the first derivative of -n**6/2160 + n**5/40 - 9*n**4/16 - 11*n**3/3 - 8*n + 40. Let d(u) be the third derivative of p(u). Factor d(g).
-(g - 9)**2/6
Solve 50/3*f - 2/3*f**2 - 200/3 = 0 for f.
5, 20
Let s(a) be the second derivative of -a**5/150 - 62*a**2 - 102*a. Let v(z) be the first derivative of s(z). Factor v(j).
-2*j**2/5
Determine s so that -25/2*s**3 + 3218*s + 644 + 4015*s**2 = 0.
-2/5, 322
Let u be (-16)/4 - (3 + (2235/63)/(-5)). Let i(z) be the third derivative of 0 + 1/105*z**5 - 10*z**2 + u*z**4 + 2/7*z**3 + 0*z. Factor i(x).
4*(x + 1)*(x + 3)/7
Let o(t) be the second derivative of t**6/135 - 17*t**5/30 + 569*t**4/54 + 77*t**3 + 162*t**2 + 6013*t. What is p in o(p) = 0?
-2, -1, 27
Let f = -709/39 - -3779/195. Solve 8/5*t**4 - 8/5*t**2 + 2/5*t**5 + 0 + f*t**3 - 8/5*t = 0.
-2, -1, 0, 1
Let u(g) be the first derivative of g**5/40 - g**4/12 - 13*g**3/12 - 5*g**2/2 - 84*g + 35. Let d(m) be the first derivative of u(m). Factor d(x).
(x - 5)*(x + 1)*(x + 2)/2
Determine l, given that -90738 - l**3 - 12400*l - 20091*l + 19924*l + 408*l**2 - 2*l**3 = 0.
-6, 71
Factor -54/11*q + 2/11*q**2 + 324/11.
2*(q - 18)*(q - 9)/11
Let l(x) = 3*x + 6 - 1 + 3 + 1. Let y be l(-2). Let -51*o - 134 - 109 - y*o**2 + 105*o = 0. What is o?
9
Let q(m) = -m**3 - 7*m**2 + 6*m - 12. Let n be q(-8). Suppose 24982*x + n*x**2 - 24986*x - 3*x**2 = 0. What is x?
0, 4
Let b(y) = y - 8. Let k be b(2). Let r be -2 - (-9)/3 - (5 + k). Determine p so that 0*p + r*p**2 - 2*p - p**2 + 0*p**2 = 0.
0, 2
Let j(x) be the first derivative of -11/9*x**3 + 23/60*x**5 - 25/48*x**4 + 0*x - 301 + 1/6*x**2. Solve j(p) = 0 for p.
-1, 0, 2/23, 2
Let g(t) be the first derivative of -t**5/5 - 463*t**4/4 + 621*t**3 - 2333*t**2/2 + 934*t - 2968. Determine u so that g(u) = 0.
-467, 1, 2
Let j be (-8)/(-6) + (-3258)/1593. Let q = j - -1559/118. Factor -1/2*v**2 + 5*v - q.
-(v - 5)**2/2
Let z(d) be the second derivative of -5*d**4/12 - 125*d**3/3 - 1125*d**2/2 - 3545*d. Suppose z(g) = 0. What is g?
-45, -5
Let x(q) be the first derivative of -q**6/2 - 39*q**5/5 - 9*q**4 + 176*q**3 - 96*q**2 - 720*q + 1919. What is s in x(s) = 0?
-10, -6, -1, 2
Suppose 3*z + 184 = 3*u - z, -2*z - 62 = -u. Let l be u/5*4/15. Factor -52/5*r**4 + 14/5*r**5 + 8*r**3 + 0 + l*r**2 + 0*r.
2*r**2*(r - 2)**2*(7*r + 2)/5
Let c(y) = y**2 + 33*y + 119. Let o be c(-4). Let f(h) be the second derivative of 1/3*h**4 + 4*h**2 + 0 + 2*h**o - 15*h. Factor f(x).
4*(x + 1)*(x + 2)
Let q = 340594/3 - 113478. Determine j so that -64/3*j**3 - 4/3*j**4 - 52/3 - 56*j**2 - q*j = 0.
-13, -1
Find o such that -13*o + 0 - 7/4*o**5 - 51*o**2 + 24*o**4 - 49/4*o**3 = 0.
-1, -2/7, 0, 2, 13
Factor 6068*y**2 + 4*y**4 + 19059*y**3 + 18874*y**3 - 37629*y**3 + 10952*y.
4*y*(y + 2)*(y + 37)**2
Let h(j) be the third derivative of -j**8/112 + j**7/10 + 17*j**6/40 + 9*j**5/20 - 369*j**2 - 6. Find t, given that h(t) = 0.
