7
Let i be (9/(-6))/(57/(-114)). Factor 0*p - 62/9*p**i + 0 + 16/9*p**2 - 8/9*p**4.
-2*p**2*(p + 8)*(4*p - 1)/9
Let p(c) be the second derivative of c**7/630 + c**6/9 + 10*c**5/3 + 7*c**4/3 + 34*c. Let u(j) be the third derivative of p(j). Determine o so that u(o) = 0.
-10
Suppose -3*a = 2*a + 30. Let y(t) = -5*t**4 - 14*t**3 - 19*t**2 - 4*t. Let u(b) = 15*b**4 + 43*b**3 + 58*b**2 + 13*b. Let j(s) = a*u(s) - 17*y(s). Factor j(i).
-5*i*(i + 1)**2*(i + 2)
Suppose 0 = -3*y - 84*x + 82*x, 2*x = -2*y - 2. What is f in -8/3*f**y - 10/3*f - 2/3 = 0?
-1, -1/4
Let f(l) be the second derivative of l**5/30 + l**4/6 - 4*l**3/9 - 4*l**2 - 10*l - 4. What is b in f(b) = 0?
-3, -2, 2
Let j be 8/56*122/2 - 49/7. Suppose -12/7 - 3/7*r**2 - j*r = 0. Calculate r.
-2
Factor 16/3*a**3 - 16/3*a + 4/3*a**4 + 4*a**2 - 16/3.
4*(a - 1)*(a + 1)*(a + 2)**2/3
Let w(g) be the third derivative of 0*g + 1/300*g**5 + 0*g**3 + 1/350*g**7 + 1/1680*g**8 + 1/200*g**6 + 0*g**4 + 14*g**2 + 0. Factor w(x).
x**2*(x + 1)**3/5
Solve -1/4*t**3 - 1/4*t - t**2 + 3/2 = 0 for t.
-3, -2, 1
Let q(i) = -15*i + 3. Let f be q(0). Let m(b) be the first derivative of 2 + 1/12*b**4 + 0*b - 1/18*b**f + 0*b**2. Solve m(c) = 0 for c.
0, 1/2
Let b(y) be the first derivative of 0*y**2 + y**3 + 0*y + 5 + 3/4*y**4. Find x, given that b(x) = 0.
-1, 0
Let n(y) be the second derivative of -y**7/63 + y**6/45 + y**5/15 + 10*y - 9. Factor n(l).
-2*l**3*(l - 2)*(l + 1)/3
Suppose 8 + 3 = 20*s + 11. Suppose -12/7*r**3 + 0 - 4/7*r**5 + s*r - 12/7*r**4 - 4/7*r**2 = 0. Calculate r.
-1, 0
Suppose -u = -5*v - 25, -2*u + u = 3*v + 15. Suppose u*k - 12 = -3*k. Suppose -4*l**4 + 2*l**3 + 3*l**4 + 3*l**k = 0. Calculate l.
-1, 0
Let b(t) be the first derivative of 1/18*t**3 + 41 - 1/4*t**2 + 0*t - 1/30*t**5 + 1/8*t**4. Factor b(l).
-l*(l - 3)*(l - 1)*(l + 1)/6
Factor -24/7*u**2 + 3/7*u**3 + 0 + 3*u.
3*u*(u - 7)*(u - 1)/7
Suppose 15*n = -3*n - n. Let w(s) be the second derivative of 3/16*s**4 - 5*s + 3/20*s**5 - 1/8*s**3 + 0 + n*s**2. Suppose w(b) = 0. What is b?
-1, 0, 1/4
Let v(s) = -12*s**3 + 61*s**2 - s - 20. Let g be v(5). Determine b, given that 1/5*b - 3/5*b**2 + 3/5*b**3 - 1/5*b**4 + g = 0.
0, 1
Determine g so that -2/7*g**2 - 48050/7 - 620/7*g = 0.
-155
Let b = 3439/17945 + 30/3589. Find q such that -1/5*q**2 - 3/5 - b*q**3 + q = 0.
-3, 1
Suppose 7*f = 6 + 8. Suppose -4*r - 4*a + f*a + 10 = 0, 4*r = 2*a + 6. Factor 1/5*n**4 - 1/5*n**r + 0 - 1/5*n**3 + 1/5*n.
n*(n - 1)**2*(n + 1)/5
Let o(q) be the first derivative of -q**7/42 - 2*q**6/15 + 7*q**4/6 + 17*q**3/6 + 3*q**2 - 19*q + 36. Let a(f) be the first derivative of o(f). Factor a(g).
-(g - 2)*(g + 1)**3*(g + 3)
Suppose -3*p + 87*t + 4 = 92*t, -8 = -p + 5*t. Factor -9/8*r**p + 0 + 1/2*r - 2*r**2.
