Suppose 0 - 2/5*u**3 + 1/5*u - 1/5*u**d = 0. What is u?
-1, 0, 1/2
Suppose a + 4*a = -4*t + 20, 5*a + 3*t = 20. Solve 9*o**2 - 6*o - 16*o**2 + 24 + a*o**2 = 0.
-4, 2
Let q(o) be the first derivative of -1/3*o**3 - 2*o**2 - 2 - 3*o. Solve q(x) = 0 for x.
-3, -1
Let d(f) = -f**3 + 5*f**2 + 62*f - 333. Let x be d(7). Suppose -3/8 + 1/8*i**x + 7/8*i - 5/8*i**2 = 0. What is i?
1, 3
Let y be (-4)/(-66) - (-6440)/18975. Suppose 4/5*o**2 + 2/5*o**3 + 0 - y*o**4 + 0*o = 0. What is o?
-1, 0, 2
Let g(l) = 7*l**3 - 5*l + 2. Let w(f) = 6*f**3 - 6*f + 3. Let o(b) = 2*b + 5. Let c be o(5). Let h be 2/(-6) + (-40)/c. Let j(t) = h*g(t) + 4*w(t). Factor j(d).
3*(d - 1)**2*(d + 2)
Let l(b) be the second derivative of -b**9/3024 + b**8/840 - b**6/180 + b**5/120 - 35*b**3/6 + 14*b. Let f(n) be the second derivative of l(n). Solve f(v) = 0.
-1, 0, 1
Let y(d) be the second derivative of 1/17*d**3 - 1/102*d**4 + 3*d + 0 - 2/17*d**2. Solve y(q) = 0.
1, 2
Let c = 575/21 + -481/7. Let q = -41 - c. Factor -q*i**2 - i - 2/3.
-(i + 1)*(i + 2)/3
Let c be 5*(32/160 + (-8)/(-10)). Let v(q) be the second derivative of 0*q**2 + 5*q + 1/30*q**3 - 1/60*q**4 - 1/100*q**c + 1/150*q**6 + 0. Factor v(p).
p*(p - 1)**2*(p + 1)/5
Factor 0 - 904/7*p**2 + 25538/7*p**3 + 8/7*p.
2*p*(113*p - 2)**2/7
Suppose -2*z = -27*z + 100. Let p(d) be the third derivative of 0*d**z + 0*d**3 + 0 - 1/60*d**5 + 8*d**2 + 0*d + 0*d**6 + 1/210*d**7. Solve p(j) = 0.
-1, 0, 1
Let n(p) be the second derivative of -3*p**5/100 - p**4/5 - 2*p**3/5 + 349*p. Factor n(y).
-3*y*(y + 2)**2/5
Let m be 30/(-21)*(-36)/135. Suppose 4/21 + m*j**3 - 2/21*j - 2/7*j**5 + 8/21*j**4 - 4/7*j**2 = 0. What is j?
-1, -2/3, 1
Suppose 878 - 862 = 5*h + 3*h. Let 2/3*i**3 - 2/3 - 2/3*i + 2/3*i**h = 0. What is i?
-1, 1
Suppose 2*u**2 - 10 - 12 - 3*u**2 + 40*u - 8*u - 9*u = 0. What is u?
1, 22
Let z(s) be the first derivative of 1/15*s**6 - 7/25*s**5 - 2/5*s**2 + 23 + 11/15*s**3 - 4/5*s + 1/10*s**4. Determine g so that z(g) = 0.
-1, -1/2, 1, 2
Factor -6*f**3 - 5*f**4 - 9*f**3 - 36*f**2 + 6*f**2 - 10*f**3.
-5*f**2*(f + 2)*(f + 3)
Let o(b) be the first derivative of -5/3*b**3 - 21 + 10*b**2 - 15*b. Factor o(d).
-5*(d - 3)*(d - 1)
Let r(h) = -15*h**2 - 105*h + 120. Let v(i) = -8*i**2 - 52*i + 60. Let d(j) = 3*r(j) - 5*v(j). Factor d(b).
-5*(b - 1)*(b + 12)
Solve -240 + 52*v + 100*v - 27*v**2 - 24*v + 23*v**2 = 0.
2, 30
Let w(v) = v**3 - 9*v**2 - 16*v - 6. Let g(q) = -2*q**3 + 17*q**2 + 32*q + 13. Let z(p) = 6*g(p) + 11*w(p). Factor z(s).
-(s - 6)*(s + 1)*(s + 2)
Suppose 2*d + 12 = d. Let g(x) = x**3 - 1. Let i(f) = 9*f**3 - 9*f**2 - 12. Let y(h) = d*g(h) + i(h). Determine l so that y(l) = 0.
-3, 0
Let f(i) be the second derivative of -i**5/20 + i**4/6 + i**3/6 + i**2/2 - 3*i. Let h be f(2). Factor -1 + 3 + 7 - 6*v - h*v**2.
