0*w = 0.
0, 1
Suppose 21*b + 11*b = 320. Let r be (b/(-4) - -3)*9. Factor -3/2*u**5 + r*u**3 + 6*u**2 - 6*u + 0 - 3*u**4.
-3*u*(u - 1)**2*(u + 2)**2/2
Let t(u) be the second derivative of 2/45*u**6 - 160/3*u**3 - 73*u + 94/9*u**4 + 0 - 16/15*u**5 + 150*u**2. Factor t(p).
4*(p - 5)**2*(p - 3)**2/3
Let h = 140905 - 140901. Factor -4/3*r**3 + 4/3 + 40/9*r**2 + 2/9*r**5 - 38/9*r - 4/9*r**h.
2*(r - 2)*(r - 1)**3*(r + 3)/9
Factor -5/6*y**2 + 0 - 25/6*y.
-5*y*(y + 5)/6
Let u(f) = -f**2 - 40*f - 142. Let y be u(-36). Factor 37*j**2 + 10*j + j**3 - 7*j**y - 19*j**2.
j*(j + 1)*(j + 10)
Let b(g) = 57*g**3 + 1334*g**2 + 48*g. Let j(q) = 343*q**3 + 8010*q**2 + 288*q. Let v(r) = -39*b(r) + 6*j(r). Factor v(c).
-3*c*(c + 24)*(55*c + 2)
Suppose -4*z + 142 - 82 = 0. Suppose -4*s + 14*u + 14 = z*u, -5*s - u + 17 = 0. Suppose -8/13*w + 8/13*w**2 - 2/13*w**s + 0 = 0. What is w?
0, 2
Factor 1/4*r**2 - 1/4*r - 3.
(r - 4)*(r + 3)/4
Suppose 5971*b = 5943*b + 84. Let x(j) be the first derivative of j - 1/6*j**b + 29 - 1/4*j**2. Suppose x(k) = 0. Calculate k.
-2, 1
Let l(i) be the first derivative of 28*i - 16*i**2 - 9 + 4/3*i**3. Suppose l(a) = 0. Calculate a.
1, 7
Let y(s) = s**3 - 219*s**2 - 78*s + 64530. Let m be y(218). Let 3/2*j**m + 384 + 48*j = 0. What is j?
-16
Let t(v) = 2*v**2 + 14*v - 24. Let p be t(2). Factor 5*c**4 + p*c + 55*c**2 - 30*c - 30*c**3 - 12*c.
5*c*(c - 3)*(c - 2)*(c - 1)
Let d = -11 - -16. Let k be (-14)/(-4)*-1*((-152361)/(-1596))/(-243). Factor -1/8*y**4 - 17/2*y - k*y**3 - d - 21/4*y**2.
-(y + 2)**3*(y + 5)/8
Let r(n) be the second derivative of 0 + 0*n**4 - 136*n + 4/3*n**3 - 2/5*n**5 + 2*n**2 - 2/15*n**6. Factor r(j).
-4*(j - 1)*(j + 1)**3
Let z(a) = -3*a**3 + 51*a**2 - 252*a - 12. Let h(m) = -3*m**3 + 52*m**2 - 252*m - 10. Let g(x) = 6*h(x) - 5*z(x). What is o in g(o) = 0?
0, 7, 12
Suppose 30*s - 525 = -465. Let q(d) be the first derivative of -30*d**s - 35 + 8/3*d**3 + 28*d. Factor q(n).
4*(n - 7)*(2*n - 1)
Suppose -q = -10 + 6. Factor v + v**3 - 3*v - 4610*v**2 + v**5 - 3*v**q + 4613*v**2.
v*(v - 2)*(v - 1)**2*(v + 1)
Let x(z) be the second derivative of z**4/6 - 608*z**3/3 + 607*z**2 + 325*z + 4. Factor x(c).
2*(c - 607)*(c - 1)
Let m be (27/108 - (-105)/(-4))*(-8)/52. Let -3/2 - 3/8*c**5 - 57/8*c**3 - 21/8*c**m - 6*c - 75/8*c**2 = 0. Calculate c.
-2, -1
Suppose -z = 2, 4*n + 15*z - 4748 = 13*z. Suppose -n*p + 1180*p + 24 = 0. Determine x so that 2/3*x**p - 4*x**2 + 4 - 2/3*x = 0.
-1, 1, 6
Suppose -2/11*o**3 - 348/11*o**2 + 0 - 346/11*o = 0. What is o?
-173, -1, 0
Suppose 459*j + 102*j + 354*j - 3660 = 0. What is v in 8/3 + 5/3*v**5 + 20/3*v - 25/3*v**3 + 2/3*v**j - 10/3*v**2 = 0?
