 1)
Let v(z) be the first derivative of z**3/7 + 57*z**2/14 - 18*z - 142. What is l in v(l) = 0?
-21, 2
What is i in -38/5*i**3 - 322/5*i + 226/5*i**2 + 2/5*i**4 - 588/5 = 0?
-1, 6, 7
Let y(q) be the third derivative of -q**5/12 - 155*q**4/4 + 935*q**3/6 + 694*q**2 - 1. Factor y(n).
-5*(n - 1)*(n + 187)
Let z(q) be the third derivative of q**8/2016 - q**7/105 + 7*q**6/144 + q**5/30 - q**4/4 - 566*q**2. Factor z(l).
l*(l - 6)**2*(l - 1)*(l + 1)/6
Let s = -74 + 134. Let l be (1/2)/(-1 + s/56). Let l*g**3 - 8*g**2 + 12*g**3 - 7*g - 13*g - 8 + 4*g**5 - 3*g**3 + 16*g**4 = 0. Calculate g.
-2, -1, 1
Suppose -26*d + 32*d - 12 = 0. Solve -1484*r - 2*r**d + 1420*r - 256 - 2*r**2 = 0.
-8
Suppose 4*x = 7*u + 21, x - 6 = -26*u + 28*u. Factor -9/5*d + x - 6/5*d**2 + 3/5*d**3.
3*d*(d - 3)*(d + 1)/5
Factor 3*f + 11086*f**4 + 24*f**3 + 13*f + 256 - 192*f**2 + 13*f**3 + 15*f**3 - 11082*f**4.
4*(f - 2)**2*(f + 1)*(f + 16)
Let 0 + 0*w - 12/5*w**4 - 8/5*w**2 + 16/5*w**5 - 36/5*w**3 = 0. Calculate w.
-1, -1/4, 0, 2
Let g(i) = -9*i**2 - 29*i - 34. Let b(j) = -10*j - 3*j**2 - 5 - 1 - 2 - 3. Suppose 48 - 13 = 5*u. Let z(m) = u*b(m) - 2*g(m). Factor z(a).
-3*(a + 1)*(a + 3)
Let c(n) be the second derivative of -5*n**4/54 - 2*n**3/9 + 32*n**2/9 - 476*n + 3. Factor c(s).
-2*(s - 2)*(5*s + 16)/9
Let b be (38/21 - 2)*31200/2420. Let n = 14/121 - b. Solve n + 2/7*h**2 + 12/7*h = 0.
-3
Suppose -3*s = 5*c - 1, 4*s - 11 = 5*c - 33. Solve 4 + 21 + 7 - 12 - 25*z**c + 5*z**4 = 0.
-2, -1, 1, 2
Let r(x) = 948*x**2 + 3791*x + 2. Let p be r(-4). What is f in -1/2*f**5 + 1/2*f**3 + p*f - 11/2*f**2 + 3/2*f**4 - 2 = 0?
-2, 1, 2
Let f(b) be the first derivative of 2*b**5/5 - 13*b**4 + 16*b**3 + 26*b**2 - 50*b - 288. Determine i so that f(i) = 0.
-1, 1, 25
Let b(p) be the first derivative of -11*p**6/200 + 27*p**5/100 + 9*p**4/20 + 183*p**2/2 + 131. Let g(o) be the second derivative of b(o). Solve g(z) = 0.
-6/11, 0, 3
Suppose -18*s + 318 = -1878. Let g be 10 - (-1456)/(-147) - s/(-42). Let 1/3 - 1/3*y**2 + 1/2*y - 1/2*y**g = 0. Calculate y.
-1, -2/3, 1
Let y(t) be the third derivative of -t**8/504 - 4*t**7/35 + 589*t**6/180 - 386*t**5/15 + 49*t**4 + 29*t**2 - 186. Solve y(q) = 0.
-49, 0, 1, 6
Let u(z) = 6863*z**2 - 2220*z + 174. Let i(s) = -918*s**2 + 2988*s + 973*s + 479*s - 349 - 5060*s**2 - 7745*s**2. Let c(o) = -6*i(o) - 11*u(o). Factor c(j).
5*(37*j - 6)**2
Let t(z) = 14 - 218*z + 32 + 216*z. Let g be t(22). Determine w so that -49*w**2 + 3*w - 39*w + 53*w**g + 32 = 0.
1, 8
Let z(p) be the third derivative of 19/24*p**4 - 10/3*p**3 + 0*p - 1/120*p**6 - 120*p**2 + 1/30*p**5 + 0. Determine n, given that z(n) = 0.
-4, 1, 5
Let f = 1219/15 + -398/5. Let p(b) be the first derivative of 0*b**2 - 1 - b**5 + 0*b - 5/2*b**4 - f*b**3. Solve p(w) = 0.