-1, 0, 9
Let t(p) be the second derivative of 4*p**2 + p + 2/3*p**3 + 4 - 1/5*p**5 + 2/15*p**6 - p**4. Determine j so that t(j) = 0.
-1, 1, 2
Let v(d) be the third derivative of 11/3*d**3 + 0*d + 0 - 61*d**2 + 1/330*d**5 + 1/6*d**4. Suppose v(y) = 0. Calculate y.
-11
Let o be (-86672)/(-121720) + 2/(-17). Let m = o - -1/179. Factor m*z + 1/5*z**2 + 2/5.
(z + 1)*(z + 2)/5
Let v be (-1)/84*-1154 - ((-2353)/156 - -15)*10. Factor -206/7*h - 2/7*h**3 + 106/7*h**2 + v.
-2*(h - 51)*(h - 1)**2/7
Let x = 2529 + -12644/5. Determine z so that 1/5*z**3 + x - 1/5*z**2 - 1/5*z = 0.
-1, 1
Suppose 35*q - 1 = -1. Suppose -u + 3*s - 2 = -q, 5*s + 2 = 3*u. Factor 0*p + 0 - 4/3*p**3 - 7/3*p**u + 0*p**2.
-p**3*(7*p + 4)/3
Let l(s) be the first derivative of -s**5/45 - 25*s**4/9 - 1250*s**3/9 + 28*s**2 + 202. Let g(k) be the second derivative of l(k). Find q such that g(q) = 0.
-25
Suppose 2*j = 3*z + 32, -5*j + 3*z = -49 - 31. Suppose -496 = -47*c + j*c. Find x, given that -20*x - 1/4*x**3 + c + 17/4*x**2 = 0.
1, 8
Let o(g) be the third derivative of 1/120*g**5 + 19/48*g**4 - 221*g - g**2 + 17/6*g**3 + 0. Factor o(d).
(d + 2)*(d + 17)/2
Factor 678/5*o**2 + 3/5*o**3 + 1347/5*o + 672/5.
3*(o + 1)**2*(o + 224)/5
Factor 101 - 230*a + 367 + 3*a**2 - 10*a.
3*(a - 78)*(a - 2)
Let n(g) be the second derivative of 182/33*g**3 - 115*g + 5/66*g**4 + 72/11*g**2 + 0. Determine y, given that n(y) = 0.
-36, -2/5
Let o(v) = v**2 - 3286*v - 16451. Let z be o(-5). Factor 256/13*c - 28/13*c**3 + 64/13*c**2 + 2/13*c**z + 0.
2*c*(c - 8)**2*(c + 2)/13
Suppose 5*l = 149*v - 144*v + 55, 3*l - 5*v - 49 = 0. Factor 2/7*w**5 - 10/7*w**4 + 0*w + 0 - 12/7*w**l + 0*w**2.
2*w**3*(w - 6)*(w + 1)/7
Let a(s) be the first derivative of 56 + 1/10*s**2 + 0*s - 1/40*s**4 - 1/30*s**3. Solve a(r) = 0 for r.
-2, 0, 1
Let f(i) = 36*i**3 - 355*i**2 - 4882*i + 1003. Let r(j) = -17*j**3 + 177*j**2 + 2441*j - 501. Let w(g) = 6*f(g) + 13*r(g). Factor w(q).
-(q - 45)*(q + 11)*(5*q - 1)
Let t(q) be the second derivative of 20/3*q**3 - 1/15*q**6 - 3 - 1/2*q**5 + 8*q + 2/3*q**4 + 0*q**2. Factor t(k).
-2*k*(k - 2)*(k + 2)*(k + 5)
Let m(q) = q + 3. Let x be m(-1). What is v in -6*v**3 - 8*v**x - 2*v**4 - 12*v**2 + 16*v**2 = 0?
-2, -1, 0
Let x(l) be the third derivative of -7*l**6/180 + 5*l**5/6 - 73*l**4/18 - 16*l**3/3 - 3*l**2 + 160. Find a such that x(a) = 0.
-2/7, 3, 8
Let t(l) be the second derivative of l**5/80 + 7*l**4/24 + 25*l**3/24 + 3*l**2/2 - 861*l. Factor t(i).
(i + 1)**2*(i + 12)/4
Let o(i) be the second derivative of 0*i**2 - 100*i - 1/45*i**6 + 0 + 0*i**4 - 2/15*i**5 + 0*i**3. Factor o(f).
-2*f**3*(f + 4)/3
Suppose 11*z = 39 + 71. Factor -9 - z*m**3 + 17 - 6*m**2 - 18*m + 18*m**2 + 8*m**3.
