62. Let a = 1165/867 + b. Factor 2/3 + 0*p**4 - a*p**3 - 2/3*p**2 + p + 1/3*p**5.
(p - 2)*(p - 1)*(p + 1)**3/3
Let g(t) be the third derivative of t**8/5880 + t**7/588 + t**6/630 - 2*t**5/105 - 68*t**3/3 - 154*t**2. Let x(l) be the first derivative of g(l). Factor x(c).
2*c*(c - 1)*(c + 2)*(c + 4)/7
Let i(q) be the first derivative of 100/3*q**3 + 0*q + 6*q**4 + 75 + 36*q**2 - 4/5*q**5. Factor i(j).
-4*j*(j - 9)*(j + 1)*(j + 2)
Let p(b) be the second derivative of -3*b**5/80 - b**4/16 + 2*b**3 - 15*b**2/2 - b - 2018. Suppose p(m) = 0. Calculate m.
-5, 2
Let h be 6/(-22) - (3/(-33) - (-620)/(-682)). Let 7/11*l**3 - 1/11*l**5 - h + 2/11*l**2 - 12/11*l + 0*l**4 = 0. What is l?
-2, -1, 2
Let b(a) be the second derivative of 2*a**6/5 - 3*a**5/4 - 39*a**4/4 - 11*a**3 + 12*a**2 + 231*a. Find y such that b(y) = 0.
-2, -1, 1/4, 4
Let w(g) be the third derivative of -g**6/1080 - 791*g**5/540 - 2167*g**4/3 + 2904*g**3 + g**2 + 597*g. Factor w(u).
-(u - 1)*(u + 396)**2/9
Determine d, given that -2001*d**2 - 3869*d + 945*d**4 - 147*d**3 - 1172*d - 948*d**4 + 280*d = 0.
-23, -3, 0
Let o(b) be the second derivative of 614125*b**2 + 85/2*b**4 - 2*b - 24 - 7225*b**3 - 1/10*b**5. Factor o(z).
-2*(z - 85)**3
Suppose -176*n + 3493 = -27. Suppose 8 = 13*g - 9*g. Find w such that 16/5 + n*w**g + 16*w = 0.
-2/5
Let t(q) be the third derivative of q**7/945 + q**6/270 - 4*q**5/45 - q**4/6 + 5*q**3 - 1245*q**2. Factor t(y).
2*(y - 3)**2*(y + 3)*(y + 5)/9
Suppose 0 = -8*c - 29 + 37. Suppose -17 - 37*v - v**2 + 55*v - v**2 + c = 0. What is v?
1, 8
Let f(j) = -4*j**2 + 40*j. Let h(l) be the second derivative of l**4 - 20*l**3 - 64*l. Let x(s) = -17*f(s) - 6*h(s). Factor x(z).
-4*z*(z - 10)
Let t = -124767 + 998139/8. What is y in 3/8*y - t*y**2 + 0 = 0?
0, 1
Suppose -17*s + 94 + 63 - 35 = 44*s. Suppose 243*k - 216*k**s + 0 - 3/4*k**4 - 105/4*k**3 = 0. Calculate k.
-18, 0, 1
Let m(v) be the first derivative of 14/3*v**3 + 226 - 64*v - 3/4*v**4 + 44*v**2. Determine s so that m(s) = 0.
-4, 2/3, 8
Let r(q) be the third derivative of 105*q**2 - 2/3*q**3 + 1/75*q**5 - 19/60*q**4 + 0 + 0*q. Factor r(d).
2*(d - 10)*(2*d + 1)/5
Let c(n) = n**2 - 80*n + 926. Let u be c(14). Suppose -54 - 12*z - 2/3*z**u = 0. Calculate z.
-9
Let g(w) be the second derivative of -w**5/90 - w**4/54 + 34*w**3/27 - 56*w**2/9 + 93*w + 16. Factor g(a).
-2*(a - 4)*(a - 2)*(a + 7)/9
Let d(c) be the second derivative of 3/2*c**3 + 5/6*c**4 - 5 - 1/2*c**2 + 7*c. Find k, given that d(k) = 0.
-1, 1/10
Let d(m) be the second derivative of m**5/70 + 815*m**4/42 + 166463*m**3/21 + 165649*m**2/7 - 3220*m. Factor d(r).
2*(r + 1)*(r + 407)**2/7
Suppose j + 4*a + a - 6 = 0, -5*j + 30 = 2*a. Let q be (-6)/42*(2 - j). What is r in 24/7*r**2 + 16/7 - 36/7*r - q*r**3 = 0?
1, 4
Let d(o) be the first derivative of o**3 + 0*o + 3*o**2 - 3/4*o**4 + 58. Factor d(f).