-r*(r + 2)*(9*r - 2)/8
Factor 12/5*k**2 + 1/5*k**3 + 2 + 21/5*k.
(k + 1)**2*(k + 10)/5
Suppose 3*c - 3 = 6. Factor 6*b - 4*b + c - 2 + b**2.
(b + 1)**2
Let -36/7*m + 0 - 24/7*m**4 + 24/7*m**2 + 4/7*m**5 + 32/7*m**3 = 0. Calculate m.
-1, 0, 1, 3
Let b(l) be the first derivative of l**6/16 + 3*l**5/20 - 9*l**4/32 + 114. Factor b(h).
3*h**3*(h - 1)*(h + 3)/8
Let s(c) be the second derivative of c**5/40 + 7*c**4/4 + 49*c**3 + 686*c**2 + 23*c. Determine d, given that s(d) = 0.
-14
Let v(z) be the second derivative of -26*z + 0*z**2 + 0 - 1/28*z**7 + 0*z**3 + 0*z**4 - 3/20*z**5 - 3/20*z**6. Factor v(w).
-3*w**3*(w + 1)*(w + 2)/2
Factor -3*s**5 - 2*s**2 - 6*s**2 - 4*s + 7*s**5 + 8*s**4.
4*s*(s - 1)*(s + 1)**3
Suppose -50 = -3*v + 5*v - 5*m, 3*m = 0. Let r = v - -27. Suppose 1/2*h + 1 - 3/2*h**r = 0. What is h?
-2/3, 1
Let u = -10138 - -50693/5. Let -3/5*l**2 + u + 0*l = 0. Calculate l.
-1, 1
Factor 4*z + 17*z**2 + 23*z**2 - 46*z**2 + 2*z**4.
2*z*(z - 1)**2*(z + 2)
Let t be (-5201)/(-2436) - 9/12. Let d = t - 3/58. Factor 4/3*z**2 - 6*z**3 - d + 6*z.
-2*(z - 1)*(z + 1)*(9*z - 2)/3
Let p be 125/(-225)*(-21)/7. What is o in p*o**3 - 10/3*o**2 + 0 + 0*o + 10/3*o**4 - 5/3*o**5 = 0?
-1, 0, 1, 2
Let o(r) be the first derivative of r**4/18 - 14*r**3/27 + 11*r**2/9 - 10*r/9 + 54. Determine x, given that o(x) = 0.
1, 5
Let d(u) be the second derivative of -27*u + 613/90*u**5 - 16/9*u**2 + 7/27*u**7 - 236/27*u**4 + 148/27*u**3 - 322/135*u**6 + 0. Suppose d(b) = 0. Calculate b.
2/7, 1, 4
Suppose -1 = 115*b - 128*b - 1. Solve 2/9*x + b + 2/9*x**2 = 0 for x.
-1, 0
What is p in -4/9*p + 2/9*p**3 - 2/9*p**2 + 0 = 0?
-1, 0, 2
Let x be ((-472)/16)/((-2)/(-32)). Let g = 1430/3 + x. Find b such that g*b**2 + 0 + 2/3*b**4 + 10/3*b**3 + 2*b = 0.
-3, -1, 0
Let f(c) = -c**2 - 132*c - 2. Let b(y) = -5*y - 1. Let a(s) = -4*b(s) + 2*f(s). Determine k, given that a(k) = 0.
-122, 0
Let y be 3 + (-6)/10 + 130/(-325). Let u(w) be the second derivative of 0 + 1/12*w**4 + 0*w**y + 9*w + 1/6*w**3. Factor u(v).
v*(v + 1)
Let d = -4 + 7. Let v = 40 + -35. Factor f**v + 0*f + f - 4*f**3 + 2*f**d + 0*f.
f*(f - 1)**2*(f + 1)**2
Let j(i) = -8*i**2 - 61*i + 54. Let a(n) = -9*n**2 - 60*n + 51. Let d(v) = -5*a(v) + 6*j(v). Factor d(u).
-3*(u - 1)*(u + 23)
Let s(o) = 18*o**2 - 6*o - 9. Let m(h) = 5 - 13*h + 8 + 35*h**2 - 30. Let l(a) = -3*m(a) + 5*s(a). Determine z so that l(z) = 0.
-2/5, 1
Let j(a) = -a**2 - 138*a + 157. Let n(x) = 5*x**2 + 834*x - 941. Let m(q) = -34*j(q) - 6*n(q). Factor m(l).
4*(l - 77)*(l - 1)
Suppose 4*f - 6 = 2. Suppose 2*u**3 - 3*u**f + 7*u**2 - 7*u**2 - 3*u**2 + 24 - 8*u = 0. Calculate u.
-2, 2, 3
Let h(x) = -3*x + 19. Let v be h(0). Let g = 6 + -3. Factor -16*c**2 + 17*c - 40*c - 16*c**4 - 24*c**g - 4*c**5 + v*c.