-1, 0
Suppose 0 = -3*l - 3*n - 9, 2*l - 45*n + 43*n - 14 = 0. Suppose 0 + 0*f**l + 2/13*f**4 - 10/13*f**3 + 0*f = 0. Calculate f.
0, 5
Solve -9/2*h**2 + 18 + 1/2*h**3 - 2*h = 0.
-2, 2, 9
Let u(v) be the third derivative of 1/180*v**6 + 25*v - 7/180*v**5 + 1/630*v**7 + 0 + 0*v**3 + 2*v**2 + 1/18*v**4. Let u(n) = 0. Calculate n.
-4, 0, 1
Let 2/11*p**5 + 292/11*p**3 + 0 + 0*p - 58/11*p**4 + 32*p**2 = 0. What is p?
-1, 0, 8, 22
Let o(z) be the third derivative of 49*z**6/660 + 553*z**5/330 + 155*z**4/132 + z**3/3 + 36*z**2 - 4*z - 3. Find x, given that o(x) = 0.
-11, -1/7
Let g = 1579 - 1754. Let z be (-1500)/g + 8/84. What is n in -2/3*n**3 + 4 + 14/3*n**2 - 2/3*n**4 + z*n = 0?
-2, -1, 3
Let p(c) be the first derivative of 31/36*c**4 - 36 - 1000/9*c - 110/9*c**3 + 650/9*c**2 - 1/45*c**5. Factor p(z).
-(z - 10)**3*(z - 1)/9
Determine b so that -1/2 - 225/4*b**4 + 57/4*b - 645/4*b**3 - 361/4*b**2 = 0.
-2, -1, 1/15
Let p be (-12)/(-10)*(-34 - (-10120)/297 - (-254)/216). Suppose -5*t = -15 - 0. Factor p*d**4 + 0*d**2 + 0 + 0*d - 3*d**t + 3/2*d**5.
3*d**3*(d - 1)*(d + 2)/2
Suppose -876 + 2890 = 1007*n. Let -72/7*w + 33/7*w**n - 3/7*w**3 - 108/7 = 0. Calculate w.
-1, 6
Factor 153 + 78*m + 3/4*m**2.
3*(m + 2)*(m + 102)/4
Let c(r) be the first derivative of -203 + 1/15*r**5 + 3*r**2 + r**4 + 0*r + 29/9*r**3. Factor c(i).
i*(i + 1)*(i + 2)*(i + 9)/3
Factor 478*v + 399847 + 1/7*v**2.
(v + 1673)**2/7
Let s be ((-1608)/60 - -4) + 24. Let l(w) be the first derivative of 0*w**2 + 1/25*w**5 + 81/5*w + 0*w**4 - s*w**3 - 32. Factor l(z).
(z - 3)**2*(z + 3)**2/5
Let q(z) = z**5 - z**4 - 10*z**2 - z - 1. Let g(i) = -8*i**5 + 20*i**4 - 28*i**3 + 164*i**2 + 36*i + 8. Let l(f) = g(f) + 16*q(f). Find k such that l(k) = 0.
-2, -1, 1/2, 1
Let o be 112/(-20)*(1860/(-105) + 16). Solve 0 + 12/5*d - 27/5*d**3 + o*d**2 = 0.
-2/9, 0, 2
Let m(g) be the third derivative of g + 5/3*g**3 + 2/15*g**5 - 3*g**2 + 0 + 3/4*g**4. Factor m(s).
2*(s + 1)*(4*s + 5)
Let r(z) be the first derivative of 0*z**2 - 5/3*z**3 + 78 + 0*z - z**5 - 5/2*z**4. Factor r(g).
-5*g**2*(g + 1)**2
Let 2392*z**2 - 730378*z**3 + 1600*z + 731166*z**3 - 4*z**4 - 5 + 5 = 0. Calculate z.
-2, -1, 0, 200
Let l(z) be the first derivative of 36/35*z**5 + 11/7*z**4 - 4 + 0*z - 64/21*z**3 - 8/7*z**2. Determine p, given that l(p) = 0.
-2, -2/9, 0, 1
Factor 2168/3*u - 293764/3 - 4/3*u**2.
-4*(u - 271)**2/3
Let c(p) = p**2 - 5*p - 14. Let g be c(7). Suppose -5*x + r = -12, 5*r = -2*x - g - 6. Solve -70*d + 26*d + 36*d + x*d**3 + 6*d**2 = 0.
-4, 0, 1
Solve 6*o**2 - 312*o - 2*o**2 + 144*o - 940 = 0 for o.
-5, 47
Let n be ((-1152)/(-18) - 31) + -30. Factor -1/6*j**2 - 7/6*j + n.