-3*(v - 1)*(v + 3)
Let s(o) be the second derivative of -8*o**7/63 - 94*o**6/45 - 152*o**5/15 - 79*o**4/9 + 20*o**3/3 - 408*o. Let s(j) = 0. Calculate j.
-6, -5, -1, 0, 1/4
Let c = -1517 - -1520. Determine g so that -3/5*g**c - 6/5*g + 0 - 9/5*g**2 = 0.
-2, -1, 0
Let a(y) = -15*y**3 - 47*y**2 - 56*y + 118. Let m(q) = -4*q**3 - 12*q**2 - 14*q + 30. Let w(i) = -6*a(i) + 22*m(i). Suppose w(u) = 0. What is u?
-6, -4, 1
Suppose -3*v - 5 = -2*q, -2*v - 65 = -5*q - 5*v. Solve -18*d + 9*d**2 + 5*d + 8*d + q - 24*d**2 + 5*d**4 + 5*d**3 = 0 for d.
-2, -1, 1
Let v(d) be the second derivative of -d**5/10 - 25*d**4/9 - 163*d**3/9 + 20*d**2 + 594*d. Find b, given that v(b) = 0.
-12, -5, 1/3
Suppose -53*w + 26*w + 81 = 0. Let j(c) be the second derivative of -w*c + 0 + 1/48*c**4 + 0*c**2 + 1/8*c**3. Determine u so that j(u) = 0.
-3, 0
Let c(r) be the third derivative of -r**6/150 - 2*r**5/75 + r**4/30 + 4*r**3/15 + 99*r**2. Let c(u) = 0. Calculate u.
-2, -1, 1
Let l(d) be the first derivative of -1/48*d**4 + 5 + 0*d**5 + 1/120*d**6 + 0*d**2 + 0*d**3 + 11*d. Let f(k) be the first derivative of l(k). Factor f(h).
h**2*(h - 1)*(h + 1)/4
Let l = -4154 - -4157. Factor -3 - 51/2*z**l - 63/2*z**2 - 15/2*z**4 - 33/2*z.
-3*(z + 1)**3*(5*z + 2)/2
Let w = 1188 - 1184. Suppose 5/3*z - 1/3*z**3 + 1/3*z**w - 2/3 - z**2 = 0. Calculate z.
-2, 1
Factor 21*o + 11*o**2 + 31/3 + 1/3*o**3.
(o + 1)**2*(o + 31)/3
Determine d so that -2*d**3 - 360 - 1575*d + 3735 + 250*d**2 - 85*d**2 - 3*d**3 = 0.
3, 15
Solve 0 + 8*n**3 + 54/7*n**2 + 2/7*n**4 + 0*n = 0.
-27, -1, 0
Let i(u) be the second derivative of 3*u**7/70 - u**6/4 + 3*u**5/20 - 27*u**2/2 + u. Let x(v) be the first derivative of i(v). Let x(j) = 0. What is j?
0, 1/3, 3
Suppose 0 = -o + 4 + 5. What is m in -o*m**3 + 14*m**3 + m**5 - m**2 - 3*m**4 - 2*m**3 + 0*m**5 = 0?
0, 1
Let t be (-70)/(-16) + 39/(-104). Find u, given that -2*u**2 - t*u + 6*u**3 + 3*u - 4*u + 2*u**4 - u = 0.
-3, -1, 0, 1
Let k(x) = -3*x**2 + 20*x + 23. Let l(v) = -12*v**2 + 81*v + 93. Let t(q) = -9*k(q) + 2*l(q). Factor t(h).
3*(h - 7)*(h + 1)
Let p = -38797/2 + 19400. Let -15/4*b + p - 9/4*b**2 = 0. Calculate b.
-2, 1/3
Let j(y) be the second derivative of -3*y**7/112 - y**6/16 + 107*y**5/160 + 79*y**4/96 - 29*y**3/24 - 3*y**2/2 + 809*y. Let j(x) = 0. What is x?
-4, -1, -1/3, 2/3, 3
Suppose -15*u - 106 - 14 = 0. Let w be ((-20)/5)/12*u/6. Factor 0 + 0*m**2 + 0*m + 2/9*m**5 + 2/9*m**3 - w*m**4.
2*m**3*(m - 1)**2/9
Let i be 18/(-135)*10/(-12). Let f(x) be the first derivative of -1 + 1/12*x**4 + i*x**3 + 0*x**2 + 0*x. Factor f(u).
u**2*(u + 1)/3
Let z(d) be the first derivative of d**3/8 + 6*d**2 + 93*d/8 + 54. Factor z(a).
3*(a + 1)*(a + 31)/8
Let d be 2*-2*((-45)/12 + 4). Let s be (6 - 34/5)*(d - 0). Determine f, given that -s + 2/5*f**2 + 2/5*f = 0.