-4*c*(c + 1)**4
Let o(i) = 3*i**2 + 3*i - 1. Let d be o(-4). Determine l so that 31*l - 69*l + d*l**4 + 8 - 78*l**2 - 31*l**3 + 34*l = 0.
-1, -2/5, 2/7, 2
Suppose -5*x = -0*z - 2*z + 46, 4*x = 2*z - 48. Suppose 50*w = z*w. Factor -3/2*v**3 + 0*v + w - 3/2*v**2.
-3*v**2*(v + 1)/2
Let h(b) = -10*b**2 - 109*b - 349. Let z(m) = 7 - 51 + 29*m**2 - 22*m - 26 - 31*m**2. Let o(k) = -4*h(k) + 22*z(k). Determine v, given that o(v) = 0.
-6
Factor -108 - 4*n**2 - 112 + 4*n + 228.
-4*(n - 2)*(n + 1)
Suppose 7 + 5 = 6*o. Factor 6/7 + 0*c**o + 9/7*c - 3/7*c**3.
-3*(c - 2)*(c + 1)**2/7
Let o = -27433 + 27433. Find i such that 5*i**2 - 11/4*i**3 + i + o = 0.
-2/11, 0, 2
Let a(x) = -2*x**3 - 26*x**2 - 28*x. Let g(r) = 2*r**3 + 27*r**2 + 26*r. Let t(p) = -5*a(p) - 4*g(p). Let t(w) = 0. What is w?
-9, -2, 0
Let f be 2352/(-432) + 6 + (0 - (-2)/(-6)). Let f*g**2 + 0 + 2/3*g = 0. What is g?
-3, 0
Let w(z) = 2*z + 1. Let k(v) = -v**3 - 4*v**2 + 6*v + 3. Let u(p) = -2*k(p) + 6*w(p). Suppose u(f) = 0. Calculate f.
-4, 0
Let a(w) = w**2 - 7*w - 6. Let h be a(8). Factor -20*b + 40*b**h + 5*b**4 - 25*b**3 - 1109 + 1109.
5*b*(b - 2)**2*(b - 1)
Let u(f) be the first derivative of 0*f**2 + 3*f + 1/100*f**5 + 1/150*f**6 + 0*f**3 + 3 - 1/30*f**4. Let o(j) be the first derivative of u(j). Factor o(c).
c**2*(c - 1)*(c + 2)/5
Suppose 4*d - 3*k + 4 = 0, 85*d - 14 = 80*d - k. Solve -d + 4*m - 9/2*m**3 + 3/2*m**2 = 0.
-1, 2/3
Let o(b) be the first derivative of -3*b**5/100 - b**4/15 + b**3/30 + b**2/5 + 5*b + 11. Let f(j) be the first derivative of o(j). Factor f(a).
-(a + 1)**2*(3*a - 2)/5
Let v(r) = r - 85. Let t be v(85). Suppose 6*h - 3*h - 12 = 0. Factor 4/5*d**h + 0*d + t + 6/5*d**3 + 2/5*d**2.
2*d**2*(d + 1)*(2*d + 1)/5
Let p(l) be the third derivative of 1/180*l**5 + 0*l**3 + 0*l + 1/360*l**6 + 0*l**4 + 0 + l**2. Factor p(t).
t**2*(t + 1)/3
Let u(d) be the third derivative of d**8/10080 + d**7/840 + d**6/180 + 2*d**5/15 + 8*d**2. Let x(r) be the third derivative of u(r). Solve x(v) = 0 for v.
-2, -1
Let a be (-165)/(-44) + 28/(-16). Let g(w) be the third derivative of 1/5*w**5 + 0*w - 1/24*w**6 + 0*w**3 - 1/6*w**4 + a*w**2 + 0. Factor g(z).
-z*(z - 2)*(5*z - 2)
Suppose -2*v = -2*j + 8, -3*j + 5*v + 3 = 1. What is y in 2*y**3 + j*y + y**2 - 9*y**2 - y**3 + 2*y**2 = 0?
0, 3
Determine r so that 4 + r + 1/2*r**3 - 5/2*r**2 = 0.
-1, 2, 4
Let a = -50664 + 50666. Find c, given that -16/7*c + 12/7 + 4/7*c**a = 0.
1, 3
Let f = 19 - 31. Let n be 52/14 - f/42. Solve -i**n - 3*i**4 + 10*i**5 - 2*i**5 = 0.
0, 1/2
Let o be (-49)/(-14) - 6/(-12). Let h(c) be the first derivative of -8*c**2 - 2*c + o - 32/3*c**3. What is q in h(q) = 0?
-1/4
Let p(t) = -t**2 - 8*t - 3. Let v be p(-5). Suppose s = 4*s - v. Suppose 2*u + 9*u**2 - s -