. Factor -2/9*v + 4/9 - z*v**2.
-2*(v - 1)*(v + 2)/9
Suppose -m = 3*b - 11, 84*b - 79*b = 3*m + 9. What is j in -11*j**2 - 1/3*j**4 + 10/3*j**b - 16/3 + 40/3*j = 0?
1, 4
Let m(a) be the first derivative of 2*a**5/35 + 37*a**4/7 - 50*a**3/7 - 218. Solve m(q) = 0 for q.
-75, 0, 1
Let v be 5*11/(-10) + 10. Determine t so that 43/2*t**2 - 6 - v*t**3 - 22*t = 0.
-2/9, 2, 3
Let q(y) be the first derivative of -35*y**4 + y**3 + 4*y + 33. Let d be q(-3). Find p such that -20*p**2 - d + 4*p**4 + 8*p**3 - 24*p + 3811 = 0.
-3, -1, 0, 2
Find c, given that 2035*c + 4290*c**3 + 4948*c**3 + 2233*c**2 - 320*c**4 + 5867*c**2 + 170 + 5873*c**3 - 4471*c**3 = 0.
-1/4, 34
Let r = 19430 + -1165799/60. Let w(c) be the third derivative of 0*c + 0 + 0*c**3 + 7/30*c**5 - r*c**6 + 0*c**4 - 11*c**2. Factor w(b).
-2*b**2*(b - 7)
Suppose 18 = 4*x + 26. Let q(i) = -9*i - 11. Let v be q(x). Factor 3*b**3 + 16*b**2 - 8*b**3 - 17*b**2 - 3*b**5 - v*b**4.
-b**2*(b + 1)**2*(3*b + 1)
Let c = -1509 - -1599. Suppose 0 = 85*g - c*g. Determine p so that g*p - 2/3 + 2/3*p**2 = 0.
-1, 1
Let s(r) be the first derivative of -r**4/18 - 2*r**3/9 + r**2 + 6*r - 6660. Let s(n) = 0. Calculate n.
-3, 3
Suppose -22*u - 260 = -18*u - 69*u. Let v(c) be the second derivative of -5/12*c**u + 0 + 5/3*c**3 + 0*c**2 - 17*c. Suppose v(q) = 0. Calculate q.
0, 2
Let w be (-65 + (74 - 9))/(-1). Factor -15/2*a**3 + a**2 + w*a + 0 - 17/2*a**4.
-a**2*(a + 1)*(17*a - 2)/2
Suppose 11 + 14 = 5*u. Suppose -25 = 24*r - 25*r. Let 11*o - 5*o + 6*o + 15*o**3 - 2*o + r*o**2 - u*o**5 - 5*o**4 = 0. Calculate o.
-1, 0, 2
Let u = 288 + -284. Find r such that 4*r**3 + 57 - 4*r + 58 - 111 - u*r**2 = 0.
-1, 1
Let j(a) be the first derivative of a**6/600 + a**5/100 + 6*a**2 + 3*a + 21. Let i(u) be the second derivative of j(u). Factor i(f).
f**2*(f + 3)/5
Let u(x) be the first derivative of x**7/42 + x**6/10 - x**5/4 - x**4/4 + 2*x**3/3 + 13*x - 56. Let y(c) be the first derivative of u(c). Factor y(d).
d*(d - 1)**2*(d + 1)*(d + 4)
Suppose 739*w**2 - 5*w**4 + 3*w**4 + 1179*w**2 - 114*w**3 + 5*w**4 - 5070*w - 6591 - 514*w**2 = 0. Calculate w.
-1, 13
Let b(f) be the third derivative of -f**7/105 + f**6/15 + 2*f**5/5 - 1240*f**2. Solve b(q) = 0.
-2, 0, 6
Let f = 871243/1547 - 7330/13. Let x = -3/7 - f. Factor -6/17 + 2/17*m**2 - x*m.
2*(m - 3)*(m + 1)/17
Let c be 1/(((-6)/(-39))/(6 + 4)). Factor 4*j**2 + j**3 - 58*j - c*j + 0*j**3 - 3*j**3 + 121*j.
-2*j*(j - 1)**2
Let p(f) be the second derivative of -5/3*f**4 + 28/3*f**3 + 0*f**2 - 4*f + 22 - 1/5*f**5. Factor p(m).
-4*m*(m - 2)*(m + 7)
Let h be (3 + (-112)/35)*(-5 - -13 - 41/2). Suppose 1/3 - 2*r**5 - 17/6*r**4 + h*r**2 + 25/6*r**3 - 13/6*r = 0. Calculate r.