-(j - 2)*(j + 9)/6
Let h = -80/79 + 1508/553. Let s(v) be the first derivative of 18/7*v**3 + h*v**6 - 19/7*v**4 - 8/7*v + 12/7*v**2 + 26 - 66/35*v**5. Let s(c) = 0. What is c?
-2/3, 1/4, 1
Let q(n) be the second derivative of n**7/147 + 52*n**6/105 + 145*n**5/14 + 625*n**4/21 + 117*n + 16. Factor q(t).
2*t**2*(t + 2)*(t + 25)**2/7
Let q = -2489 - -1345. Let z = q - -9155/8. Let -7/8*b + 5/8*b**2 - 1/8*b**3 + z = 0. Calculate b.
1, 3
Let l(r) be the second derivative of r**6/135 + 13*r**5/90 + 41*r**4/54 + 47*r**3/27 + 2*r**2 + 2*r - 861. Solve l(m) = 0 for m.
-9, -2, -1
Determine y, given that 9*y**3 + 558*y**3 + 2*y**5 + 122*y**4 + 861*y**3 - 546419*y - 768643*y - 8946126 - 47628*y**2 = 0.
-21, 23
Let s(t) be the second derivative of -1/18*t**4 + 6 - 8/3*t**2 + 2/3*t**3 - t. Determine f so that s(f) = 0.
2, 4
Let c(x) be the second derivative of -2/3*x**4 + x - 1/5*x**5 - 2/3*x**3 + 10 + 0*x**2. Determine l so that c(l) = 0.
-1, 0
Let s = -155/82 + 3601/1558. Let b be (-46)/(-19) - (-14)/(3 + -10). Let -b*n + s + 2/19*n**2 = 0. Calculate n.
2
Suppose -13 = -4*y - k, 2*y + 4 = 3*y + k. Let -146367*w**2 + 146367*w**2 - y*w**3 + 27*w = 0. What is w?
-3, 0, 3
Factor -6*c**3 + 291/2*c**2 + 216 - 900*c.
-3*(c - 12)**2*(4*c - 1)/2
Let w = 5/21061 + 2190329/63183. Suppose -2/3*s**2 - 1352/3 + w*s = 0. Calculate s.
26
Let h(a) be the third derivative of a**7/840 - a**6/45 - a**5/10 - 115*a**4/24 + 104*a**2. Let u(v) be the second derivative of h(v). Factor u(z).
(z - 6)*(3*z + 2)
Let v(a) = a**2 - 4*a + 4. Let l be v(4). Suppose 0*g**4 + 8*g**2 - 2*g**l - 5*g + 3*g - 2*g**3 + 10*g = 0. What is g?
-2, -1, 0, 2
Let u(y) = 2*y**4 + y**3 + y**2 + 2*y. Let x(l) = -75*l**4 - 540*l**3 + 18670*l**2 - 310580*l + 1928205. Let a(s) = 40*u(s) + x(s). Solve a(w) = 0.
23, 27
Factor -32*p**3 - 68/5*p**4 + 0*p - 64/5*p**2 - 8/5*p**5 + 0.
-4*p**2*(p + 4)**2*(2*p + 1)/5
Factor 72/5 - 3/5*t**3 + 102/5*t + 27/5*t**2.
-3*(t - 12)*(t + 1)*(t + 2)/5
Let r = 333 + -331. Let h(i) = 20*i**3 - 452*i**2 - 186*i. Let n(p) = 40*p**3 - 904*p**2 - 373*p. Let d(w) = r*n(w) - 5*h(w). Factor d(y).
-4*y*(y - 23)*(5*y + 2)
Let o(k) be the third derivative of -1/70*k**7 + 13 + 3*k**2 + 0*k**3 - 1/4*k**5 - 1/4*k**4 + 0*k - 1/10*k**6. Factor o(n).
-3*n*(n + 1)**2*(n + 2)
Let j(b) = 300*b**3 - 3295*b**2 - 69955*b - 66745. Let q(c) = -11*c**3 + 122*c**2 + 2591*c + 2472. Let a(y) = 2*j(y) + 55*q(y). Factor a(t).
-5*(t - 38)*(t + 1)*(t + 13)
Factor -2/13*f**2 + 82/13*f - 800/13.
-2*(f - 25)*(f - 16)/13
Factor 2157*b - 57*b**2 - 2497*b + 5*b**3 - 278*b**2.
5*b*(b - 68)*(b + 1)
Let y(i) be the third derivative of -i**6/120 - 2*i**5/15 - 2*i**2 - 733*i. Factor y(d).
-d**2*(d + 8)
Let w(g) = -2*g - 3*g**3 - 51 - 8*g**2 + 73 - 4*g**2. Let x(k) = 3*k**3 + 12*k**2 + 3*k - 24. Let p(i) = 6*w(i) + 5*x(i). Fa