-3*f*(f - 2)*(f + 1)
Let w be 9 + -4 - 10 - ((-2)/6)/((-605)/(-10527)). Solve -2/5*q**2 + 48/5 - w*q = 0.
-6, 4
Let p(h) be the first derivative of h**3/4 + 6*h**2 + 45*h/4 - 885. Find q such that p(q) = 0.
-15, -1
Let u = 79/340 - -3/170. Let l(g) be the second derivative of -2*g**2 - u*g**5 + 0 + 38*g + 7/12*g**4 + 4/3*g**3. Let l(o) = 0. What is o?
-1, 2/5, 2
Let r be (4 - -28)*103/1648. Let 1 - 1/9*s**r + 8/9*s = 0. What is s?
-1, 9
Let w(h) be the first derivative of 4/3*h**3 - 141 - 1/4*h**4 + 5/2*h**2 + 0*h. Factor w(d).
-d*(d - 5)*(d + 1)
Let h be 4 + 354/(-60) - (-4 + 2). Let j(g) be the first derivative of -h*g**6 + 0*g**3 + 0*g**2 + 14 - 9/20*g**4 + 0*g + 12/25*g**5. What is p in j(p) = 0?
0, 1, 3
Let j = -172 - -120. Let k = j - -52. Let -1/4*b + k + 1/8*b**3 + 1/8*b**2 = 0. What is b?
-2, 0, 1
Let l(q) = -2*q - 2. Let r be l(-3). Suppose 3*c - 5*c = -r. Let a - 7*a**2 - a**2 - 2 + 9*a**c = 0. Calculate a.
-2, 1
Factor 56*w - 66/5*w**2 + 2/5*w**3 + 0.
2*w*(w - 28)*(w - 5)/5
Let s be (-4)/16 - 255/(-60). Let x be (-4)/(-16) - (-46)/8. Factor s*b + 9*b**3 - 25*b**3 - 8*b**2 + b**4 + 12*b**3 + b**4 + x.
2*(b - 3)*(b - 1)*(b + 1)**2
Let b(y) be the second derivative of -y**5/30 - y**4/12 + 10*y**2 - 23*y. Let i(t) be the first derivative of b(t). Let i(o) = 0. What is o?
-1, 0
Let y(u) be the third derivative of 5*u**6/36 - 83*u**5/90 + 2*u**4/3 - 6372*u**2. Factor y(b).
2*b*(b - 3)*(25*b - 8)/3
Let l = 232035/52 - 57973/13. Factor -l*f**4 + 19/4*f + 1/2*f**2 - 1/4*f**5 - 9/2*f**3 + 9/4.
-(f - 1)*(f + 1)**3*(f + 9)/4
Let z(q) be the second derivative of 12 + 0*q**5 - 3*q + 1/6*q**4 + 0*q**2 - 1/15*q**6 + 0*q**3. Let z(p) = 0. What is p?
-1, 0, 1
Let h(u) be the third derivative of u**7/280 + 253*u**6/160 - 127*u**5/40 - 2*u**2 - 4*u + 73. Factor h(s).
3*s**2*(s - 1)*(s + 254)/4
Let o(l) be the third derivative of -1/42*l**5 - 1/12*l**4 + 0 + 0*l + 59*l**2 + 0*l**3. Solve o(r) = 0 for r.
-7/5, 0
Let f(z) be the first derivative of -z**3/3 + 275*z**2/2 + 554*z - 9663. Factor f(q).
-(q - 277)*(q + 2)
Let h(x) = x**2 - 2045*x - 14360. Let v be h(-7). Let p be (-5)/35 - 482/(-42). Factor v*m**3 - 4/3 + 6*m + p*m**2.
2*(m + 1)*(m + 2)*(6*m - 1)/3
Factor -5092 - 261*u + 2*u**3 + 12990 + 14366 - 795*u - 42*u**2.
2*(u - 22)**2*(u + 23)
Find b such that 2/3 - 2273/3*b - 2275/3*b**2 = 0.
-1, 2/2275
Let p = 432 - 432. Factor 3*r**2 - 10*r**2 - 3*r - 4 + p + 6*r**2 + 2.
-(r + 1)*(r + 2)
Factor -3336/5*v**2 - 1854816/5*v - 343759232/5 - 2/5*v**3.
-2*(v + 556)**3/5
Let w(r) be the first derivative of r**3/3 + 15*r**2/2 - 52*r + 107. Let a be w(-18). Factor -3/7*c + 3/7*c**4 - 3/7*c**a + 0 + 3/7*c**3.
