3)/7
Let l(m) be the second derivative of -m**7/2520 - 19*m**6/180 - 361*m**5/30 + m**4/4 + 5*m**3/6 - 7*m. Let j(r) be the third derivative of l(r). Factor j(h).
-(h + 38)**2
Suppose -3*z + 4*q = -6, -5*q + 2 = -z + 4. Let f(w) be the second derivative of 2*w + 1/84*w**4 + 1/14*w**3 - 5/7*w**z + 14. Factor f(v).
(v - 2)*(v + 5)/7
Let u(c) be the third derivative of c**8/6720 + c**7/420 + c**6/144 + c**4/12 + 19*c**3/2 + 52*c**2. Let x(v) be the second derivative of u(v). Factor x(b).
b*(b + 1)*(b + 5)
Factor -96/7 + 6/7*l**3 + 62/7*l**2 + 100/7*l.
2*(l + 3)*(l + 8)*(3*l - 2)/7
Suppose -2*z - 8 = 3*c, -9*c - 8 = -5*c. Let w(m) = -m**4 - m**2 + m. Let l(s) = 7*s**4 - 35*s**3 + 57*s**2 - 27*s. Let r(n) = z*l(n) - 2*w(n). Factor r(h).
-5*h*(h - 5)*(h - 1)**2
Let f(v) be the first derivative of 26*v - 50*v**2 - 1/3*v**4 - 8 - 20/3*v**3. Let a(n) be the first derivative of f(n). Factor a(q).
-4*(q + 5)**2
Let d(c) be the first derivative of -c**7/5040 + c**6/432 + c**5/720 - 5*c**4/144 + 64*c**3/3 - 172. Let t(q) be the third derivative of d(q). Factor t(b).
-(b - 5)*(b - 1)*(b + 1)/6
Let l(d) = -d**3 + 7*d**2 - 5*d - 14. Let m be l(3). Factor -2*g - m*g - 4*g**2 + 0*g - 3*g.
-4*g*(g + 3)
Suppose -1/2*h**3 - 174*h - 172 - 45*h**2 = 0. What is h?
-86, -2
Let t(f) be the second derivative of -3*f**5/20 - 707*f**4/4 + 354*f**3 + 23*f - 2. Determine k, given that t(k) = 0.
-708, 0, 1
Let k(g) = 9*g + 74. Let h be k(-8). Factor -12 - 8*l + 15*l**h - 4*l**2 - 7*l**2.
4*(l - 3)*(l + 1)
Let k(u) be the third derivative of -41/40*u**5 - 68921/12*u**3 + 0 - 112*u**2 - 1681/16*u**4 + u - 1/240*u**6. Factor k(s).
-(s + 41)**3/2
Let l(b) be the first derivative of b**5 - 315*b**4/2 + 20465*b**3/3 - 19530*b**2 + 19220*b + 2020. Determine v so that l(v) = 0.
1, 62
Let y be (-2457)/(-33) + -10 + (-232)/(-22). Suppose g + 5 = 2*l, -3*g + 70*l + 29 = y*l. Suppose -16/5*p + 24/5 - 2/5*p**2 + 2/5*p**g = 0. Calculate p.
-3, 2
Suppose 4*f = -208*p + 213*p - 20, f = 0. Let a(k) be the first derivative of 1/15*k**3 + 1/10*k**p + 0*k**2 + 1/25*k**5 + 26 + 0*k. Factor a(g).
g**2*(g + 1)**2/5
Suppose -72*m + 519 = 101*m. Let n(u) be the third derivative of 0*u**m + 5*u**2 + 0 + 0*u - 1/20*u**4 - 1/100*u**5. Suppose n(z) = 0. What is z?
-2, 0
Suppose -5*j + 8*j = l + 132, 4*l + 528 = 3*j. Let h = -130 - l. Factor 19*a**3 - a**4 - 3 - 19*a**3 + 4*a**h + 2*a**3 - 2*a.
-(a - 3)*(a - 1)*(a + 1)**2
Suppose -53 = 12*x - 7*x - 63. Let u(g) be the first derivative of 0*g + 0*g**2 + x + 4/9*g**3 - 1/9*g**6 + 0*g**5 + 1/2*g**4. Factor u(k).
-2*k**2*(k - 2)*(k + 1)**2/3
Let u(s) be the third derivative of -s**6/16 - 57*s**5/20 - 11*s**4/2 - 1907*s**2. Factor u(r).
-3*r*(r + 22)*(5*r + 4)/2
Solve -128596*a - 4*a**2 + 132468*a - 937024 + 0*a**2 = 0 for a.