-2, -1, -2/5, 1, 2
Let j(t) = 465 - 465 - 72*t - 4*t**2. Let l(i) = -i**2 - 24*i. Let a(y) = 5*j(y) - 16*l(y). Factor a(m).
-4*m*(m - 6)
Let g(t) be the second derivative of -41*t - 5/3*t**4 - 1/21*t**7 + 0*t**2 + 19/10*t**5 + 0 - 8/15*t**6 + 0*t**3. Find d, given that g(d) = 0.
-10, 0, 1
Let z(d) be the second derivative of -d**7/42 + 23*d**6/10 - 17*d**5/5 - 7431*d. Suppose z(n) = 0. Calculate n.
0, 1, 68
Let c(y) = -y**5 + 24*y**4 + 140*y**3 + 156*y**2 + 4*y. Let d be (1*2/4)/(25/(-200)). Let q(a) = -a**5 - a**4 + a**2 - a. Let r(s) = d*q(s) - c(s). Factor r(f).
5*f**2*(f - 8)*(f + 2)**2
Let y = 3246 + -3246. Let n(z) be the second derivative of 0*z**3 - 1/10*z**5 + 0 - 1/6*z**4 - 12*z + y*z**2. Factor n(h).
-2*h**2*(h + 1)
Suppose -14*u = -4*z - 16*u - 150, z + 41 = 3*u. Let q be (3 - 2)/(z/(-24)). Let 2/19*d - q + 2/19*d**2 = 0. What is d?
-3, 2
Determine u so that 4*u**2 + 1946 + 676*u + u**2 - 7*u**2 + 617*u + 651*u = 0.
-1, 973
Let p(d) be the third derivative of d**5/180 + d**4/9 - 8*d**3/3 - 1495*d**2. Factor p(w).
(w - 4)*(w + 12)/3
Let i = -188 - -210. Let 0*u**2 + 8*u**2 - 38*u - i*u**2 + 12 = 0. What is u?
-3, 2/7
Let y(z) be the first derivative of 2*z**2 + 10/9*z**3 - 98 - 2/15*z**5 - 1/3*z**4 + 0*z. Factor y(x).
-2*x*(x - 2)*(x + 1)*(x + 3)/3
Let s(z) be the first derivative of 25/2*z**3 + 0*z + 3/8*z**4 - 39/2*z**2 - 167. Suppose s(u) = 0. Calculate u.
-26, 0, 1
Let z(j) be the first derivative of 2*j**6/21 - 52*j**5/35 + 59*j**4/7 - 68*j**3/3 + 216*j**2/7 - 144*j/7 + 9899. Determine r so that z(r) = 0.
1, 2, 3, 6
Let s(k) be the second derivative of 16/5*k**5 + 1/3*k**4 - 16*k**2 - 1/21*k**7 + 14/15*k**6 - 31/3*k**3 - 2*k + 9. Factor s(n).
-2*(n - 16)*(n - 1)*(n + 1)**3
Let n(m) be the third derivative of 8/15*m**5 + 30*m**3 + 26*m**2 - 1/60*m**6 - 23/4*m**4 + 0*m + 0. Let n(p) = 0. Calculate p.
3, 10
Let v = -105 - 17. Let c = v - -370/3. Find y such that -14/3*y**3 + 0 + 10/3*y**2 + c*y = 0.
-2/7, 0, 1
Let n = 21028/5 - 147186/35. Factor -n*s**3 - 8/7*s**2 - 6/7*s + 0.
-2*s*(s + 1)*(s + 3)/7
Suppose -15 = 5*k - 10*k - 3*a, -4*k + 10 = 2*a. Let f be 1/(-7)*(k + 0/(-16)). Factor 32/3*d**2 - 4/3*d**3 + f - 64/3*d.
-4*d*(d - 4)**2/3
Suppose 461*w - 463*w + 4 = 0. Factor -5*l**3 + 28601 + 10*l - 28601 - 5*l**w.
-5*l*(l - 1)*(l + 2)
Suppose -33*p + 0*p + 6039 = 0. Solve -900 + p*f - 4*f**2 + 273*f - 576*f = 0.
-15
Let k(s) be the second derivative of -53*s - 1/6*s**4 + 2 - 1/20*s**5 + 1/3*s**2 + 1/135*s**6 - 1/54*s**3. Find g such that k(g) = 0.
-1, 1/2, 6
Let b(v) = -56*v**4 + 12*v**3 - 36*v**2 + 32*v - 12. Let i(h) = 5*h**4 - h + 1. Let g(z) = b(z) + 12*i(z). Factor g(q).
4*q*(q - 1)**2*(q + 5)
Suppose 22*x - 10*x - 48 = 0. Suppose -2*k - 6*k**4 - 4*k + 11*k**2 - x*k**3 - 9*k**4 + 14*k**4 = 0. Calculate k.