3*c*(c - 1)*(c + 1)**2/7
Let z(c) = -c**3 - 12*c**2 + 14*c + 47. Let i be z(-13). Find t such that -3*t**2 - 2 - 54 - 93*t - i = 0.
-30, -1
Let r be (111/(-27) - 0 - -3)/(2/(-15)). Determine d, given that 20/3 + r*d**2 + 40/3*d + 5/3*d**3 = 0.
-2, -1
Let o be (-12)/36 + (-31)/(-3). Suppose -o = -12*r + 7*r. Find a, given that 9*a - 3*a - 689*a**r + 692*a**2 = 0.
-2, 0
Let n = 144 - 72. Let j = -66 + n. Suppose -j - 9*q**4 - 51*q + 54*q**2 - 48*q**4 - 42*q**2 + 51*q**2 + 51*q**3 = 0. Calculate q.
-1, -2/19, 1
Let v(g) = 3*g**2 - 11073*g + 66332. Let a be v(6). Factor 14/3*f - 2/3*f**3 + 4 + 0*f**a.
-2*(f - 3)*(f + 1)*(f + 2)/3
Let j(y) be the first derivative of y**6/3 + 13*y**5/4 + 45*y**4/8 - 10*y**3/3 + y**2/2 - 37*y + 88. Let r(u) be the second derivative of j(u). Factor r(w).
5*(w + 1)*(w + 4)*(8*w - 1)
Suppose 12 = -16944*g + 16950*g. Let p(k) be the second derivative of 0*k**3 + 0 + 1/9*k**4 - 13*k + 1/30*k**5 + 0*k**g. Factor p(l).
2*l**2*(l + 2)/3
Let y(k) = -k**3 - 9*k**2 - 8*k + 18. Let j(h) = -3*h + 31. Let f be j(13). Let r be y(f). Factor -30*d**4 + 21*d - 35*d + 17*d - r*d**2 + 9*d**5 + 36*d**3.
3*d*(d - 1)**3*(3*d - 1)
Find k, given that -58*k - 80 + 43/2*k**2 - 1/2*k**3 = 0.
-1, 4, 40
Let g = -3066 - -3068. Factor -4/3 + 1/6*k**g - 1/3*k.
(k - 4)*(k + 2)/6
Let b(q) be the first derivative of q**3/3 + 2*q + 117. Let y(f) = 10*f**2 - 4*f + 22. Let d(w) = -22*b(w) + 2*y(w). What is a in d(a) = 0?
-4, 0
Factor 1/8*o**3 + 1/4*o**2 - 1/8*o**4 + 0 + 0*o.
-o**2*(o - 2)*(o + 1)/8
Solve -1/2*o + 5/4*o**2 - 3/4 + o**3 = 0.
-1, 3/4
Suppose -7*w = -11*w + 8820. Find f, given that -1489*f**3 - 307*f**3 + 290*f**3 - 945*f + 135 - 209*f**3 + w*f**2 = 0.
3/7
Let f(p) = 4*p**2 - 308*p - 8. Let r(v) = 2*v**2 - 306*v - 6. Let x(o) = -3*f(o) + 4*r(o). Factor x(j).
-4*j*(j + 75)
Let x(u) be the third derivative of -u**8/336 + 118*u**7/105 + 119*u**6/30 + u**5/30 - 475*u**4/24 - 119*u**3/3 - 1791*u**2. Solve x(n) = 0.
-1, 1, 238
Let x = -280 - -283. Let s(f) be the first derivative of -4*f**x - 21 + 0*f - 3*f**5 - 6*f**4 - 1/2*f**6 + 0*f**2. Factor s(m).
-3*m**2*(m + 1)*(m + 2)**2
What is p in 54/19*p**3 + 2/19*p**2 - 54/19*p - 2/19*p**4 + 0 = 0?
-1, 0, 1, 27
Let t(s) be the third derivative of -s**5/100 - 637*s**4/10 - 811538*s**3/5 - 15*s**2 + 150. Factor t(q).
-3*(q + 1274)**2/5
Let y(s) = s**2 + 2*s - 2. Let l(m) = m**2 - 45*m - 45. Let t(n) = n**2 - 45*n - 46. Let o(d) = -6*l(d) + 7*t(d). Let r(z) = o(z) - 2*y(z). Factor r(a).
-(a + 1)*(a + 48)
Let s(p) be the third derivative of 0*p**3 - 1/40*p**6 + 0*p + 0*p**4 + 0 - 1/70*p**7 + 1/20*p**5 - 27*p**2 + 1/112*p**8. What is y in s(y) = 0?
-1, 0, 1
Let s(a) be the third derivative of -17*a**5/30 - 1379*a**4/12 - 54*a**3 + 168