
Let r(i) be the first derivative of i**5/15 + 11*i**4/12 + 8*i**3/3 - 2*i**2/3 - 32*i/3 - 248. Suppose r(j) = 0. Calculate j.
-8, -2, 1
Let t = -11 + 15. Factor -1 + 42*p**5 + 4*p**4 + 1 - t*p**2 - 40*p**5 - 2*p.
2*p*(p - 1)*(p + 1)**3
Let f = -307 + 309. Let t(y) be the third derivative of 0*y**3 + 3*y**f + 1/300*y**5 + 1/60*y**4 + 0 + 0*y. Suppose t(z) = 0. What is z?
-2, 0
Suppose 2/15*u**4 + 0*u**3 + 0 + 0*u - 2/15*u**2 = 0. What is u?
-1, 0, 1
Let m be (-4)/((-4)/(-3)) + 5. Let 25 + m*n**2 + 256 + 64*n + 231 = 0. Calculate n.
-16
Let n(r) = r**3 - 4*r**2 - 5*r - 1. Let a be n(5). Let x be (1 + a)/(2 + 5/(-5)). Determine i so that x - 1/4*i**4 + 1/2*i**2 + 1/4*i**3 + 0*i = 0.
-1, 0, 2
Let d = 57/34 + -97/68. Find j such that -1/2 + d*j + 1/4*j**2 = 0.
-2, 1
Let h(o) be the second derivative of o**6/210 + o**5/8 - 9*o**4/56 - 7*o**3/3 + 5*o. Let w(p) be the second derivative of h(p). Solve w(g) = 0 for g.
-9, 1/4
Let q be -3*(-1)/5 - 2494/(-3010). Factor -4/7*f + 0 + 6/7*f**2 + q*f**3.
2*f*(f + 1)*(5*f - 2)/7
Let g(u) be the second derivative of 121*u**4/6 - 11*u**3/2 + 9*u**2/16 + 44*u - 2. Factor g(v).
(44*v - 3)**2/8
Let m be (60/18 + -2)/4. Let h(s) be the third derivative of -m*s**5 + 2/105*s**7 + 3*s**2 - 1/84*s**8 + 0*s**3 + 0 + 1/10*s**6 + 0*s + 1/3*s**4. Factor h(q).
-4*q*(q - 1)**3*(q + 2)
Let y = 937 + -937. Let y*m**2 + 2/3 + 1/3*m**3 - m = 0. What is m?
-2, 1
Factor -4/19*p**3 + 0*p + 0 - 2/19*p**2 - 2/19*p**4.
-2*p**2*(p + 1)**2/19
Suppose 7*k - 61 = 16. Factor 4 + 0*l + 13*l**2 - 10 + k*l + 4.
(l + 1)*(13*l - 2)
Factor -1/11*f**4 + 0*f + 0 - 4/11*f**2 - 4/11*f**3.
-f**2*(f + 2)**2/11
Let p = -3883/21 + 185. Let a(s) be the first derivative of p*s**3 - 2/7*s**2 - 5 + 2/7*s. Factor a(b).
2*(b - 1)**2/7
Let z(t) = -t**2 + 7*t - 5. Let l(d) = d - 1. Let y be ((-1)/(-1) - 4) + 7. Suppose -y*u - u = 10. Let c(f) = u*z(f) + 10*l(f). Suppose c(o) = 0. What is o?
0, 2
Let s(h) be the second derivative of -h**5/50 + 4*h**4/15 - 16*h**3/15 + 130*h + 1. Factor s(t).
-2*t*(t - 4)**2/5
Let j be (-16)/160 - 84/(-40). Suppose -16/17*d + 2/17*d**j + 32/17 = 0. What is d?
4
Let -695/4*q**2 - 315 + 15/4*q**4 + 1005*q - 20*q**3 = 0. Calculate q.
-7, 1/3, 6
Let c(u) = -17*u**3 + 8*u**2 + 10*u. Let g(k) = -31*k**3 + 16*k**2 + 21*k. Let a(b) = 11*c(b) - 6*g(b). Suppose a(o) = 0. Calculate o.
-4, 0
Let p(d) = d**3 - 11*d**2 - d + 11. Let r be p(11). Suppose 4*l - 26 = -3*z, 2*l + r = 3*z + 4. Factor -6*c + 21*c**4 - 18*c**2 + 6*c**3 - 5*c**2 + 2*c**z.
3*c*(c - 1)*(c + 1)*(7*c + 2)
Let f(v) be the second derivative of -11/8*v**3 + 0 + 9/16*v**4 + 3/4*v**2 + 15*v. Factor f(x).
3*(x - 1)*(9*x - 2)/4
Let r(b) = -5*b**2 + 5. Let w(p) = 2*p**2 - 9*p + 9. Let x be w(7). Let n(l) = 13 - 8*l**2 + x*l**2 - 36 - 13. Let v(m) = 6*n(m) + 44*r(m). Factor v(i).