-6, 0, 1
Let r(i) = 8*i**2 + 423*i + 94. Let z(w) = -w + 2. Suppose 0 = 4*u + 2*y + 14, -y + 15 = 12. Let m(q) = u*z(q) - r(q). Solve m(v) = 0.
-52, -1/4
Let t(u) = 2*u**2 - 8*u - 26. Let r be -4 + 2/(-2)*-13. Let s be t(r). Factor 2*d**3 - 6*d + 26*d**2 + 34*d**2 - s*d**2.
2*d*(d - 3)*(d + 1)
Let o(u) be the second derivative of -u**6/120 + 3*u**5/20 + 9*u**4/16 + 7*u**3/12 - 1283*u. Suppose o(n) = 0. What is n?
-1, 0, 14
Let b(i) be the second derivative of i**4/6 + 7*i**3/8 - 9*i**2/8 - 84*i. Determine z so that b(z) = 0.
-3, 3/8
Let v(w) be the third derivative of -2*w**7/105 - 76*w**6/15 + 31*w**5/3 + 51*w**4 - 2016*w**2. Determine l, given that v(l) = 0.
-153, -1, 0, 2
Factor -2/5*j**2 - 22/5*j + 204/5.
-2*(j - 6)*(j + 17)/5
Factor -44/3 + 86/7*j + 2/21*j**3 + 16/7*j**2.
2*(j - 1)*(j + 11)*(j + 14)/21
Let w = -32 + 20. Let b = w + 15. Solve p**3 + p**4 - 3*p - p - 7*p**b + 0*p**3 + 9*p**2 = 0.
0, 1, 4
Let w(j) = 2*j**4 + j**3 + j**2 + 2*j + 2. Let z(c) = 6*c**4 - 2*c**2 - 4*c - 4. Let x(a) = -4*w(a) - 2*z(a). Factor x(h).
-4*h**3*(5*h + 1)
Let i = -215 - -230. Suppose -i*l**2 + 3*l**2 + 3*l**2 + 2048 + 11*l**2 + 128*l = 0. Calculate l.
-32
Find p, given that -4*p**2 + 192*p + 127 - 81 + 31 + 323 = 0.
-2, 50
Let s = 854 + -957. Let w = 223 + s. Factor w*f**3 + 0 + 32/3*f - 176/3*f**2 - 108*f**4 + 36*f**5.
4*f*(f - 1)*(3*f - 2)**3/3
Let q(r) be the first derivative of -2/3*r**3 + 27 - 1/4*r**4 + 1/10*r**5 + 3/2*r + 1/2*r**2. Find c, given that q(c) = 0.
-1, 1, 3
Let x(w) = -28*w**3 - 186*w**2 - 1824*w - 1241. Let u(o) = -10*o**3 - 54*o**2 - 608*o - 414. Let p(b) = -17*u(b) + 6*x(b). Let p(z) = 0. What is z?
-2, -1, 102
Suppose z = 2, -6*v = -v - 4*z - 692. Let y be (3 + 1)/(1/(v/8)). Factor -b**2 + 34*b + 4*b**2 - y*b + 108.
3*(b - 6)**2
Suppose -42*v + 81*v + 55*v**2 - 102 + 71*v**2 - 24*v**2 + 3*v**3 - 42*v = 0. Calculate v.
-34, -1, 1
Let w(v) be the third derivative of v**8/2352 + 5*v**7/294 - v**6/280 - 73*v**5/420 + 25*v**4/84 - 166*v**2 - 5*v. Let w(k) = 0. Calculate k.
-25, -2, 0, 1
Let c be ((-13)/((-26)/(-28)) - 4)/((-130)/39). Suppose -51/5*o**2 + 3/5*o**4 - c*o + 0 - 21/5*o**3 = 0. Calculate o.
-1, 0, 9
Let j(t) be the first derivative of 4*t**5/5 + 23*t**4 + 116*t**3 - 1222*t**2 - 2704*t - 1315. Solve j(i) = 0.
-13, -1, 4
Let d(i) be the second derivative of i**4/108 + 10*i**3/9 + 3463*i. Determine v, given that d(v) = 0.
-60, 0
Determine s so that -12*s**3 - 10*s**4 + 17*s**4 + 5*s**2 - 9*s**4 - 3*s**3 - 3*s**4 + 15*s = 0.
-3, -1, 0, 1
Let o be 7/((-49)/2) + 58/7. Find x such that -60 - o*x**2 - 2*x**4 + 8*x**3 - 6*x + 14*x - 4*x**2 + 58 = 0.
1
Let s(b) = -17*b + 40. Let t be s(-4). Let r = t + -526/5. Factor 2/5*m**4 + 16/5*m**2 + r*m**3 + 0 - 32/5*m.
2*m*(m - 1)*(m + 4)**2/5
Let w(h) be the second derivative of h**