-2, 1
Let h(z) be the third derivative of 707281*z**7/945 + 24389*z**6/27 + 4205*z**5/9 + 3625*z**4/27 + 625*z**3/27 - 26*z**2 + z. Factor h(u).
2*(29*u + 5)**4/9
Factor -80*m**2 - 38*m**3 + 384*m - 72*m**3 + 106*m**3.
-4*m*(m - 4)*(m + 24)
Determine p so that -3200/17 - 2/17*p**2 + 160/17*p = 0.
40
Let c(a) be the first derivative of a**5/5 - a**4/2 - a**3 + 3*a**2 + 4*a + 1. Let w(x) = x. Let j = 107 - 113. Let p(k) = j*w(k) + 3*c(k). Factor p(h).
3*(h - 2)**2*(h + 1)**2
Let h = 10/7 - 36/35. Let w be ((-171)/3420)/((-6)/(-4)*1/(-6)). What is c in -w*c + 1/5*c**2 - h = 0?
-1, 2
Let g = 194 - 115. Factor 15*i**2 + 8 + 12*i**2 - g*i + 67 - 11*i.
3*(3*i - 5)**2
Let m = 51 - 36. Factor -m*y**2 + 0*y**2 - 14*y + 7*y**3 + 2*y**4 - 3*y**4 + 23*y.
-y*(y - 3)**2*(y - 1)
Let w(c) be the second derivative of -c**6/30 - c**5/2 + 11*c**4/12 - 2*c + 23. Factor w(g).
-g**2*(g - 1)*(g + 11)
Let q(a) = a**3 - 1. Let y(b) = 9*b**3 + 2*b**2 + b - 8. Suppose -5*v + 20 = -v. Let z(g) = v*y(g) - 40*q(g). Factor z(l).
5*l*(l + 1)**2
Suppose 0 = -u + 75 + 14. Let o = u + -87. Solve -4/3 + a**5 + 3*a**o + 4/3*a - 5/3*a**4 - 7/3*a**3 = 0 for a.
-1, 2/3, 1, 2
Let -22*a - 120*a + 48*a**2 + 56 + 6*a**3 - 12*a + 18*a + 26*a**2 = 0. Calculate a.
-14, 2/3, 1
Suppose u - 3 + 1 = 0. Suppose 4*v - 7*v + 6*v + 3*v**u = 0. What is v?
-1, 0
Factor 0 + 16/3*g**3 - 20/3*g**2 + 0*g + 4/3*g**4.
4*g**2*(g - 1)*(g + 5)/3
Let w(t) be the second derivative of -t**6/120 - 3*t**5/40 - t**4/4 - 5*t**3/3 - 9*t. Let u(a) be the second derivative of w(a). Factor u(h).
-3*(h + 1)*(h + 2)
Suppose u**3 + 18*u**2 - 2*u**4 + 55*u + 2*u**2 - 3*u**4 - 59*u = 0. What is u?
-2, 0, 1/5, 2
Factor 1/2*y**5 + 3/2*y**2 + 0 - y + 1/2*y**3 - 3/2*y**4.
y*(y - 2)*(y - 1)**2*(y + 1)/2
Let p(g) be the third derivative of 0 + 1/15*g**5 + 1/315*g**7 + 1/9*g**4 + 1/45*g**6 + g**2 + 1/9*g**3 + 0*g. Factor p(x).
2*(x + 1)**4/3
Let w = -1339 - -1341. Find p such that 2/7*p + 2*p**3 + 20/7*p**4 - 16/7*p**5 + 2/7 - 22/7*p**w = 0.
-1, -1/4, 1/2, 1
Let m = -722 + 3622/5. Let u be 2*(-348)/(-1160)*1/3. Solve -9/5*b**2 - 3/5*b + 23/5*b**3 + u - m*b**4 = 0.
-1/3, 1/4, 1
Let h be 0*(-8)/12*(-15)/10. Let u(k) be the first derivative of 7/6*k**6 + 1/2*k**4 + 9/5*k**5 - 1 + h*k + 0*k**2 + 0*k**3. Let u(l) = 0. What is l?
-1, -2/7, 0
Let d(o) be the first derivative of -16*o + 7*o**2 + 2/3*o**3 + 25. Determine m, given that d(m) = 0.
-8, 1
Let 16 - 100/3*h + 52/3*h**2 + 4/3*h**3 - 4/3*h**4 = 0. What is h?
-4, 1, 3
Let a be ((-294)/196)/(42/(-4)). Determine f so that 0 + 4/7*f**4 + a*f**5 + 6/7*f**3 + 4/7*f**2 + 1/7*f = 0.
-1, 0
Let g be (6/(-8))/(7 - ((-147)/(-12) + -5)). 