose -14*c - 105 = c - 105. Suppose 0 + c*o**2 + 2/3*o**5 + 0*o - 4/3*o**3 - 2/3*o**4 = 0. What is o?
-1, 0, 2
Let u(f) = -5*f**2 + 10*f. Let a(p) = 3*p**2 - 12*p. Let s(m) = 4*a(m) + 3*u(m). Let s(v) = 0. Calculate v.
-6, 0
Let l(d) be the second derivative of d**7/840 + d**6/160 + d**5/120 + 21*d**2/2 + 43*d. Let q(z) be the first derivative of l(z). Solve q(h) = 0.
-2, -1, 0
Let w(c) = -c + 15. Let p be w(15). Suppose 16*x - 10*x = p. Determine k so that 3/2*k**2 - 3/4*k**4 - 3/4 + 0*k**3 + x*k = 0.
-1, 1
Let o(c) = -c**3 + 6*c**2 + 3*c - 14. Let u be o(6). Factor -6*h + 21*h**3 + 22*h**u - 13*h**4 - 6*h.
3*h*(h + 1)*(h + 2)*(3*h - 2)
Let q = 232 - 218. Suppose q*o = 8*o - o. Factor o*g + 0 - 6/7*g**2 + 2/7*g**3.
2*g**2*(g - 3)/7
Let z(h) = -11*h - 24. Let m be z(-4). Determine o, given that 13 + 15 - 10 - 5*o**2 + m*o + 7 = 0.
-1, 5
Let c(g) be the second derivative of 2*g**6/5 - 137*g**5/5 + 117*g**4 - 202*g**3 + 172*g**2 + 39*g + 2. Suppose c(t) = 0. Calculate t.
2/3, 1, 43
Let f(p) be the first derivative of -1/12*p**3 + 1/4*p + 2 + 0*p**2. Factor f(v).
-(v - 1)*(v + 1)/4
Suppose -48 = -5*b - 168. Let w = -22 - b. Find s, given that 354*s**4 - 4*s**5 - 4*s**3 - 346*s**4 - s**2 + s**w = 0.
0, 1
Let i(q) = 8*q**4 - 78*q**3 - 30*q**2. Let x(f) = 15*f**4 - 156*f**3 - 59*f**2. Let a(t) = 13*i(t) - 6*x(t). Factor a(s).
2*s**2*(s - 6)*(7*s + 3)
Factor 0 + 0*r + 1/6*r**4 - 5/6*r**3 + 1/6*r**5 + 1/2*r**2.
r**2*(r - 1)**2*(r + 3)/6
Let o be (3 + -4 + 0)*-11. Factor 0*a - o*a**4 + 13*a**4 + 0*a.
2*a**4
Factor d**3 + d**3 + 32*d**2 - 6*d**3.
-4*d**2*(d - 8)
Let u(r) = -4*r**3 - 44*r**2 + 236*r. Let a(b) = -b**3 - b. Let c(k) = 44*k**2 - 240*k. Let w(x) = 3*a(x) - c(x). Let g(z) = 5*u(z) - 6*w(z). Factor g(s).
-2*s*(s - 11)**2
Solve 51*q**2 - 30*q**2 - q**3 - 23*q**2 + 2 + q = 0.
-2, -1, 1
Let x(t) be the third derivative of -5/3*t**3 + 0 + 0*t**5 + 1/24*t**6 - 5/8*t**4 - 2*t**2 + 0*t. Determine o so that x(o) = 0.
-1, 2
Let d(h) be the first derivative of 0*h - 1 + 4*h**2 + 8/9*h**3 + 1/18*h**4. Find r, given that d(r) = 0.
-6, 0
Suppose -4 = -56*z + 38 + 70. Let -3/7*w + 4/7 - 1/7*w**z = 0. What is w?
-4, 1
Let j be ((-22)/11 - 32/(-14)) + (-139)/(-28). Factor 3/2 - 27/4*x + j*x**2.
3*(x - 1)*(7*x - 2)/4
Let k(r) be the second derivative of 8*r + 3/140*r**5 - 1/42*r**4 + 0*r**2 - 1/98*r**7 + 0 + 0*r**3 + 1/105*r**6. Determine g, given that k(g) = 0.
