- 1)**2*(4*z - 1)**2/5
Let u(a) be the third derivative of 0*a - 1/96*a**4 - 1/12*a**3 - 4*a**2 + 1/240*a**5 + 0. Find c, given that u(c) = 0.
-1, 2
Let r be ((-11155)/(-3128))/(2/4) + 2/17. Let y(v) be the second derivative of 63/20*v**5 + 6*v**2 + 18*v + 0 + 2*v**3 - r*v**4. Suppose y(d) = 0. Calculate d.
-2/7, 2/3, 1
Let s be ((-1127)/(-1470) + 6/(-9))*((-36)/(-2) - 2). Find a such that -2/5*a**4 + 8/5 - 8/5*a**3 - 6/5*a**2 + s*a = 0.
-2, -1, 1
Let n(p) = p**2 - 22. Let x(d) = -20*d**2 + 172*d + 1008. Let b(i) = -24*n(i) - x(i). Factor b(q).
-4*(q + 3)*(q + 40)
Let d(s) be the second derivative of -16*s + 3/140*s**5 - 1/14*s**4 + 12/7*s**2 - 2/7*s**3 + 0. Find g, given that d(g) = 0.
-2, 2
Let c be (-4)/14*((-4942)/(-168) - 30). Let u(k) be the second derivative of 1/20*k**5 - 17*k + 0 - 1/6*k**4 + c*k**3 + 0*k**2. Let u(p) = 0. What is p?
0, 1
Let w = -13036 + 13039. Let l(g) be the first derivative of 32 - 32*g - 2/3*g**w - 8*g**2. Factor l(b).
-2*(b + 4)**2
Determine o so that 1/2*o**3 - 160*o - 1050 - 1/2*o**2 = 0.
-10, 21
Let j = 283 + -281. Let f(p) be the second derivative of j*p**2 - 2/3*p**3 + 15*p - 1/3*p**4 + 0 + 1/5*p**5. Factor f(l).
4*(l - 1)**2*(l + 1)
Let d(k) be the first derivative of -29*k**5/120 + 31*k**4/48 - k**3/6 - k**2 - 102. Let g(u) be the second derivative of d(u). Find b, given that g(b) = 0.
2/29, 1
Factor 0 - 14/3*k**2 - 2/9*k**3 + 200/9*k.
-2*k*(k - 4)*(k + 25)/9
Let m(v) be the third derivative of -11*v**6/24 + 181*v**5/60 + 20*v**4/3 - 8*v**3/3 + 4799*v**2. Factor m(b).
-(b - 4)*(5*b + 4)*(11*b - 1)
Let h(j) be the third derivative of 218*j**2 + 1/70*j**7 + 1/336*j**8 + 0*j + 0 + 0*j**4 - 9/20*j**5 - 3/40*j**6 + 0*j**3. Let h(p) = 0. Calculate p.
-3, 0, 3
Let p(r) be the first derivative of -r**6/4 + 363*r**5/5 - 43923*r**4/8 + 6744. Factor p(z).
-3*z**3*(z - 121)**2/2
Suppose -252 = -4*u + 4*c, 4*u - 4*c - 248 = -2*c. Suppose 0 = -5*b + 3*l, -2*l - l = -15. Factor -u*o**b + 63*o**3 - 16*o**2 + 4*o**2.
2*o**2*(o - 6)
Let j be 132/(-726)*4/(16/(-77)). Factor -y + j*y**2 - 7/2*y**3 + y**4 + 0.
y*(y - 2)*(y - 1)*(2*y - 1)/2
Let s(h) = -6*h + 150. Let x be s(25). Let d(o) be the second derivative of 0*o**3 + 1/36*o**6 + x - 10*o - 5/36*o**4 + 0*o**5 + 5/12*o**2. Factor d(v).
5*(v - 1)**2*(v + 1)**2/6
Let b(s) = s**3 + 29*s + s**2 - 61*s + 33*s. Let z(c) = 9*c**3 - 6*c**2 + 4*c. Let i(d) = 4*b(d) - z(d). Factor i(f).
-5*f**2*(f - 2)
Let r(w) = -5*w**4 + 37*w**3 + 9*w**2 - 62*w - 47. Let i(j) = 4*j**4 - 32*j**3 - 8*j**2 + 62*j + 46. Let k(p) = 6*i(p) + 4*r(p). Factor k(y).
4*(y - 11)*(y - 2)*(y + 1)**2
Let k = -53 - -49. Let g be (-27)/18 + (-98)/k. Find y such that 6*y - 13*y**2 - g*y**2 - 5*y**4 - 14*y - 15*y**4 - 48*y**3 = 0.