-4*(i - 1)*(i + 1)
Factor 35/3*q**2 + 6*q - 1/3*q**4 + 0 + 16/3*q**3.
-q*(q - 18)*(q + 1)**2/3
Let v(c) be the second derivative of 7*c**6/30 - 29*c**5/60 - 16*c**4/3 - 6*c**3 - 8*c**2/3 + 11*c. Find d such that v(d) = 0.
-2, -1/3, -2/7, 4
Factor 3/5*q**3 - 24/5 + 36/5*q - 18/5*q**2.
3*(q - 2)**3/5
Let r(t) be the third derivative of -t**7/105 + 2*t**6/15 - 2*t**5/3 + 4*t**4/3 + 6*t**2. Factor r(a).
-2*a*(a - 4)*(a - 2)**2
Let f(g) = -g**2 - 30*g + 259. Let u be f(-37). Let l(z) be the second derivative of -1/78*z**4 + u*z**3 - 7*z + 0*z**5 + 0*z**2 + 1/195*z**6 + 0. Factor l(c).
2*c**2*(c - 1)*(c + 1)/13
Suppose -2*m + 4 = 17*k - 13*k, -4*k = -2*m - 20. Determine c so that 2*c**k + 12/5*c + 34/5*c**2 + 0 = 0.
-3, -2/5, 0
Let l = 334/19 + -964/57. Factor 0*q + 0 - l*q**2.
-2*q**2/3
Let j(o) = -3*o**3 + o**2 + 1. Let q(v) = -8*v**3 - 26*v**2 + 2. Let p(x) = 2*j(x) - q(x). Factor p(y).
2*y**2*(y + 14)
Let v(j) be the second derivative of -j**5/30 + 5*j**4/12 - 2*j**2 + 16*j. Let w(d) be the first derivative of v(d). Factor w(t).
-2*t*(t - 5)
Let u(a) be the second derivative of -9*a**5/40 - 25*a**4/16 + 3*a**3/2 + 4*a**2 - 7*a. Let d(o) be the first derivative of u(o). Factor d(g).
-3*(g + 3)*(9*g - 2)/2
Let j(d) be the first derivative of -3/20*d**4 + 3/5*d - 1/5*d**3 - 8 + 3/10*d**2. Suppose j(v) = 0. What is v?
-1, 1
Let x(k) be the third derivative of -1/840*k**7 + 0 + 125/24*k**4 - 625/24*k**3 + 0*k - 31*k**2 + 1/24*k**6 - 5/8*k**5. Factor x(y).
-(y - 5)**4/4
Let b(o) be the third derivative of o**6/10 + 47*o**5/15 - 8*o**4/3 - 680*o**2. Solve b(s) = 0.
-16, 0, 1/3
Factor 24*d**2 + 51*d**3 + 20*d - 23*d**3 - 24*d**3.
4*d*(d + 1)*(d + 5)
Let w(a) be the third derivative of a**6/540 + 4*a**5/135 + 13*a**4/108 + 2*a**3/9 - 5*a**2 - 5. Determine p, given that w(p) = 0.
-6, -1
Let m(c) be the third derivative of -1/330*c**6 + 0 + 20*c**2 + 1/110*c**5 + 0*c + 0*c**4 - 1/1155*c**7 + 0*c**3. Factor m(u).
-2*u**2*(u - 1)*(u + 3)/11
Let w be 0/(-3*10/15). Let j(f) be the third derivative of 5/27*f**4 + 13/270*f**5 + 4/27*f**3 + 0*f - 4*f**2 + 1/105*f**7 + w - 1/18*f**6. Factor j(g).
2*(g - 2)**2*(3*g + 1)**2/9
Find g such that 1/2*g**3 + 0 + 4*g - 3*g**2 = 0.
0, 2, 4
Solve 34/15*y + 8/15 - 8/15*y**5 + 32/15*y**2 - 26/15*y**3 - 8/3*y**4 = 0.
-4, -1, -1/2, 1
Let b be (6/5)/((-8)/(-100)). Let f be b/6 - 4/8. Solve -3*h**2 - h + 5*h**3 + h**4 - h**3 - 3*h**3 - f + 4 = 0 for h.
-2, -1, 1
Factor -5*s**4 - 509*s - 10*s**3 + 509*s.
-5*s**3*(s + 2)
Determine j, given that 78/17*j - 12/17*j**4 - 20/17 - 2/17*j**5 + 4*j**3 - 112/17*j**2 = 0.
-10, 1
Let o(s) be the third derivative of 5/108*s**4 + 0*s + 0 + 1/270*s**5 + 19*s**2 + 2/9*s**3. Let o(p) = 0. Calculate p.