-1, 0, 2/3, 1
Let q(y) be the first derivative of -2*y + 2/9*y**3 - 2/3*y**2 + 11. Suppose q(x) = 0. What is x?
-1, 3
Suppose -u - 384 + 60 = 0. Let s = 1622/5 + u. Factor 0 + 2/5*o**2 - s*o.
2*o*(o - 1)/5
Determine g, given that 4*g**2 - 5*g**2 + 16*g - 3*g**2 + 4*g = 0.
0, 5
Let z = -148/15 + -439/30. Let w = z - -27. Factor -w*r**3 - 1/2*r + 4*r**2 - 1.
-(r - 1)**2*(5*r + 2)/2
Suppose 3*s - 8 + 2 = 0. Solve -2*b**4 + 2*b + s*b**2 + b**2 + 0*b**4 + b**4 = 0 for b.
-1, 0, 2
Let f(r) be the second derivative of -r**5/10 + 3*r**4/2 - 8*r**3/3 - 151*r. Solve f(s) = 0 for s.
0, 1, 8
Let d(u) be the third derivative of u**6/24 - 3*u**5/4 + 90*u**3 + 27*u**2 - 3*u. What is n in d(n) = 0?
-3, 6
Let f(r) be the second derivative of -r**4/27 + 44*r**3/27 - 242*r**2/9 - 6*r. Factor f(g).
-4*(g - 11)**2/9
Let m be 95/(-76)*((-102)/24 + (-2)/(-8)). Find w, given that -1/2*w**3 + 1/4*w**m + 1/4*w + 0*w**2 + 0*w**4 + 0 = 0.
-1, 0, 1
Let j(v) be the third derivative of -v**3 + 1/20*v**5 - 4*v**2 + 1/8*v**4 + 0*v + 0. Factor j(b).
3*(b - 1)*(b + 2)
Let w be (-3)/10*20/(-3). Factor -3*i + 7/2*i**3 + 0 + 19/2*i**w.
i*(i + 3)*(7*i - 2)/2
Let f(o) be the second derivative of -o**6/15 + 9*o**5/25 + 4*o**4/15 - o + 25. Suppose f(j) = 0. What is j?
-2/5, 0, 4
Suppose -f + 21 = 6*f. Determine p so that -9*p**4 - 32*p + 3*p**5 + 9*p**2 + 32*p - 3*p**f = 0.
-1, 0, 1, 3
Suppose -298 = -147*f + 27 + 116. Let 456/5*a**2 + 164/5*a**f + 14/5*a**4 - 144/5*a + 0 = 0. What is a?
-6, 0, 2/7
Let a(r) = -99*r**4 + 711*r**3 - 118*r**2 - 8*r - 8. Let t(l) = -33*l**4 + 237*l**3 - 39*l**2 - 3*l - 3. Let p(m) = 3*a(m) - 8*t(m). Let p(k) = 0. Calculate k.
0, 2/11, 7
Let v be (2 - 2)/(-25 - -24). Let p(a) be the first derivative of -2/15*a**3 + 1/5*a**2 + v*a + 2. Factor p(d).
-2*d*(d - 1)/5
Let b(r) be the third derivative of r**5/24 + 55*r**4/8 + 1815*r**3/4 - 95*r**2. Factor b(a).
5*(a + 33)**2/2
Suppose 6 = -5*k - w + 23, 14 = 5*k + 2*w. Let -6*r - 15*r**2 - 6*r**k + 0*r**4 + 3*r**4 - 12*r**3 = 0. What is r?
-2, -1, 0
Let o be ((54/(-27))/(3 - 1))/(-9). Let z(c) be the second derivative of -1/30*c**5 - 10*c - 1/9*c**3 + o*c**4 + 0*c**2 + 0. Suppose z(q) = 0. Calculate q.
0, 1
Let q(w) be the third derivative of -1/336*w**8 + 0 - 33*w**2 - 1/20*w**6 + 1/2*w**3 - 1/42*w**7 + 1/30*w**5 + 7/24*w**4 + 0*w. Factor q(y).
