 -2/7, 0, 1
Let q = 1/65 - -1621/260. Let v = q - 317/52. Factor -4/13*s**3 + 0 + 6/13*s**2 - v*s.
-2*s*(s - 1)*(2*s - 1)/13
Suppose -13 - 11 = -8*s. Suppose 0 = 3*p - 15, s*m - 5 = -5*p + 29. Factor -27/2*t**m + 4 - 18*t + 27*t**2.
-(3*t - 2)**3/2
Let q(f) be the third derivative of f**8/90720 + 11*f**7/11340 + 121*f**6/3240 - f**5/4 + 14*f**2. Let j(i) be the third derivative of q(i). Factor j(g).
2*(g + 11)**2/9
Determine y, given that 10*y**2 + 12*y**3 + 19*y**2 + 20287*y - y**4 - 20299*y - 28 = 0.
-2, -1, 1, 14
Let f be (0*(-7)/70)/9. Let z(v) be the third derivative of f + 0*v - 1/18*v**3 - 1/36*v**4 - 6*v**2 - 1/180*v**5. Let z(n) = 0. Calculate n.
-1
Let d(m) = -4*m**2 - 7*m + 5. Let z(t) = t + t - 22*t + 7 + 9*t - 6*t**2. Let i(r) = -7*d(r) + 5*z(r). Factor i(w).
-2*w*(w + 3)
Let t = -135 + 271/2. Let j(d) be the first derivative of 3/20*d**4 - 1/5*d + t*d**2 - 7/15*d**3 - 4. Factor j(h).
(h - 1)**2*(3*h - 1)/5
Let n(u) be the first derivative of 0*u**2 - 1/30*u**4 + 1/20*u**5 + 0*u**3 - 8*u - 3. Let m(x) be the first derivative of n(x). Find y, given that m(y) = 0.
0, 2/5
Let h be 116/30 - 112/(-840). Let i be (1 - h) + (-18)/(-4). Suppose 0*t**2 + 0*t + 9/4*t**4 + i*t**3 + 0 + 3/4*t**5 = 0. Calculate t.
-2, -1, 0
Factor 20*y**2 + 253 + 13*y**3 - 12*y**3 - 253 + 56*y - 5*y**3.
-4*y*(y - 7)*(y + 2)
Solve 2/3*c**2 - 2/3*c - 1/6*c**5 + 0 + 1/2*c**3 - 1/3*c**4 = 0 for c.
-2, 0, 1
Let j(d) = -d**3 + 12*d**2 + 27*d + 16. Let h be j(14). Let v(x) be the second derivative of 0*x**3 - 5*x + 0*x**h - 1/4*x**4 + 0. What is i in v(i) = 0?
0
Suppose 0 = 2*n - 1 - 11. Let d = 60 - 39. Factor d*u - 2*u**2 + 11*u**2 + 6 - n*u + 3*u**2 + 3*u**3.
3*(u + 1)**2*(u + 2)
Suppose 0 = 5*g + 21 - 16. Let t(w) = 5*w**2 + 20*w + 25. Let j(n) = -n - 1. Let x(h) = g*t(h) - 25*j(h). Factor x(m).
-5*m*(m - 1)
Suppose 3*k + x - 64 = 0, 2*k - 5*x - 25 - 12 = 0. Let g be (-27)/k + 1 + (-76)/(-21). Let -g*m + 4/3 - 14/3*m**2 = 0. Calculate m.
-1, 2/7
Let x be 265/(-212)*(-8)/5. Find g such that -2/3*g**3 + x*g**2 - 8/3 + 0*g = 0.
-1, 2
Let i(c) = 11 + 0 - c**3 + 34 + 15*c**2 - 6*c**2 - 20*c. Let j be i(7). Determine p, given that -20/3*p + 35/3*p**j + 0 + 0*p**2 - 5*p**4 = 0.
-2/3, 0, 1, 2
Let z(w) = -7*w**2 + 7*w - 3. Suppose 1 = -2*v - 47. Let a be 16/v*(-7 - -1). Let u(x) = -7*x**2 + 6*x - 3. Let f(p) = a*z(p) - 3*u(p). Factor f(m).
-(m - 1)*(7*m - 3)
Suppose -9*a**3 + a**2 + 54 + 44*a**2 + 5*a**3 + 24*a**4 - 23*a**4 - 81*a - 7*a**3 = 0. What is a?
2, 3
Let o be 76/(-1680) + (-2)/(-21). Let v(y) be the third derivative of -2*y**2 + 0*y**3 + 0 - o*y**5 + 1/8*y**4 + 0*y. Let v(j) = 0. What is j?
0, 1
Let v(y) = -3*y**2 - 41*y + 214. Let g be v(4). Find t, given that 4/3 + 2/3*t - 2/3*t**g = 0.