-3, -2
Let h(p) = p**3 + 2*p**2 - 2*p + 1. Let f(n) = 15*n**3 + 184*n**2 - 340*n - 85. Let a(u) = f(u) - 7*h(u). Find g, given that a(g) = 0.
-23, -1/4, 2
Factor -26/3 + 2*x**2 - 76/3*x.
2*(x - 13)*(3*x + 1)/3
Let m = 1727/5127 + -6/1709. Let p be -3 + 2 - (-3 - 0). Determine n, given that -m - n - 2/3*n**p = 0.
-1, -1/2
Suppose -16*r + 10*r = -6. Factor -2*b**2 - 7 + 0 + 10*b - r + 0*b**2.
-2*(b - 4)*(b - 1)
Suppose -8*d + 27 + 13 = 0. Suppose -4*m - 2*q + 8 = 0, -q - 1 + 17 = d*m. Find r, given that 0 - 1/5*r**5 + 0*r**2 + 2/5*r**m + 0*r - 1/5*r**3 = 0.
0, 1
Find x, given that -13*x**3 - 5*x**2 - 32*x**4 + 28*x**4 + 10*x**3 - 18*x**3 = 0.
-5, -1/4, 0
Solve 24*y**4 + 7*y**3 - 5*y**2 - 73*y**4 - 5*y + 24*y**4 - 2*y**3 + 30*y**4 = 0 for y.
-1, 0, 1
Let l = 26479/15 - 1765. Let j(d) be the second derivative of 1/7*d**7 - 3*d - 1/2*d**5 + 0*d**3 + l*d**6 + 0*d**2 - 1/3*d**4 + 0. Find q, given that j(q) = 0.
-2, -1/3, 0, 1
Let i(x) be the second derivative of -x**5/10 - 7*x**4/6 - 16*x**3/3 - 12*x**2 - 91*x. Determine l, given that i(l) = 0.
-3, -2
Determine a so that 84/5*a + 202/5*a**2 + 2/5*a**5 + 0 + 154/5*a**3 + 38/5*a**4 = 0.
-14, -3, -1, 0
Let n(s) be the second derivative of 0*s**2 + 28*s + 1/21*s**4 + 4/7*s**3 + 0. Factor n(o).
4*o*(o + 6)/7
Let o(m) be the first derivative of -m**6/2 - 3*m**5/5 + 3*m**4/2 + 2*m**3 - 3*m**2/2 - 3*m - 302. Factor o(w).
-3*(w - 1)**2*(w + 1)**3
What is n in 57 + 82*n - 3*n**3 + 29*n**2 + 22*n**2 + 50*n - 21*n = 0?
-1, 19
Let p(w) = 3*w**2 - w. Let s be p(1). Let m be s/3*12/32. Factor m - 1/2*i**2 + 1/2*i**3 - 1/4*i + 1/4*i**4 - 1/4*i**5.
-(i - 1)**3*(i + 1)**2/4
Let y = 1064/353 - 3017131/2824. Let t = y - -1067. Suppose 1/8*u + 3/4*u**4 - 1/8 + 7/8*u**2 - t*u**3 = 0. Calculate u.
-1/3, 1/2, 1
Let q = -4101 + 36917/9. Determine a, given that 0 - 8/9*a - 2/9*a**3 + q*a**2 = 0.
0, 2
Let u(j) be the third derivative of j**7/1260 - j**6/360 - 11*j**5/360 + j**4/12 + j**3 + 161*j**2. Solve u(r) = 0.
-2, 3
Let s = 76 - 70. Suppose 25*x - s - 8 - 10*x**2 + 1 - 2 = 0. What is x?
1, 3/2
Solve 3*o**4 - 21*o + 11 - 7 - 4*o**2 + 2 + 31*o**2 - 15*o**3 = 0 for o.
1, 2
Let d(b) be the second derivative of 5*b**7/42 - b**6/3 - 3*b**5/4 + 5*b**4/3 + 10*b**3/3 + 74*b. Determine j, given that d(j) = 0.
-1, 0, 2
Let w be (1 - 1)*23/(-115). Factor -i**3 + 1/2*i**4 + 0*i**2 + w*i + 0.
i**3*(i - 2)/2
Factor 14/5 + 2/5*w**2 - 29/5*w.
(w - 14)*(2*w - 1)/5
Let c(x) = x**2 + 2*x + 20. Let l be c(0). Let z be (-8)/18*(-90)/l. Find y such that 5*y**3 - y**4 - y + y**z + 3*y**3 - 7*y**3 = 0.
-1, 0, 1
Let p be 6 + (-2 - -5)*-1. Let h be 7 + p/15 + (-84)/20. Let 0*t + 2/3*t**h - 2/3*t**2 + 0 = 0. What is t?
0, 1
Factor 53/4*z - 1/8*z**2 - 2809/8.
-(z -