et k(b) = -3*b**4 + 78*b**3 - 57*b**2 - 63*b + 60. Let d(s) = -2*s**4 + 41*s**3 - 28*s**2 - 32*s + 30. Let j(a) = -5*d(a) + 3*k(a). Factor j(f).
(f - 1)**2*(f + 1)*(f + 30)
Let l(z) = 18*z**4 + 134*z**3 + 25*z**2 - 104*z - 43. Let i(y) = 9*y**4 + 69*y**3 + 13*y**2 - 52*y - 21. Let c(h) = -5*i(h) + 3*l(h). Factor c(q).
(q - 1)*(q + 6)*(3*q + 2)**2
Let z(l) = -l**3 - 18*l**2 - 13*l + 27. Let w(y) = -y - 1. Let c(o) = -2*w(o) - z(o). Let m be c(-17). Let -7*f + f - f**2 + m*f - 4*f = 0. Calculate f.
-1, 0
Suppose -42 = -16*i + 6. Solve i*b**3 + 120*b + 4*b**2 - b**4 - 120*b = 0 for b.
-1, 0, 4
Let a(r) be the second derivative of r**5/100 - 5*r**4/12 + 16*r**3/15 + 896*r**2/5 - 32*r - 23. Factor a(c).
(c - 16)**2*(c + 7)/5
Let l(c) be the second derivative of -3/4*c**4 - 1/120*c**6 + 0*c**2 - 95*c - 3/20*c**5 + 0 + 0*c**3. Determine u, given that l(u) = 0.
-6, 0
Find q, given that 9 - 15/2*q - 42*q**2 - 51/2*q**3 = 0.
-1, 6/17
Let a(c) = -c**3 + 29*c**2 + 144*c - 384. Let k be a(-6). Factor 33/4*w**4 + 8*w**3 + 4 - k*w - 10*w**2 + 7/4*w**5.
(w - 1)*(w + 2)**3*(7*w - 2)/4
Let k(a) be the second derivative of -a**4/2 - 7*a**3/12 + 5*a**2/4 - 24*a + 17. Factor k(v).
-(v + 1)*(12*v - 5)/2
Let h(g) be the second derivative of g**4/4 - 68*g**3 + 6936*g**2 + 1099*g. Let h(v) = 0. What is v?
68
Suppose 1/9*j**3 + 235*j - 91/9*j**2 - 225 = 0. Calculate j.
1, 45
Let d = 16979 + -509363/30. Let u(y) be the third derivative of 0*y + 4/5*y**5 + 10*y**4 + 28*y**2 + 32/3*y**3 + 0 - d*y**6. Suppose u(v) = 0. What is v?
-2, -2/7, 4
Suppose 384 - 1/6*j**3 - 515/2*j + 131/3*j**2 = 0. Calculate j.
3, 256
Let -48*z - 64*z**2 + 74*z**3 + z**5 - 12*z**2 + 8*z**2 + 3*z**5 + 38*z**4 = 0. Calculate z.
-6, -4, -1/2, 0, 1
Factor -730378 - 1992*w - 4217*w**2 + 4215*w**2 + 234370.
-2*(w + 498)**2
Find u, given that -5211/5*u - 486/5 - 1089/5*u**3 - 5757/5*u**2 - 57/5*u**4 = 0.
-9, -1, -2/19
Let d(n) be the second derivative of 10*n**7/21 - 8*n**6/5 - 241*n**5/5 - 164*n**4 - 248*n**3/3 + 288*n**2 - 4011*n. Suppose d(x) = 0. Calculate x.
-4, -2, -1, 2/5, 9
Let x(b) = -610*b**2 + 1010*b - 1050. Let s(v) = -415*v**2 + 673*v - 700. Let a(f) = -25*s(f) + 17*x(f). Factor a(n).
5*(n - 1)*(n + 70)
Suppose 14*c - 4677 - 1147 = 0. Let k = c - 2077/5. What is o in -12/5*o + 0 + k*o**3 + 9/5*o**2 = 0?
-4, 0, 1
Let s(a) = -8*a + 1. Let l be s(1). Let g be (-2634)/l - (180/42 + -4). Factor -14 + g*m**2 - 375*m**2 + 2*m + 6.
(m - 2)*(m + 4)
Let p = 121 - -136. Let r(s) = -3*s**3 - 5*s**2 + 3*s - 2. Let z be r(-5). Suppose 474 + 44*k - p - 10*k**2 - z = 0. Calculate k.
2/5, 4
Suppose -99*a = -100*a + 43. Factor 16 + l - 5*l + 44*l**2 + a*l**2 - 89*l**2.