-1, 2
Let q(u) be the second derivative of u**4/18 + 8*u**3/9 - 3*u**2 - 39*u. Find m, given that q(m) = 0.
-9, 1
Let d(m) = 3*m**2 - 24*m - 9. Let s(o) = -2*o - 11. Let a be s(-6). Let y(n) = -n**2 + 4 - 3 - 3*n + a + 9*n. Let i(u) = -2*d(u) - 9*y(u). Factor i(z).
3*z*(z - 2)
Let 0 + 3/5*b - 6/5*b**2 + 3/5*b**3 = 0. Calculate b.
0, 1
Factor -16*y**4 - 48*y + 1 + 22*y**4 - 37 + 9*y**2 - 9*y**4 + 18*y**3.
-3*(y - 6)*(y - 2)*(y + 1)**2
Let j(b) be the second derivative of b**4/18 - 7*b**3/9 + b + 21. Let j(w) = 0. What is w?
0, 7
Let w be 3 + -12 + 0/(-1). Let a be 6/w + 16/6. Find q, given that 26 - q**5 + q**3 + q**4 - 26 - q**a = 0.
-1, 0, 1
Let o(f) = f**3 - 2*f**2 - f. Let b(r) = 3*r**4 + 6*r**3 - 20*r**2 - 11*r. Let n(w) = -2*b(w) + 22*o(w). Let n(k) = 0. Calculate k.
0, 2/3, 1
Let u(p) = p**2 - 32*p + 9. Let o(l) = -8*l + 2. Suppose -5*b - 4*i + 2*i = -86, b + 4*i - 10 = 0. Let a(m) = b*o(m) - 4*u(m). Find z, given that a(z) = 0.
-4, 0
Factor 5/4*z**4 + 0*z + z**2 + 0 - 2*z**3 - 1/4*z**5.
-z**2*(z - 2)**2*(z - 1)/4
Suppose -20*b = -26*b + 18. Find y, given that 2/5*y**4 - 6/5*y - 6/5*y**5 + 2/5 + 12/5*y**b - 4/5*y**2 = 0.
-1, 1/3, 1
Let d(h) be the second derivative of 35/3*h**4 - 5*h**5 + 4/5*h**6 - 20*h - 40/3*h**3 + 8*h**2 + 0. Solve d(b) = 0 for b.
1/2, 2/3, 1, 2
Let n(g) = g**5 - 2*g**2 - 1. Let w(k) = 7*k**5 + 21*k**4 - 18*k**3 - 11*k**2 + 6*k + 5. Let p(y) = -5*n(y) - w(y). Determine c so that p(c) = 0.
-2, -1, 0, 1/4, 1
Let k(b) = -b**3 + 2*b**2 - b - 1. Let v(a) = 7*a**3 - 26*a**2 + 37*a - 14. Let l(o) = -4*k(o) - v(o). Factor l(m).
-3*(m - 3)*(m - 2)*(m - 1)
Let k = -350 - -10501/30. Let j(d) be the second derivative of 0 - d + 0*d**5 + 0*d**3 + 1/42*d**7 - k*d**6 + 0*d**2 + 0*d**4. Determine q, given that j(q) = 0.
0, 1
Let f(q) = q**2 + 23*q - 24. Let g be f(-24). Suppose g = d - 7*d. Let d + 0*o**2 + 2/3*o**3 + 0*o - 2/3*o**4 = 0. Calculate o.
0, 1
Let i be (4*(-3 - -4))/((-2)/(-32)). Let d = i + -190/3. Factor -d - 1/3*p**2 - p.
-(p + 1)*(p + 2)/3
Let b(a) be the third derivative of -a**6/80 + 97*a**5/120 - 2*a**4/3 + 36*a**2. Suppose b(f) = 0. Calculate f.
0, 1/3, 32
Suppose u + 3*s = 50 - 54, 4*s + 6 = -u. Find q, given that 0 + 6*q**u + 0*q - 15/2*q**3 = 0.
0, 4/5
Let c(j) be the third derivative of -j**8/1064 + j**7/1995 + 4*j**6/57 + 62*j**5/285 + 4*j**4/19 - 404*j**2. Find r such that c(r) = 0.
-4, -1, -2/3, 0, 6
Let m(q) = 9*q**4 - 2*q**3 + 8*q**2 - 12*q - 1. Let z(x) = -2*x**4 + x**3 - x**2 + x - 1. Let l(y) = 3*m(y) + 15*z(y). Factor l(s).
-3*(s - 3)*(s - 2)*(s + 1)**2
Let m(c) be the third derivative of 9*c**2 - 1/24*c**5 + 0 + 0*c - 1/240*c**6 + 1/8*c**4 + 0*c**3. Determine n, given that m(n) = 0.
-6, 0, 1
Suppose -197*u**2 + 66*u**3 + 195*u - 321*u - 106*u**2 - 45*u**4 + 141*u**3 + 432 + 3*u**5 = 0. What is u?
