e the third derivative of g(z). Let s(t) = 0. What is t?
-2, -1, 1, 2
Let h(z) be the second derivative of -z**5/40 - 215*z**4/8 - 46225*z**3/4 - 9938375*z**2/4 - 917*z. Factor h(k).
-(k + 215)**3/2
Let x(b) be the second derivative of b**8/23520 + b**7/1764 + b**6/630 + 35*b**4/4 + 2*b - 87. Let q(y) be the third derivative of x(y). Factor q(o).
2*o*(o + 1)*(o + 4)/7
Factor -378/5*m - 327/5*m**2 - 108/5*m**3 - 12/5*m**4 - 147/5.
-3*(m + 1)**2*(2*m + 7)**2/5
Let d(c) = 3*c**2 - 2*c - 6. Let o(n) = -2*n**3 + 6*n**2 + 2*n - 4. Let p be o(3). Let k be d(p). Factor 2/11*j**k + 4/11 - 6/11*j.
2*(j - 2)*(j - 1)/11
Let k(p) be the second derivative of p**5/20 - 11*p**4/8 + 14*p**3 - 239*p**2/2 - 64*p - 1. Let v(s) be the first derivative of k(s). What is w in v(w) = 0?
4, 7
Let j = 5316 - 5302. Let z(s) be the first derivative of 21/10*s**4 + 0*s + j - 16/5*s**3 + 98/25*s**5 + 4/5*s**2. Factor z(u).
2*u*(u + 1)*(7*u - 2)**2/5
Solve -256/11 + 16/11*h + 2/11*h**2 = 0.
-16, 8
Let i(c) = -12*c**3 - 42*c**2 + 177*c - 522. Let t(h) = h**3 + h**2 - h + 38. Let x(p) = -i(p) - 9*t(p). Solve x(v) = 0.
-15, 2
Let h = 1615 - 1613. Suppose -5*t + 12*n - 13*n = -15, 6 = h*t - 4*n. Factor 0*g - 10/3*g**4 + 0*g**2 + 0 + 5/3*g**t + 5/3*g**5.
5*g**3*(g - 1)**2/3
Let t(v) be the second derivative of v**7/42 + v**6/30 - 7*v**5/10 - 2*v**4 - 62*v - 9. Let t(x) = 0. Calculate x.
-3, -2, 0, 4
Let h(d) = 21*d + 55. Let c be h(-3). Let z be -10*c/60*3. Find r, given that 0*r**2 + 0*r + 2/7*r**3 - 1/7*r**z + 0 = 0.
0, 2
Factor -169/3*x + 28561/6 + 1/6*x**2.
(x - 169)**2/6
Let r = -1967 + 64913/33. Let d(k) be the first derivative of 1/11*k**2 - 3 - r*k**3 - 1/22*k**4 + 2/11*k. Factor d(x).
-2*(x - 1)*(x + 1)**2/11
Let x be 18/33 - 0 - 622430/(-47905). Factor 2/13*m**5 - 448/13*m**2 - 256/13 + 544/13*m - 32/13*m**4 + x*m**3.
2*(m - 8)*(m - 2)**4/13
Let p(r) = 5*r**2 + 161*r + 189. Let g be p(-31). Let b(c) be the second derivative of 0 - 3*c**2 - 3/20*c**5 + 0*c**4 + 3/2*c**g - 16*c. What is d in b(d) = 0?
-2, 1
Let n(j) = j**4 - j**3 - j**2 + 2*j - 10. Let l(k) = 6*k**4 - 15*k**3 + 23*k**2 + 4*k - 95. Let c(u) = -l(u) + 5*n(u). Solve c(o) = 0 for o.
-1, 3, 5
Factor 4796/7*q**2 + 1439996/7*q + 1435204/7 + 4/7*q**3.
4*(q + 1)*(q + 599)**2/7
Suppose -85 = -9*u + 95. Determine z so that -3487*z**2 - 650*z - 4*z**5 - 646*z - 132*z**4 + 751*z**2 - u*z**4 + 0*z**5 - 1588*z**3 = 0.
-18, -1, 0
Let g(i) be the first derivative of i**4/21 + 4*i**3/7 + 18*i**2/7 - 6*i + 148. Let y(s) be the first derivative of g(s). Factor y(z).
4*(z + 3)**2/7
What is i in 129/2*i - i**3 + 0 + 83/2*i**2 = 0?
-3/2, 0, 43
Let b be ((-5)/(-7))/(8 - (-275)/(-35)). Suppose -8 = -5*u + i, b*u - 4*i + 3 - 5 = 0. Factor 0 - 1/2*l**4 + 1/2*l**u + 3/4*l - l**3 + 1/4*l**5.
l*(l - 3)*(l - 1)*(l + 1)**2/4
Let x be 4/5*1716/(-176)*16/(-312). Suppose 4/5*k + 0 + x*k**3 - 6/5*k**2 = 0. Calculate k.
0, 1, 2
Let d = 1/2762 + 20713/5524. Suppose -3*x**2 - 3/8*x**3 - d + 57/8*x = 0. What is x?
-10, 1
Suppose -2*z = 2*k - 8, 4*z + 8*k - 3*k = 16. Find x, given that 2/3*x**3 - 6/5*x + 0 + 2/15*x**z + 2/5*x**2 = 0.
-3, 0, 1
Let d(q) be the third derivative of q**6/240 - 3*q**5/10 - q**4/48 + 3*q**3 - 9*q**2 - 79*q. Solve d(i) = 0.