-2*(l - 2)*(l + 4)
Let -3/2*m**2 - 81/2 + 18*m = 0. Calculate m.
3, 9
Let s(h) be the second derivative of -h**5/100 + 3*h**4/4 - 209*h**3/10 + 2527*h**2/10 - 6340*h. Let s(c) = 0. What is c?
7, 19
Let y(o) be the third derivative of -o**10/52920 - o**9/26460 + o**8/5880 + 4*o**4/3 + 2*o**2 - 7*o. Let h(x) be the second derivative of y(x). Factor h(f).
-4*f**3*(f - 1)*(f + 2)/7
Let p(t) be the third derivative of 361/8*t**4 + 1/120*t**6 + 6*t**2 + 6859/6*t**3 - 1 + 19/20*t**5 + 0*t. Factor p(y).
(y + 19)**3
Let j(s) = -7*s**3 + 26*s**2 + 22*s - 33. Let q(b) = b**3 - b**2 + 2. Let t(o) = j(o) + 6*q(o). Let m be t(21). Factor 1/2*f**3 - 1/6*f**4 + m + 0*f**2 - 2/3*f.
-f*(f - 2)**2*(f + 1)/6
Let a be (-2)/(-8) - 38/(-104). Let t be 168/(-14) - (3 - 4) - 3190/(-286). Factor -t*i**2 + 6/13*i + a.
-2*(i - 4)*(i + 1)/13
Let 225*m - 73*m - 83*m**2 + 171*m**2 - 86*m**2 = 0. What is m?
-76, 0
Let n(s) be the third derivative of -1/20*s**5 + 2*s**3 + 0*s + 69*s**2 + 0 + 0*s**4. Suppose n(w) = 0. Calculate w.
-2, 2
Factor 14/3*n**3 - 24/5 - 842/15*n**2 + 848/5*n.
2*(n - 6)**2*(35*n - 1)/15
Let b(l) be the first derivative of 2*l**2 + 0*l + 7/3*l**3 - 32. Factor b(k).
k*(7*k + 4)
Factor -684/5*o - 2/5*o**2 - 272.
-2*(o + 2)*(o + 340)/5
Suppose -54*o + 348 = 33*o. Let j(m) be the first derivative of 6*m**2 + o*m - 10 - 16/3*m**3. Find d, given that j(d) = 0.
-1/4, 1
Let c(u) be the first derivative of u**5/15 - u**4 + 6*u**3 - 27*u**2 + 41. Let j(p) be the second derivative of c(p). Factor j(d).
4*(d - 3)**2
Factor -2/15*j**2 - 7265672/15 + 7624/15*j.
-2*(j - 1906)**2/15
Let q(c) be the first derivative of 2*c**3/39 - 1481*c**2/13 - 228*c - 4061. Determine a so that q(a) = 0.
-1, 1482
Let c(k) = k**2 - 77*k - 4680. Let u be c(-40). Solve u + 1/5*n**2 - 1/5*n = 0.
0, 1
Let c(b) = -8*b**2 - 12*b**2 - 7*b**2 + 18*b**2 + 3*b - 8 - 4*b**2. Let r(t) = t**2 + t + 1. Let q(n) = c(n) + 6*r(n). Factor q(o).
-(o - 1)*(7*o - 2)
Let z(x) be the first derivative of x**4/4 - 22*x**3 - 511*x**2/2 + 11721. Factor z(r).
r*(r - 73)*(r + 7)
Let j(d) = 7*d**2 + 582*d + 587. Let f(b) = 16*b**2 + 1166*b + 1176. Let t(v) = -6*f(v) + 13*j(v). Factor t(n).
-5*(n - 115)*(n + 1)
Suppose -2*j + 8 = -3*t, 16 = 4*j - 3*t + 2*t. Suppose -18 = j*p - 10*p. Determine v, given that 2*v**3 + p*v**3 - 7*v**3 = 0.
0
Let q(j) be the first derivative of -32/9*j**3 + 2/15*j**5 + 0*j + 75 - 4*j**2 - 1/2*j**4. Determine g, given that q(g) = 0.
-2, -1, 0, 6
Suppose 156*g = 199*g - 801*g + 2274. Factor 363/4*j + 33/4*j**2 + 1/4*j**g + 1331/4.
(j + 11)**3/4
Let k(q) be the first derivative of q**6/15 + 378*q**5/25 + 1209*q**4 + 545848*q**3/15 + 714984*q**2/5 - 320. Factor k(w).
2*w*(w + 3)*(w + 62)**3/5
Let k(v) = 12*v**2 - 674*v - 213. Let a(x) = -27*x**2 + 1351*x + 423. Let d(h) = -3*a(h) - 7*k(h). Factor d(g).