-1, -2/5, 0
Determine l, given that 2*l**3 + 49947*l**2 - 168 - 62*l - 26*l - 49865*l**2 = 0.
-42, -1, 2
Let w(h) = 55*h**2 - 1030*h - 245. Let t(q) = -105*q**2 - 16 - 9*q**2 + 61*q**2 + 203 + 1029*q + 55. Let k(l) = 5*t(l) + 4*w(l). Let k(x) = 0. Calculate x.
-2/9, 23
Let i(n) be the first derivative of -2*n**5/25 - n**4/5 + 14*n**3/15 - 4*n**2/5 - 2086. Find d such that i(d) = 0.
-4, 0, 1
Let a = 548989/76245 - 5/15249. Factor 27/5*s + 6/5 + 3*s**3 + a*s**2.
3*(s + 1)**2*(5*s + 2)/5
Factor -5/9*k - 1/3*k**3 + 0 + k**2 - 1/9*k**4.
-k*(k - 1)**2*(k + 5)/9
Factor -2*m**2 + 8/3*m - 2/3*m**3 + 0.
-2*m*(m - 1)*(m + 4)/3
Let z = 571 + -577. Let j be z + 6 - 0 - (-5)/4. Factor -1/4*n**5 - j*n**4 - 2*n**3 + 0 + 0*n - n**2.
-n**2*(n + 1)*(n + 2)**2/4
Let n(p) = 13*p**3 + 4806*p**2 + 969577*p + 2865618. Let a(w) = 7*w**3 + 2403*w**2 + 484789*w + 1432809. Let x(z) = -7*a(z) + 4*n(z). Let x(r) = 0. Calculate r.
-399, -3
Let b(m) = 5*m**2 - 3*m - 42. Let d be b(-5). Let x be ((408/21)/4)/(168/d). Suppose -y - x*y**2 + 7/6*y**4 + 8/3*y**3 + 0 = 0. Calculate y.
-3, -2/7, 0, 1
Let t(k) be the first derivative of -k**6/12 + 9*k**5/10 + 11*k**4/8 - 3*k**3/2 - 5*k**2/2 + 2614. Find b such that t(b) = 0.
-1, 0, 1, 10
Let c = -337 - -340. Suppose 3*t - 4*v + 3*v = 4, -c*v = -4*t + 12. Factor 0*a + t*a**3 + 2/11*a**4 + 0 + 0*a**2.
2*a**4/11
Suppose -4*o - 6 = -18. Let 0*s + 0*s - 3*s**2 - 239*s**3 + 242*s**o = 0. What is s?
0, 1
Let g(t) be the second derivative of t**5/90 - t**4/27 - 44*t**3/9 - 56*t**2 + 45*t + 1. Factor g(h).
2*(h - 14)*(h + 6)**2/9
Find p such that 16852*p**2 - 4284*p**3 - 1770*p + 6426*p**4 - 578*p**5 - 3601*p**3 - 13095*p**3 + 50 = 0.
1/17, 1, 5
Let n(m) be the second derivative of m**6/10 + 12*m**5/5 + 31*m**4/2 - 56*m**3 - 2205*m**2/2 + 1575*m. Suppose n(j) = 0. Calculate j.
-7, -5, 3
Let b = 366516 + -366514. Factor -3/2*k**3 - 8/3*k - 7/2*k**b - 2/3.
-(k + 1)*(3*k + 2)**2/6
Let u(y) be the first derivative of 4/5*y**2 + 6/5*y + 2/15*y**3 - 98. Factor u(k).
2*(k + 1)*(k + 3)/5
Let a = 89 - 93. Let h(n) = -28*n**2 - 252*n - 96. Let y(t) = -30*t**2 - 253*t - 96. Let w(c) = a*y(c) + 5*h(c). Find m such that w(m) = 0.
-12, -2/5
Let n(q) be the first derivative of q**4 - 44*q**3 + 342*q**2 + 7220*q - 1029. Factor n(m).
4*(m - 19)**2*(m + 5)
Let c(j) be the second derivative of -2*j**6/15 + 59*j**5/5 - 159*j**4 + 918*j**3 - 2700*j**2 + 70*j + 3. Let c(z) = 0. What is z?
3, 50
Let p = 9395/224904 - 1/9371. Let z(w) be the third derivative of p*w**4 - 22*w**2 + 0 + 0*w + 0*w**3 + 1/240*w**5. Factor z(n).
n*(n + 4)/4
Suppose -11*z + 20 + 112 = 11*z. Let g(w) be the second derivative of -w**4/4 - w**3/3 - 2*w. Let n(k) = 3*k**2 + 3*k. Let m(x) = z*g(x) + 5*n(x). Factor m(c).