-2*(m - 4)*(m - 1)**2
Let b(i) be the first derivative of -3*i**4/4 + 1095*i**3 - 1199025*i**2/2 + 145881375*i + 2158. Factor b(d).
-3*(d - 365)**3
What is r in 0 + 0*r - 2/5*r**3 + 6/5*r**2 = 0?
0, 3
Suppose 1806438*v**3 + 2747081*v**3 - 949514*v**3 + 7224990*v**2 + 40 + 33980*v = 0. What is v?
-2, -2/849
Let x(p) = 2*p**2 - 8*p - 9. Let z = 9 + -3. Let f be x(z). Factor -27*t - 23*t + 24 - t**2 - 53*t**2 + 14*t - f*t**3.
-3*(t + 2)**2*(5*t - 2)
Let u = 124 + -121. Determine b so that 15 + 2 + 5*b**2 + 13*b - 10 - b**u = 0.
-1, 7
Let c(x) be the second derivative of -x**7/36 + 17*x**6/60 + 7*x**5/8 + 29*x**4/72 - x**3/2 + 3355*x. Solve c(z) = 0 for z.
-1, 0, 2/7, 9
Let a(c) be the second derivative of -c**5/5 - 137*c**4/12 - 17*c**3/3 + 17*c - 6. Factor a(h).
-h*(h + 34)*(4*h + 1)
Factor -165*a - 76 + 84 - 980*a**2 - 248 - 20*a**3 - 889*a + 89*a.
-5*(a + 48)*(2*a + 1)**2
Let o(t) be the first derivative of -73 - 16/5*t - 2/15*t**3 + 9/5*t**2. Let o(z) = 0. Calculate z.
1, 8
Let v(k) = -141*k**4 - 306*k**3 - 1329*k**2 - 1059*k - 21. Let d(w) = 27*w**4 + 61*w**3 + 266*w**2 + 212*w + 4. Let x(y) = -21*d(y) - 4*v(y). Factor x(o).
-3*o*(o + 1)*(o + 6)*(o + 12)
Let b(y) be the first derivative of 137 - 26*y**2 + 4/3*y**3 + 88*y. Determine c, given that b(c) = 0.
2, 11
Suppose k + 6 = 37*l - 35*l, 12 = -2*l - 2*k. Let c(i) be the second derivative of l + 1/20*i**4 + 4/5*i**3 - 10*i + 24/5*i**2. Find q such that c(q) = 0.
-4
Let b(t) = 2*t**2 - 63*t - 492. Let x be b(38). Factor -4/3*n**x + 2/3*n + 2/3*n**3 + 0.
2*n*(n - 1)**2/3
Let i be 14/2 + (-1780)/9. Let n = i - -191. Factor 0 - n*h**2 + 2/9*h.
-2*h*(h - 1)/9
Let b(p) be the first derivative of -4/5*p**3 + 43 - 11/5*p**2 - 1/10*p**4 - 12/5*p. Factor b(l).
-2*(l + 1)*(l + 2)*(l + 3)/5
Let m be ((-12)/9)/((-3)/(-72)*4). Let j = 11 + m. Suppose -7*p**3 - 3*p**j + p**2 + 7*p**3 + 5*p**4 - 3*p**2 = 0. Calculate p.
-2/5, 0, 1
Let y = -376/231 - -52727/462. Find h such that -183/4*h**2 - 48*h**4 + y*h**3 + 21/4*h + 0 - 24*h**5 = 0.
-7/2, 0, 1/4, 1
Let g = -58562 - -58565. Factor 9/4*h + 9/4 - 1/4*h**g - 1/4*h**2.
-(h - 3)*(h + 1)*(h + 3)/4
Let k = 239652499/1587684 + -80/18901. Let n = -1056/7 + k. Factor 1/2 + 2/3*c**2 + 13/12*c + n*c**3.
(c + 1)**2*(c + 6)/12
Let q(x) be the third derivative of -x - 1/180*x**6 + 1/36*x**4 + 2/9*x**3 + 1/315*x**7 - 1/30*x**5 - 2*x**2 + 0. Factor q(f).
2*(f - 2)*(f - 1)*(f + 1)**2/3
Let q be 40/36*(-12)/5 - (0 - 3). Let d(k) be the first derivative of 0*k + q*k**6 - 18/35*k**5 + 0*k**3 + 0*k**2 + 17 + 1/7*k**4. Factor d(n).
2*n**3*(n - 1)*(7*n - 2)/7
Let u(n) be the second derivative of 0 + 7/3*n**4 - 2/15*n**6 - 10/3*n**3 + 24*n + 