et o(u) be the first derivative of 8/3*u**4 + 0*u**2 + 60 + 49/18*u**6 - 77/15*u**5 - 4/9*u**3 + 0*u. Factor o(j).
j**2*(j - 1)*(7*j - 2)**2/3
Find s such that -5/4*s**3 - 5/4*s**2 + 0 + 15/2*s = 0.
-3, 0, 2
Let m(b) be the first derivative of -b**5/150 - b**4/30 + b**3/5 - 23*b**2/2 + 44. Let l(d) be the second derivative of m(d). Find t, given that l(t) = 0.
-3, 1
Let d(r) = 2*r**3 + r**2 - r. Let j(n) = -7*n**3 - 13*n**2 - 12*n + 4. Let h(u) = -3*d(u) - j(u). Let t be h(-8). Factor 0*g**2 + 0 + 0*g - 1/7*g**t + 1/7*g**3.
-g**3*(g - 1)/7
Let c(u) be the third derivative of 1/25*u**5 - u**2 + 21 + 0*u**4 + 0*u**3 + 1/300*u**6 + 0*u. Find p such that c(p) = 0.
-6, 0
Let d = 206 - 147. Suppose -25 - d = -28*j. Factor -26/9*s**2 + 8/3*s + 4/3*s**j - 2/9*s**4 - 8/9.
-2*(s - 2)**2*(s - 1)**2/9
Let a(i) be the first derivative of -2*i**5/65 - 41*i**4/26 - 158*i**3/39 - 3*i**2 - 1887. Factor a(y).
-2*y*(y + 1)**2*(y + 39)/13
Factor 16/3*i**2 + 20/3 - 14*i.
2*(i - 2)*(8*i - 5)/3
Factor -147*o**3 - 28646*o**2 - 103*o**3 - o**4 - 966319 + 7730*o**2 - 592454*o + 394532.
-(o + 1)*(o + 83)**3
Let a(x) be the third derivative of x**6/72 - 7*x**5/20 + 2*x**4/3 - 4*x**3/3 - 107*x**2. Let j(q) be the first derivative of a(q). Factor j(w).
(w - 8)*(5*w - 2)
Let h = 384483 - 384481. Factor 16/9*m**h + 0 + 2*m**3 + 2/9*m**4 + 0*m.
2*m**2*(m + 1)*(m + 8)/9
Let j be (-2216)/(-1662)*(-3)/(-2). Let n(f) be the third derivative of -j*f**2 - 45 + 1/210*f**5 - 1/840*f**6 + 1/168*f**4 - 1/21*f**3 + 0*f. Factor n(x).
-(x - 2)*(x - 1)*(x + 1)/7
Let f(z) be the second derivative of -z**7/7 - 9*z**6/10 + 117*z**5/10 - 31*z**4/4 - 18*z**3 + 130*z. Find x such that f(x) = 0.
-9, -1/2, 0, 1, 4
Let j(f) = 6*f**2 + 9*f - 31. Let d(q) = q**2 + 2*q - 6. Let w(y) = -y - 14. Let p be w(-7). Let z = -15 + p. Let l(k) = z*d(k) + 4*j(k). Factor l(x).
2*(x - 2)**2
Let t(r) be the first derivative of -3*r**5/100 + 6*r**4/5 - 23*r**3/10 + 118*r + 86. Let h(v) be the first derivative of t(v). Determine d so that h(d) = 0.
0, 1, 23
Let c(a) = 4*a**3 - 7*a**2 + 22*a + 8. Let o be c(6). Factor -o*i**2 + 747*i**2 - 109 - 71 - 60*i.
-5*(i + 6)**2
Let m(j) be the third derivative of j**6/720 - 13*j**5/60 + 169*j**4/12 + 121*j**3/6 + 27*j**2 + 4*j. Let y(k) be the first derivative of m(k). Factor y(d).
(d - 26)**2/2
Let h = 7278 - 7276. Let l(z) be the second derivative of -9/8*z**h + 7*z - 1/48*z**4 + 1/4*z**3 + 0. Factor l(k).
-(k - 3)**2/4
Let i = 596 + 904. Suppose -i*q + 16 = -1492*q. Solve 5/4*t**4 - 1/4*t**q - 1 + 7/4*t**5 + 4*t - 23/4*t**3 = 0.
-2, -1, 2/7, 1
Factor -m**4 + 484*m**2 - 255*m**2 - 3*m**4 + 418*m**2 - 47*m**2 + 76*m**3.
-4*m**2*(m - 25)*(m + 6)
Determine o, given that 654*o**3 + 150*o**4 - 5190*o**2 + 5013*o**5 - 4275*o - 1414*o**3 - 5018*o**5 = 0.