-2, -1, 1/4, 1/3, 1
Suppose -1 = -r - 46. Let s = r + 47. Factor 3*n**2 + s*n + n + 0*n**2 - 15*n.
3*n*(n - 4)
Let j(p) be the first derivative of p**3/6 - 75*p**2/4 + 238*p + 4005. Determine a, given that j(a) = 0.
7, 68
Let c(q) be the second derivative of -q**7/840 - q**6/30 + q**4/3 - 2*q**3 - 4*q + 2. Let a(z) be the third derivative of c(z). Find v, given that a(v) = 0.
-8, 0
Let m be (-68)/(-18) - ((-272)/(-72) - 4). Solve -i - 16 - 9*i + 3*i - 5*i + m*i**2 = 0.
-1, 4
Let r(y) be the first derivative of -y**4/12 - 4*y**3/3 + 10*y**2 - 64*y/3 - 2777. Find v such that r(v) = 0.
-16, 2
Let z(r) be the first derivative of 2*r**5 + 11*r**4 - 48*r**3 - 352*r**2 - 256*r + 1285. Factor z(g).
2*(g - 4)*(g + 4)**2*(5*g + 2)
Solve 1143*l - l**4 - 2419*l + 1178*l + 40 + 15*l**2 + 116*l**3 - 54*l**4 - 3*l**5 - 15*l**3 = 0 for l.
-20, -1, 2/3, 1
Suppose 65 - 76 = -j. Suppose y - j = -4*t + 2*y, -t - 5*y + 8 = 0. Factor -6/7*r**2 + 0 + 3/7*r**t + 3/7*r.
3*r*(r - 1)**2/7
Let q(u) be the first derivative of -5/6*u**3 + 1/10*u**5 - 103 - 3*u**2 + 2*u + 15/8*u**4 - 1/4*u**6. What is v in q(v) = 0?
-2, -1, 1/3, 1, 2
Let x = 6080/17 - 24303/68. Let f(m) be the second derivative of 5*m**3 + 0 - x*m**4 - 21*m - 27/2*m**2. Factor f(o).
-3*(o - 9)*(o - 1)
Find n such that 3/4*n**5 + 0 - 51/4*n**2 + 0*n - 3/4*n**3 + 51/4*n**4 = 0.
-17, -1, 0, 1
Suppose 2*b = 2*l - 18 - 22, -b = 3*l - 48. Let k(c) be the third derivative of 0*c + 0 + l*c**2 - c**3 - 1/30*c**5 + 1/3*c**4. Factor k(h).
-2*(h - 3)*(h - 1)
Suppose -21*g - 25 = -67. Let o be 2 + 1/2 - (-2)/4. Factor 1/4*f**o + 0 + 3/4*f + f**g.
f*(f + 1)*(f + 3)/4
Factor 885/2*p - 3/2*p**2 - 441.
-3*(p - 294)*(p - 1)/2
Let o(d) be the first derivative of d**6/2 - 13*d**5/20 - 35*d**4/16 + 5*d**3/4 + 23*d**2/8 - d/2 - 2477. Suppose o(s) = 0. Calculate s.
-1, 1/12, 1, 2
Let k = -6205/6 - -1035. Let z(b) be the second derivative of 0 + 0*b**5 + 0*b**2 - 1/3*b**6 + k*b**3 - 5/42*b**7 - 22*b + 5/6*b**4. Factor z(r).
-5*r*(r - 1)*(r + 1)**3
Suppose -52841*j = -52787*j - 216. Factor 0*k**2 + 2/3*k**j + 4/3*k - 4/3*k**3 - 2/3.
2*(k - 1)**3*(k + 1)/3
Suppose 163/5*z - 168 + 1/5*z**2 = 0. Calculate z.
-168, 5
Let z(w) be the first derivative of -w**4/42 - 9*w**3/7 + 4*w**2 + 114*w + 16. Let g(j) be the first derivative of z(j). Factor g(o).
-2*(o - 1)*(o + 28)/7
Let n(u) be the third derivative of u**8/5040 - u**7/420 + 11*u**5/15 - u**3/2 - 11*u**2 + 4*u. Let k(g) be the third derivative of n(g). Factor k(r).
4*r*(r - 3)
Let d(p) = -2*p + 18. Let y be d(6). Let 49*j**2 + 6*j**3 - y*j**3 + 4*j**3 - 53*j**2 = 0. What is j?
0, 1
Let j(b) be the first derivative of -57 + 12/5*b**2 + 26/15*b**3 - 2/5*b. Find f, given that j(f) = 0.
-1, 1/13
Find q such that -48 + 1247*q**2 + 38*q**4 + 20*q**5 - 20*q**4 + 176*q + 34*q**4 - 84*q**3 - 1363*q**2 = 0.