-1, 2, 3, 8
Suppose o = -3*o + s + 460, -2*o + 252 = 5*s. Let 32*m - 20*m**5 + 95*m**3 - o*m**4 - 116*m**3 - 195*m**3 - 112*m**2 = 0. What is m?
-2, 0, 1/5
Find q, given that 100*q**2 + 321*q**4 - 120*q**3 + 84*q - 3*q**5 - 4*q + 13*q**5 - 316*q**4 = 0.
-4, -1/2, 0, 2
Let m(b) be the second derivative of -b**5/30 - 7*b**4/9 - 44*b**3/9 - 40*b**2/3 + 3*b. Factor m(l).
-2*(l + 2)**2*(l + 10)/3
Suppose 15 = 5*q - 5. Let z = -81/11 + 427/55. Factor 2/5 - 6/5*v**q - z*v**5 + 4/5*v**2 - 4/5*v**3 + 6/5*v.
-2*(v - 1)*(v + 1)**4/5
Let g(d) be the third derivative of -d**8/420 + d**7/105 + d**6/90 - d**5/15 - 4*d**3/3 - 10*d**2. Let u(f) be the first derivative of g(f). Solve u(k) = 0.
-1, 0, 1, 2
Let o(w) be the third derivative of -w**4/24 + w**3/6 - 17*w**2. Let b(a) = -a**2 + 1. Let y(q) = -2*b(q) - 2*o(q). Suppose y(m) = 0. What is m?
-2, 1
Let k(p) be the second derivative of -5*p**7/21 - 5*p**6/6 - 3*p**5/4 + 5*p**4/12 + 5*p**3/6 + p - 1. Solve k(t) = 0.
-1, 0, 1/2
Let h(v) be the first derivative of -1/4*v**5 - 5/2*v**2 + 9*v - 5/2*v**3 - 1 - 5/4*v**4. Let f(o) be the first derivative of h(o). Factor f(j).
-5*(j + 1)**3
Let s(g) be the second derivative of -49*g**7/6 + 49*g**6/30 + 2163*g**5/10 + 901*g**4/3 + 508*g**3/3 + 48*g**2 + 331*g. Factor s(t).
-(t - 4)*(t + 3)*(7*t + 2)**3
Let m be ((-50)/(-16) - 3) + 195/40. Let h be (25/10)/m*0. Factor 0*d**2 + h - 3/5*d**3 + 3/5*d.
-3*d*(d - 1)*(d + 1)/5
Let x(z) = -11*z**5 - 42*z**4 - 96*z**3 - 29*z**2 + 3. Let f(p) = -2*p**5 + p**2 + 1. Let l(v) = 3*f(v) - x(v). Factor l(i).
i**2*(i + 4)**2*(5*i + 2)
Let q be ((0 - -2) + -1 - 4) + 284 + -278. Factor 0 + 0*b + 10/9*b**q + 2/9*b**4 + 4/3*b**2.
2*b**2*(b + 2)*(b + 3)/9
Let q = -121 + 105. Let s be ((-132)/40 + 3)*q/6. Factor -s*o**3 + 0 + 0*o + 0*o**2 - 6/5*o**4 + 2*o**5.
2*o**3*(o - 1)*(5*o + 2)/5
Suppose 10*b - 3*b - 28 = 0. Let m(j) = -2*j**2 - 6. Let a(s) = -s**2 + s - 6. Let x(f) = b*a(f) - 3*m(f). Find w, given that x(w) = 0.
-3, 1
Let j(p) = -p**3 + p**2 + p. Let r = -44 + 45. Let x(l) = -2*l**4 - 8*l**3 + 4*l**2 + 8*l + 2. Let v(i) = r*x(i) - 4*j(i). Factor v(d).
-2*(d - 1)*(d + 1)**3
Let l be (-186)/(-24) + 5 + 1/4. Factor -t**2 + l*t + 36 + 2*t**2 - 25*t.
(t - 6)**2
Let w(i) be the first derivative of 2/9*i**3 + 11 - 1/12*i**4 - 2/3*i + 1/6*i**2. Factor w(u).
-(u - 2)*(u - 1)*(u + 1)/3
Factor 0*c + 0*c**2 - 2/11*c**5 - 2/11*c**3 - 4/11*c**4 + 0.
-2*c**3*(c + 1)**2/11
Let u(w) be the second derivative of w**5/20 + 2*w**4/3 + 5*w**3/6 - 7*w**2 - 358*w. Solve u(n) = 0.
-7, -2, 1
Let 0*a**2 + 0*a + 1/7*a**3 - 8/7*a**4 + 0 + 16/7*a**5 = 0. What is a?
0, 1/4
Let q be 6*(-4)/(-36) - (-14)/(-3). Let c(n) = n**3 + n. Let v(x) = 2*x**3 + x**2 - 