-3, -1, 0, 15, 19
Let y(n) be the first derivative of -4*n**3/3 + 3468*n**2 - 3006756*n + 3260. Factor y(h).
-4*(h - 867)**2
Suppose -2*c**4 + 104/3*c**3 + 32 + 0*c**2 - 10/3*c**5 - 256/3*c = 0. What is c?
-3, -2, 2/5, 2
Let k(i) be the third derivative of 2/3*i**3 - 1/150*i**5 - 3/20*i**4 - 12*i**2 + 0*i + 5. Factor k(g).
-2*(g - 1)*(g + 10)/5
Suppose 2*t = t + 61. Let x(v) be the first derivative of -1 - t*v**2 + v**3 - 2 + 14 + 52*v**2 + 27*v. Factor x(a).
3*(a - 3)**2
Let n = -70005 + 70007. Factor -7*x - 1/4*x**4 + 4 + 3*x**n + 1/4*x**3.
-(x - 2)**2*(x - 1)*(x + 4)/4
Suppose -2*v - 201*m = -205*m - 2, v - 5*m + 14 = 0. Factor 2*n**2 + 25/4*n**5 + 0 + 35/2*n**4 + 0*n + v*n**3.
n**2*(n + 2)*(5*n + 2)**2/4
Let s be (-252)/(-70)*(-40)/3. Let n be 31/1581*s/(-2). Factor 0 + 8/17*q**2 + 0*q - n*q**3 + 2/17*q**4.
2*q**2*(q - 2)**2/17
Let c(g) be the second derivative of 14*g - 3 + 1/6*g**4 + 121*g**2 - 22/3*g**3. Factor c(x).
2*(x - 11)**2
Let g be ((-6)/13)/((-252)/312). Let l(d) be the first derivative of -1/14*d**4 - g*d**3 + 1 - 16/7*d - 12/7*d**2. Suppose l(o) = 0. Calculate o.
-2
Let u(x) be the second derivative of -x**7/252 + x**6/90 + x**5/60 - x**4/9 + 7*x**3/36 - x**2/6 - 98*x + 7. Let u(b) = 0. Calculate b.
-2, 1
Let w = -49201 + 147605/3. Solve -2/9*b**2 + 4/9 - 2/9*b**4 + w*b - 2/3*b**3 = 0 for b.
-2, -1, 1
Let n(b) be the first derivative of b**4/30 + 106*b**3/15 + 152*b**2/15 - 632*b/5 - 2301. Let n(c) = 0. What is c?
-158, -3, 2
Let b = -63772 - -191327/3. What is d in 0 - b*d + 1/3*d**2 = 0?
0, 11
Suppose 14*z = 14 + 14. Determine l so that 149*l**z + 151*l**2 - 300*l**2 - 4*l**3 = 0.
0
Let o(c) be the third derivative of -1/160*c**5 + 80*c**2 + 1/24*c**4 - 1 + 0*c + 1/16*c**3. Factor o(r).
-(r - 3)*(3*r + 1)/8
Suppose 4*j + 2*j - 30 = 0. Factor 4*m**4 - 2*m**j - 8*m + 38 + 8*m**3 + 10*m**3 - 44*m**2 + 10 + 0*m**4.
-2*(m - 2)**3*(m + 1)*(m + 3)
Suppose -271 = -k + 5*a + 473, 4*k - 5*a = 2991. Let c = k - 747. Suppose 0 + 2/9*y**c - 2/9*y = 0. Calculate y.
0, 1
Let d be (-2)/3 - 8/(-3). Suppose -13*r + 14 = -25. Factor -r*m**d + 4*m**3 - 1576 + 1576 - m**4.
-m**2*(m - 3)*(m - 1)
Let h be (-28 - (-369)/12) + (-453)/(-84). Determine n so that 18/7 + h*n**2 + 75/7*n = 0.
-1, -6/19
Find i, given that 0 + 1/2*i**3 + 21*i - 17/2*i**2 = 0.
0, 3, 14
Let n = -101850 - -916651/9. Factor -n*g**3 + 32/9*g + 4 + 5/9*g**2.
-(g - 9)*(g + 2)**2/9
Suppose 3*v = -51 - 189. Let h = 84 + v. Factor -h*y**5 - 4 + 4*y**2 + 3*y**5 + 6*y - 8*y**3 + 3*y**5.
2*(y - 1)**3*(y + 1)*(y + 2)
Let k = -15 - -24. Let u(z) = -z**4 + z**3 - 7*z**2 - 15*z - 4. Let w(v) = 5*v**4 - 4*v**3 + 28*v**2 + 61*v + 15. Let q(l) = k*u(l) + 2*w(l). Factor q(x).