-3, -2, 2/5, 1
Let -298*k**2 + 317*k**3 - 353*k**3 - 116*k + 29*k + 101*k**2 - 10 = 0. What is k?
-5, -1/4, -2/9
Factor m**3 + 2815*m - 1538*m**2 - 13406 - 5802 + 2771*m + 1334*m**2 + m**3.
2*(m - 49)**2*(m - 4)
Let i(w) be the first derivative of -3*w**6 - 334*w**5/19 - 1093*w**4/38 - 706*w**3/57 + 88*w**2/19 + 24*w/19 - 2693. Solve i(n) = 0.
-3, -1, -2/19, 2/9
Let v(a) = -a**3 + a**2 - 1. Let o(h) = 10*h**3 + 80*h**2 - 400*h + 425. Let s(t) = o(t) + 5*v(t). Factor s(q).
5*(q - 2)**2*(q + 21)
Let o = 1292485/3 - 430827. Factor -r**3 + 0 - 1/3*r**4 + o*r**2 + 0*r.
-r**2*(r - 1)*(r + 4)/3
Let m(z) = -25*z**2 + 9*z + 7. Let i(o) = 82*o**2 - 28*o - 20. Let s(y) = -6*i(y) - 20*m(y). Factor s(q).
4*(q + 1)*(2*q - 5)
Determine s so that 12117/2*s + 3/4*s**2 + 48940563/4 = 0.
-4039
Let d(f) be the first derivative of 5*f**6/24 + 3*f**5/2 + 9*f**4/2 - f**3 + f - 85. Let k(c) be the third derivative of d(c). Solve k(w) = 0.
-6/5
Let a(g) = -11820*g - 472798. Let d be a(-40). Let o be 1/4 - (-51)/36. Factor -10/3*u + o*u**d - 40/3.
5*(u - 4)*(u + 2)/3
Let j(g) = 68*g**2 - 344*g - 152. Let z(w) = -23*w**2 + 115*w + 51. Let o be ((-6)/2)/(8 + 183/(-24)). Let n(d) = o*z(d) - 3*j(d). Factor n(t).
-4*(t - 6)*(5*t + 2)
Let t = 24 - 18. Suppose 156 = -t*y + 8*y. Let d**4 - 40*d**3 + y*d**3 - 41*d**3 = 0. What is d?
0, 3
Let u = 208849/48 - 4351. Let s(v) be the third derivative of 1/24*v**5 + 1/60*v**6 + u*v**4 + 5*v**2 + 0 + 0*v**3 + 0*v. Factor s(c).
c*(c + 1)*(4*c + 1)/2
Let x(f) be the second derivative of 3/100*f**5 - 17 + 3*f**2 - 19/10*f**3 + 2/5*f**4 - f. Determine y, given that x(y) = 0.
-10, 1
Let b(q) be the first derivative of -q**4/24 - 2*q**3/9 - 5*q**2/12 - q/3 + 2314. Factor b(v).
-(v + 1)**2*(v + 2)/6
Let z(w) be the first derivative of w**4/2 - 50*w**3/3 - 28*w**2 + 104*w - 1060. Determine b, given that z(b) = 0.
-2, 1, 26
Let h(a) = -a**4 - a**3 - a**2 - 3*a. Let q(x) = 8*x**4 + 20*x**3 + 30*x**2 + 18*x. Let u(s) = 6*h(s) + q(s). Suppose u(k) = 0. What is k?
-4, -3, 0
Let g(r) be the third derivative of r**8/6720 - r**7/280 + r**6/48 + r**5/30 + 28*r**3/3 - 13*r**2 - 1. Let l(p) be the third derivative of g(p). Factor l(f).
3*(f - 5)*(f - 1)
Let w(i) be the third derivative of i**6/96 - 481*i**5/240 + i**4 + 14*i**2 + 11*i - 3. Let w(g) = 0. What is g?
0, 1/5, 96
Let p(i) = i**2 - 2*i + 1. Let u(d) = d**3 - 57*d**2 - 393*d + 449. Let b(t) = -35*p(t) - 5*u(t). Suppose b(h) = 0. What is h?
-8, 1, 57
Let w(n) be the first derivative of 3*n**4/20 + 93*n**3/5 - 567*n**2/10 + 57*n + 758. Suppose w(f) = 0. Calculate f.
-95, 1
Factor -2/5*q**3 - 1056/5*q + 94/5*q**2 - 1152/5.
-2*(q - 24)**2*(q + 1)/5
Let o(y) be the third derivative of y**6/780 + 28*y**5/195 - y**4/156 -