-(y - 1)*(y + 1)**3*(y + 3)
Let x(i) be the second derivative of -1/35*i**7 + 4/75*i**6 + 0*i**3 + 0*i**2 + 0*i**4 + 0 - 1/50*i**5 - 23*i. Let x(g) = 0. Calculate g.
0, 1/3, 1
Let r be (-45)/(-21) + 1 + (-3)/21. Factor -r*v**2 - 398 + v**4 + 2*v**3 + 398.
v**2*(v - 1)*(v + 3)
Let a(b) be the first derivative of -21/5*b + 1/5*b**3 - 56 - 9/5*b**2. Factor a(k).
3*(k - 7)*(k + 1)/5
Let h(m) be the second derivative of m**10/90720 + m**9/45360 - m**8/10080 + 7*m**4/6 + 29*m. Let x(c) be the third derivative of h(c). Factor x(q).
q**3*(q - 1)*(q + 2)/3
Factor -14450/13*s + 0 - 340/13*s**2 - 2/13*s**3.
-2*s*(s + 85)**2/13
Let y(v) be the first derivative of v**4/6 - 10*v**3/3 - 51. Factor y(g).
2*g**2*(g - 15)/3
Let s(z) be the second derivative of -z**8/11760 + z**6/315 + 3*z**4/2 - 30*z. Let l(h) be the third derivative of s(h). Factor l(k).
-4*k*(k - 2)*(k + 2)/7
Solve -1/3*x**4 + 2/3*x**3 + 9*x**2 + 52/3*x + 28/3 = 0.
-2, -1, 7
Let s = -452/21 - 457/14. Let z = -54 - s. Suppose 1/6 + z*j - 1/3*j**2 = 0. What is j?
-1/2, 1
Let b(c) be the first derivative of -c**5/4 - 5*c**4/6 - 5*c**3/6 + 24*c - 32. Let t(g) be the first derivative of b(g). Factor t(n).
-5*n*(n + 1)**2
Let g(c) be the third derivative of c**6/120 + c**5/60 + 7*c**2. Let b(z) = -20*z**3 - 35*z**2 - 25*z - 10. Let s(f) = b(f) + 15*g(f). Solve s(v) = 0.
-2, -1
Factor 8/3*j - 2 - 2/3*j**2.
-2*(j - 3)*(j - 1)/3
Let i(p) = 2*p - 6. Let v be i(3). Let d(c) be the third derivative of v*c**3 + c**2 + 0 + 1/120*c**5 - 1/240*c**6 + 0*c + 0*c**4. Factor d(x).
-x**2*(x - 1)/2
Suppose 2/17*c**3 - 112/17*c**2 + 0 + 0*c = 0. What is c?
0, 56
Let r be (-1794)/(-104) + -4 - 13. Factor 0*s + 0 - 1/4*s**3 - r*s**2.
-s**2*(s + 1)/4
Suppose -100*a - 4*a**5 + 78*a**3 - 29*a**4 + 96*a**2 + 26*a**3 - 67*a**4 = 0. Calculate a.
-25, -1, 0, 1
Find m, given that 8/5*m**2 + 1/5*m**3 + 4*m + 16/5 = 0.
-4, -2
What is l in 25/3*l**3 + 1/3*l**4 + 0 + 143/3*l**2 - 169/3*l = 0?
-13, 0, 1
Let q be (3/2)/(20/(14960/153)). Factor -q*g**2 + 4/3 - 6*g.
-2*(g + 1)*(11*g - 2)/3
Let q(l) be the third derivative of -l**7/42 - 7*l**6/120 - l**5/30 - 2*l**2 + l. Factor q(f).
-f**2*(f + 1)*(5*f + 2)
Let b be -5*(-12)/40*2. Suppose 18 = b*z + k, -2*z - 3*k + 29 = -8*k. Factor -60*l**3 + 105*l**4 - 94*l**3 - 4*l**2 - 8*l - z*l**4 + 68*l**2.
2*l*(l - 1)*(7*l - 2)**2
Suppose 3*p - 2*j + 37 = 0, -5*p - 4*j - 47 + 0 = 0. Let g = p - -15. Find u, given that 2*u**2 + 9*u**3 - 4*u**2 - 8*u - g*u**2 + 6 - u