(x - 3)*(x + 1)**2*(x + 2)
Factor -2/9*j**2 + 128 + 0*j.
-2*(j - 24)*(j + 24)/9
Let h(y) be the third derivative of -1/294*y**7 + 1/2352*y**8 + 1/10*y**5 - 10*y**2 + 9/14*y**3 + 0 - 3/8*y**4 + 0*y - 1/420*y**6. What is z in h(z) = 0?
-3, 1, 3
Let k = -18122 - -18122. Let a = -4 + 6. Factor 18 + 0*o**a + 5*o**2 + 27 + 30*o + k*o**2.
5*(o + 3)**2
Suppose 3*t - 6 = -0. Let z be (t + -2 - (0 - 1)) + 32. Factor 16*s - 12*s - 4*s + z*s**3 + 48*s**4 + 21*s**5 + 6*s**2.
3*s**2*(s + 1)**2*(7*s + 2)
Suppose -35798011 - 5*b**2 + 3059650 - 28350*b - 7447764 = 0. What is b?
-2835
Factor -126/11*z**2 + 38/11*z**3 - 4 + 2/11*z**4 + 130/11*z.
2*(z - 1)**3*(z + 22)/11
Let a = -193 - -196. Let p be (-7)/(-35)*(8 - 2). Factor 2/15 + 8/15*w**a + 4/5*w + p*w**2.
2*(w + 1)**2*(4*w + 1)/15
Let d(n) = -19*n**2 + 2063*n - 2056. Let g(i) = -156*i**2 + 16506*i - 16449. Let t(h) = -33*d(h) + 4*g(h). Factor t(u).
3*(u - 684)*(u - 1)
Let m(g) be the third derivative of -4/45*g**5 - 2/105*g**7 + 0 + 1/15*g**6 + 1/504*g**8 + 3*g**2 + 0*g**4 + 0*g**3 - 4*g. Factor m(j).
2*j**2*(j - 2)**3/3
Let o(p) be the second derivative of -5*p**4/12 - 455*p**3/3 + 915*p**2/2 + 2624*p. Factor o(j).
-5*(j - 1)*(j + 183)
Find j such that -46889928*j**2 - 3888*j**4 - 517407966 - 2858612259 + 697248*j**3 + 1401487848*j - 12332322738 = 0.
269/6
Let p(l) be the third derivative of -l**8/6720 - l**7/1680 + 79*l**5/30 - 2*l**2 - 4. Let w(q) be the third derivative of p(q). Factor w(z).
-3*z*(z + 1)
Let i(j) be the second derivative of -j**4/4 + 50*j**3 - 11*j - 75. Determine l, given that i(l) = 0.
0, 100
Let l(u) be the first derivative of 8*u**7/945 + 17*u**6/540 + u**5/27 + u**4/108 - 3*u**2/2 - 2*u + 29. Let b(p) be the second derivative of l(p). Factor b(f).
2*f*(f + 1)**2*(8*f + 1)/9
Let u = -60214 + 60216. Factor 42/11 + 2/11*v**u + 4*v.
2*(v + 1)*(v + 21)/11
Suppose 4*f - 32 = 4*d, -13*d + 20 = 5*f - 8*d. Solve 0*r**2 - 4*r**2 + 5*r**4 - f*r - 3*r**4 - 6*r**2 + 12 - 4 + 6*r**3 = 0 for r.
-4, -1, 1
Suppose -98*b + 127*b + 168*b = -888*b. Let z = 39/517 - -5/47. Factor -6/11*s**2 + b + z*s**3 + 4/11*s.
2*s*(s - 2)*(s - 1)/11
Let o = 8137/14 + -12202/21. Factor 10/3 + o*t**2 - 7/2*t.
(t - 20)*(t - 1)/6
Suppose 3*x = 3*b + 15, 2*x - 2*b - 3*b - 19 = 0. Factor -6*g**2 + 4*g**2 + 5*g**2 - g**x.
2*g**2
Let u(p) be the third derivative of 17/2*p**3 + 2*p**4 - 201*p**2 - 1/20*p**5 + 0 + 0*p. Factor u(a).
-3*(a - 17)*(a + 1)
Let d(a) be the second derivative of -5/6*a**3 - 13*a - 5/24*a**4 - 2 + 15/4*a**2. Suppose d(z) = 0. What is z?
-3, 1
Solve -14/13*j**2 + 14/13*j**4 + 0*j + 2/13*j**5 - 2/13*j**3 + 0 = 0.
-7, -1, 0, 1
Let q(c) be the first derivative of -c**3/7 - 15*c**2/14 + 312*c/7 - 2865. Factor q(o).
-3*(o - 8)*(o + 13)/7
Let o(q) be the second deriva