484
Let n(m) = 21*m + 24*m - 41*m. Let q be n(1). Factor -24*o**2 - 4*o - 2*o**5 - 12*o**q - 26*o**3 + 0*o - 4*o.
-2*o*(o + 1)**2*(o + 2)**2
Let x(y) be the second derivative of y**4/6 + 122*y**3/3 + 121*y**2 - 836*y. Factor x(s).
2*(s + 1)*(s + 121)
Let r = -128 - -130. Let u(b) = b + 17. Let s be u(-17). Factor s + 6/5*m + 2/5*m**r.
2*m*(m + 3)/5
Suppose -1543*d + 3*r = -1548*d + 33, 39 = 3*d + 5*r. Factor 4/3 + 2/3*o - 2/3*o**d - 4/3*o**2.
-2*(o - 1)*(o + 1)*(o + 2)/3
Let t(k) be the first derivative of -1/10*k**5 + 1/4*k**4 + 27 + 0*k**2 + 0*k**3 + 0*k. Let t(p) = 0. Calculate p.
0, 2
Let d(l) = 8*l**2 - 157*l + 773. Let f be d(10). Factor -56/3 - 38*r - 2/3*r**f - 20*r**2.
-2*(r + 1)**2*(r + 28)/3
Determine l so that 122495059 + 1651692*l + 15*l**3 - 11*l**3 + 4452*l**2 + 50190319 + 31573866 = 0.
-371
Let l(n) be the third derivative of -n**7/525 + 13*n**6/150 - 13*n**5/30 - 23*n**4/15 - 77*n**2 + 3*n. Suppose l(h) = 0. Calculate h.
-1, 0, 4, 23
Let h(f) be the first derivative of 69 - 40*f - 55*f**2 + 125/4*f**4 + 475/3*f**3. Factor h(r).
5*(r + 4)*(5*r - 2)*(5*r + 1)
Let m(s) be the first derivative of -3*s**5/20 + 123*s**4/16 + s**3/4 - 123*s**2/8 - 1762. Let m(z) = 0. Calculate z.
-1, 0, 1, 41
Let q be -10 - -6 - -3*22/3. Factor -64 + 15*j + 12*j**2 - 4*j**3 - 12*j + 11*j + q*j - j**4.
-(j - 2)**2*(j + 4)**2
Let w = -2423/50 - -7519/150. Let -10/3 + 13/3*x - 1/3*x**4 + x**2 - w*x**3 = 0. Calculate x.
-5, -2, 1
Suppose -q - 4*q + 95 = 0, 2*k + 272*q - 273*q + 15 = 0. Find w such that -4800/7 - 3/7*w**4 - 18/7*w**3 + 720/7*w + 213/7*w**k = 0.
-8, 5
Solve 73*p**2 - 62*p**2 - 9*p**2 - 1196 + 594*p = 0.
-299, 2
Suppose 9*h - 1335 = -273. Solve -24 + 25*k**4 + 465*k**2 - h*k + 2*k - 235*k**3 + 94 - 209*k = 0 for k.
2/5, 1, 7
Let k(i) be the third derivative of -i**8/252 + i**7/9 - 221*i**6/180 + 101*i**5/15 - 19*i**4 + 24*i**3 + 150*i**2 + 2*i. Determine n so that k(n) = 0.
1/2, 2, 3, 6
Let m = 1146 - 1143. Let k(l) be the first derivative of 8*l + 2*l**2 - 17 + 1/6*l**m. Factor k(z).
(z + 4)**2/2
Let i(l) be the second derivative of 0 + 1875/2*l**2 + 316*l + 1/4*l**4 + 25*l**3. Suppose i(t) = 0. Calculate t.
-25
Let a = 30 - 30. Suppose a*m + 50 = 5*m. Suppose 36*h + m*h**2 - 40*h - 6*h**2 = 0. Calculate h.
0, 1
Let q = -505 - -507. Factor 3*m + q*m**2 - 30*m**2 - 4*m**4 - 33*m - 7*m**2 + 9*m**4.
5*m*(m - 3)*(m + 1)*(m + 2)
Let b = -123 + 123. Let v(y) be the first derivative of -1/9*y**2 + b*y - 8/27*y**3 - 1 - 1/27*y**6 - 8/45*y**5 - 1/3*y**4. Factor v(x).
-2*x*(x + 1)**4/9
Let x(p) = -8*p + 111. Let y be x(15). Let q be 198/12 - (3 + y). Factor -5*n - q*n**3 - 35/2*n**2 - 5/2*n**5 - 25/2*n**4 + 0.