-3*c*(c - 1)
Let b = -25798 + 103199/4. What is f in -11/4*f + b*f**2 + 5/4 - 1/4*f**3 = 0?
1, 5
Factor -1/6*h**3 + 446/3 + 148*h + 73/2*h**2.
-(h - 223)*(h + 2)**2/6
Let q(z) = 519 + 4*z**2 + 546 - 23*z - 1048. Let p be q(5). Solve 4/3*y - 2/3*y**p + 16/3 = 0 for y.
-2, 4
Suppose 0 = -10*h + 7*h + 39. Let i(q) = -11*q**3 + 55*q**2 + 83*q + 35. Let v(r) = 24*r**3 - 112*r**2 - 166*r - 69. Let n(p) = h*i(p) + 6*v(p). Factor n(f).
(f + 1)**2*(f + 41)
Let l = -248 - -295. Find i, given that -16 + l*i - 131*i - 900*i**2 - 44*i - 115*i + 3*i = 0.
-2/15
Let 4*f**2 - 40306*f - 212 - 40598*f + 81112*f = 0. What is f?
-53, 1
Let i(y) be the first derivative of -y**6/360 + y**5/120 + y**4/4 - 18*y**3 - 73. Let q(n) be the third derivative of i(n). Factor q(l).
-(l - 3)*(l + 2)
Find b such that -106532*b + 106108*b + 2*b**2 + 4*b**3 - 125*b**2 - 81*b**2 = 0.
-2, 0, 53
Let v(z) be the first derivative of 112/3*z**3 - 28/5*z**5 - 2*z**4 + 0*z + 16*z**2 - 22. Determine l so that v(l) = 0.
-2, -2/7, 0, 2
Let j = 6193 - 130037/21. Let u(i) be the first derivative of 0*i**2 - 1/7*i**4 - j*i**3 + 0*i + 21. Suppose u(a) = 0. What is a?
-4, 0
Let f(o) be the third derivative of 8/3*o**3 + 37/15*o**5 + 6/35*o**7 - 12*o**2 + o**6 + 10/3*o**4 + 0*o + 3. Determine n so that f(n) = 0.
-1, -2/3
Let f(k) = -5533*k - 243450. Let v be f(-44). Suppose 52/5 - 134/5*z + 2*z**v = 0. Calculate z.
2/5, 13
Factor -45*d**4 - 5*d**5 - 353*d**3 - 1024*d + 904*d - 220*d**2 + 203*d**3.
-5*d*(d + 2)**3*(d + 3)
Let j(o) be the second derivative of o**4/54 - 17*o**3/27 + 10*o**2/3 + 2*o + 89. Determine y so that j(y) = 0.
2, 15
Let t(o) = 6*o**2 - 44*o + 83. Let k be t(4). Let a(r) be the first derivative of 2/45*r**k - 2/15*r**2 - 16/15*r - 23. Find i such that a(i) = 0.
-2, 4
Suppose -57*v = 8477 + 4291. Let m = -222 - v. Suppose 0 + 8/9*k**4 + 8/9*k - 32/9*k**m - 2/9*k**3 = 0. Calculate k.
-2, 0, 1/4, 2
Let s(o) be the third derivative of -o**7/175 - o**6/75 + o**5/30 + o**4/30 - o**2 + 142*o - 3. Find d such that s(d) = 0.
-2, -1/3, 0, 1
Suppose -z + 2*z - 2 = 0. Suppose -5*d + 3*b = -6*d + 9, z*d - 3*b = 54. Factor 4*i**2 + d - 21.
4*i**2
Let w(o) = -o**5 - o**4 + 35*o**3 + 57*o**2 + 28*o + 2. Let n(k) = 8*k**5 + 9*k**4 - 281*k**3 - 455*k**2 - 224*k - 17. Let m(p) = 2*n(p) + 17*w(p). Factor m(z).
-z*(z - 7)*(z + 1)**2*(z + 4)
Let c(v) = 1 + 0 + v**3 + 3*v + 0*v - 2*v. Let d(s) = -4*s**3 - 2*s**2 + 16*s + 8. Let b(t) = 5*t - 4. Let k be b(2). Let a(n) = k*c(n) - d(n). Factor a(w).
2*(w - 1)*(w + 1)*(5*w + 1)
Let g be -3 + 980/126 + 2/9. Suppose 4*u**3 - 11*u**2 - 17*u**2 - 4*u**g - 12*u**4 + 40*u**2 = 0. Calculate u.
-3, -1, 0, 1
Let z(u) be the third derivative of 1/140*u**6 + 44*u + 2*u**2 + 0*u**4 + 1/98*u**7 + 0*u**5 - 3/784*u**8 + 0*u**3 + 0. Find l, gi