-(g - 222)*(3*g + 1)
Let a(r) be the third derivative of r**7/42 - 13*r**6/4 + 1357*r**5/12 + 2665*r**4/2 + 16810*r**3/3 - 1047*r**2. Let a(f) = 0. Calculate f.
-2, 41
Suppose -37*y + 40*y + 4*l - 29 = 0, 0 = 5*y + 5*l - 55. Suppose 0 = -3*c - 2*j + y - 1, 4*c = -5*j + 28. Find i, given that 1/10*i**c - 4/5*i + 7/10 = 0.
1, 7
Let p(f) be the first derivative of 10 - 5/72*f**4 + 5/2*f**2 + 1/3*f**3 + 0*f + 1/180*f**5. Let t(i) be the second derivative of p(i). Factor t(c).
(c - 3)*(c - 2)/3
Let v(b) be the second derivative of 35*b + 4/13*b**2 + 1/78*b**4 + 4/39*b**3 + 0. Suppose v(y) = 0. Calculate y.
-2
Let m(b) be the first derivative of -b**4/6 + 2*b**3/3 + 3*b**2 + 37*b - 2. Let c(w) be the first derivative of m(w). Factor c(r).
-2*(r - 3)*(r + 1)
Let s(f) be the third derivative of f**6/540 - 3*f**5/10 + 599*f**4/108 - 365*f**3/9 + 25*f**2 + 89. Factor s(v).
2*(v - 73)*(v - 5)*(v - 3)/9
Suppose -63*q - 241 = -35*q - 997. Let m(o) be the first derivative of -1/2*o**4 - 6*o**3 + q - 14*o - 15*o**2. Determine d so that m(d) = 0.
-7, -1
Solve 115/4*i**2 - 55 - 5/4*i**3 - 25*i = 0 for i.
-1, 2, 22
Solve -627*d**2 + 209*d**2 + 203*d**2 + 332*d + 468*d + 213*d**2 = 0 for d.
0, 400
Solve -2/11*z**4 - 96/11*z**3 + 6760/11 + 5928/11*z - 926/11*z**2 = 0.
-26, -1, 5
Let v be 8/(-28) + 260/28. Suppose -35 + 8 = -v*t. Find g such that -8 - 3*g**4 + 9*g**t + 3*g**2 + 9 - 1 - 3*g**5 - 6*g = 0.
-2, -1, 0, 1
Let k(s) be the third derivative of 2*s**2 + 3/40*s**5 - 7/8*s**4 + 0 - 90*s + 2*s**3. Factor k(g).
3*(g - 4)*(3*g - 2)/2
Determine j so that -33/4*j**3 - 1/4*j**5 + 17/2*j + 0 - 19/4*j**2 + 19/4*j**4 = 0.
-1, 0, 1, 2, 17
Determine c so that 4 + 2/9*c**3 - 8/9*c**2 - 2/3*c = 0.
-2, 3
Suppose 6*q = -4*k + 36, 92*k - 20 = -q + 89*k. Factor 1/6*c**3 - 2/3*c**q + 1/2*c + 0.
c*(c - 3)*(c - 1)/6
Let w(l) be the first derivative of -l**3/3 + 127*l**2 + 512*l - 2928. Determine u, given that w(u) = 0.
-2, 256
Let k = 2668478/5 + -533694. Factor -1/5*m**4 + 7/5 - k*m**3 - 6/5*m**2 + 8/5*m.
-(m - 1)*(m + 1)**2*(m + 7)/5
Let b(o) = -9*o**2 - 27*o. Let j(t) be the first derivative of 4*t**3/3 + 7*t**2 - 131. Let c(m) = 6*b(m) + 13*j(m). Factor c(k).
-2*k*(k - 10)
Let d = 45 - 42. Suppose -5*y = 5*i - 48 - 27, -55 = -d*y + 2*i. Factor -3*g**4 - 15*g**3 - 18*g**3 + y*g**3 - 4*g**5 - 17*g**4.
-4*g**3*(g + 1)*(g + 4)
Let m(o) be the second derivative of 25*o**2 - 55/6*o**3 + 5/12*o**4 + 9 + 4*o. Let m(p) = 0. Calculate p.
1, 10
Let d(p) be the first derivative of p**5/570 - 5*p**4/38 + 75*p**3/19 + 3*p**2/2 - 4*p - 38. Let z(w) be the second derivative of d(w). Solve z(n) = 0.
15
Let h be (18/7)/((-162)/756). Let r be (69/9 - -3)*(-2)/h. Determine t so that -4/3*t**2 - 22/9*t**3 - 2/3*t**4 + 8/3*t + r = 0.
-2, -2/3