-5*n*(n + 1)**3*(n + 2)/2
Let z = 8532 + -8526. Let m(s) be the third derivative of -17*s**2 + 0*s**z + 0*s**3 + 1/1344*s**8 + 0 - 1/96*s**4 + 0*s - 1/420*s**7 + 1/120*s**5. Factor m(v).
v*(v - 1)**3*(v + 1)/4
Let l(m) be the third derivative of -m**8/112 - 3*m**7/10 - 2*m**6 - 27*m**2. Let l(d) = 0. What is d?
-16, -5, 0
Suppose -2*n = 3*m - n + 83, 0 = 3*m - 5*n + 53. Let z = m + 29. Factor z + 4*h + 4*h**2 - 3*h - 3*h**2 + 3*h.
(h + 1)*(h + 3)
Let g(k) = -k**3 - k. Let f be g(-1). Let n(m) = -14*m + 312. Let h be n(22). Factor 9/4*r**3 - 1 + h*r - 21/4*r**f.
(r - 1)*(3*r - 2)**2/4
Let p(u) be the second derivative of u**6/330 + 3*u**5/220 - u**4/22 - 14*u**3/33 - 12*u**2/11 - 3*u + 163. What is o in p(o) = 0?
-2, 3
Let y be (-2)/(-4) + (1370655/(-18))/13. Let z = y - -13102. Factor -4*q**2 + 7245 - z.
-4*q**2
Factor -63/2 - 25/4*j - 1/4*j**2.
-(j + 7)*(j + 18)/4
Suppose 0 = -5*o - a + 105, -3*o + 63 = -3*a + a. Let f(p) be the first derivative of 0*p**3 - 3/20*p**5 - 3/16*p**4 + 0*p - o + 0*p**2. Factor f(h).
-3*h**3*(h + 1)/4
Let q(m) be the third derivative of m**7/420 + 43*m**6/80 + 176*m**5/5 + 256*m**4/3 + 742*m**2. Let q(k) = 0. What is k?
-64, -1, 0
Factor 513/8*t - 3/4 + 525/4*t**2.
3*(2*t + 1)*(175*t - 2)/8
Let g(l) be the third derivative of l**8/336 - 47*l**7/210 + 359*l**6/60 - 1897*l**5/30 + 4465*l**4/24 + 9025*l**3/6 - 50*l**2 + 55. Factor g(a).
(a - 19)**2*(a - 5)**2*(a + 1)
Let k(p) be the first derivative of -1/6*p**4 - 1/30*p**5 + 2/3*p + 1/3*p**2 + 71 - 1/6*p**3. Factor k(h).
-(h - 1)*(h + 1)*(h + 2)**2/6
Let t(a) be the second derivative of a**6/15 + 124*a**5/5 - 1003*a**4/6 + 1258*a**3/3 - 504*a**2 + 478*a - 2. Suppose t(q) = 0. What is q?
-252, 1, 2
Let p be 14/42*(-63)/(-35). Find v such that 218/5*v**3 + 49/5 - 47/5*v**4 + p*v**5 - 258/5*v**2 + 7*v = 0.
-1/3, 1, 7
Let v(a) be the first derivative of 17*a**5 + 5/6*a**6 + 100*a**4 - 5 + 0*a**2 + 320/3*a**3 + 0*a. Find y such that v(y) = 0.
-8, -1, 0
Let z(y) be the third derivative of y**5/450 + 13*y**4/4 - 321*y**2 + 4*y. Factor z(k).
2*k*(k + 585)/15
Let q = 217257 + -217257. Factor -42/5*o**3 + q + 6*o**4 + 0*o + 18/5*o**2 - 6/5*o**5.
-6*o**2*(o - 3)*(o - 1)**2/5
Let x = -1188 + 490. Let u = x + 703. Solve 2/5*t**u + 0*t**4 + 0*t**2 + 0*t - 2/5*t**3 + 0 = 0 for t.
-1, 0, 1
Let r(z) = -15*z**2 - 81*z + 5. Let q(s) = 18*s**2 + 102*s - 6. Let y(d) = -d**2 + d. Let o(m) = 2*q(m) - 2*y(m). Let w(g) = -5*o(g) - 12*r(g). Factor w(j).
-2*j*(5*j + 19)
Let c = -2182/9 + 15292/63. Let m(t) be the first derivative of 1/21*t**6 - 2/35*t**5 + 4/21*t**3 + 1/7*t**2 - c*t - 1/7*t**4 + 1. Factor m(l).
2*(l - 1)**3*(l + 1)**2/7
Let b(q) be the third derivative of q**5/3 + 37*q**4/24 - 43*q**3/6 + 14*q**2 - 2. Let y(g) = 6*g**2 + 12*g - 14. Let z(o) = 2*b(o) - 7*y(o). Factor