-1, 1, 36
Let l(a) be the third derivative of -a**5/330 + 247*a**4/132 + 248*a**3/33 - 2*a**2 + 82*a - 10. Factor l(s).
-2*(s - 248)*(s + 1)/11
Let o = -9 + 18. Find z, given that 2*z**5 - o*z**5 - 15*z**2 - 5*z**4 + 0*z**5 + 2*z**5 + 25*z**3 = 0.
-3, 0, 1
Let d = 10 + -16. Let z = 14 + d. Solve -162*f**4 + 109*f**2 - 162 - 13*f**5 + 13*f**2 + 567*f - z*f**5 - 330*f**3 - 14*f**2 = 0.
-3, 2/7, 1
Let y = 139459/4 - 697087/20. Factor 108/5*x + y + 4/5*x**3 + 12*x**2.
4*(x + 1)**2*(x + 13)/5
Let q(r) be the third derivative of -1/40*r**5 + 0*r - 1/240*r**6 + 0*r**4 - 11/6*r**3 + 0 + 26*r**2. Let z(c) be the first derivative of q(c). Factor z(u).
-3*u*(u + 2)/2
Let q be (2/5)/(116/(-696)*(-54)/10). Let t(g) be the first derivative of -1/9*g**2 + 24 - q*g + 8/27*g**3 + 1/6*g**4. Factor t(k).
2*(k + 1)**2*(3*k - 2)/9
Suppose -1791 - 609 = -480*h. Factor 121/5*q - 44*q**2 + 78/5*q**3 + 1/5*q**h + 0 + 4*q**4.
q*(q - 1)**2*(q + 11)**2/5
Suppose -2/9*t**2 + 2/9*t**4 + 0 + 106/9*t**3 - 106/9*t = 0. What is t?
-53, -1, 0, 1
Let z(t) be the second derivative of 133*t**6/50 + 401*t**5/100 + t**4/30 - 218*t. Let z(r) = 0. What is r?
-1, -2/399, 0
Let j(k) be the second derivative of k**5/15 - 25*k**4/3 + 1250*k**3/3 - 70*k**2 + 103*k. Let u(b) be the first derivative of j(b). Suppose u(w) = 0. What is w?
25
Suppose 10*m + 3*c = 9*m + 13, c = 3*m - 9. Let f(n) be the first derivative of 13 + 15*n**3 + 0*n + 5*n**2 + 35/4*n**m. Factor f(o).
5*o*(o + 1)*(7*o + 2)
Let j(b) be the third derivative of b**5/135 + 31*b**4 + 51894*b**3 - 24*b**2 - 32. Factor j(n).
4*(n + 837)**2/9
Let j(p) = -8*p**2 - 1150*p + 3462. Let t(r) = 10*r**2 + 1153*r - 3459. Let d(o) = -3*j(o) - 2*t(o). Determine u so that d(u) = 0.
-289, 3
Factor -36 - 1/5*f**2 + 92/5*f.
-(f - 90)*(f - 2)/5
Suppose 296*l + 1084 = 838*l. Factor -3 - 1/3*o**l + 2*o.
-(o - 3)**2/3
Let g(a) be the third derivative of 7*a**6/72 + 17*a**5/360 + a**4/144 - 2*a**2 - 344. Factor g(m).
m*(7*m + 1)*(10*m + 1)/6
Let p(l) be the first derivative of -l**6/2 + 12*l**5/5 + 39*l**4/4 - 40*l**3 - 72*l**2 + 2900. Find u such that p(u) = 0.
-3, -1, 0, 4
Let w = -55261/26 + 10113/13. Let f = w + 1349. Let 3/4 + 1/2*q**3 - 1/4*q + 3/4*q**4 - 1/4*q**5 - f*q**2 = 0. What is q?
-1, 1, 3
Let y(a) be the third derivative of a**5/210 + 437*a**4/84 - 84*a**3 - 219*a**2 + a - 3. What is k in y(k) = 0?
-441, 4
Let f be ((-12)/(-72))/(2/21). Let x be (-62)/(-496) + 2/16. Suppose -5/4*t**2 - 3/4 - f*t - x*t**3 = 0. What is t?
-3, -1
Factor 143/3*q + 1/9*q**3 - 1694/9 - 4*q**2.
(q - 14)*(q - 11)**2/9
Let n be 36/3*1/2. Let l be (2 + 2)/(2/n). Solve 9 - 3*d - 13 - 5*d + l*d**2 = 0.
-1/3, 1
Suppose -5*i = -5*a + 15, 7*i - 2*i + 3*a = 5*a. Factor 0 + 0*r - 1/5*r**3 + 6/5*r**4 - 6/5*r**i + 1/5*r**5.
r**2*(r - 1)*(r + 1)*(r + 6)/5
Let s(i) = -2*i**2 + 14*i - 13. Let q be s(5). Suppose 0*u - u - 5*m + q = 0, 0 = 4*u + 2*m - 10. Solve -8/7*a**3 - 2*a**u - 4/7*a + 2/7 = 0.
-1, 1/4
Suppose 4*n - 110 = -102. Factor -37 - 39 + 72 + 8*r - 4*r**n.
-4*(r - 1)**2
Let c(g) be the first derivative of g**5/105 - g**4/84 + g**2 + 89. Let a(y) be the second derivative of c(y). Find f, given that a(f) = 0.
0, 1/2
Let -120*v**3 + 861*v**3 - 3236*v**2 + 347*v**3 + 2152*v - 4*v**4 = 0. What is v?
0, 1, 2, 269
Let u(q) be the first derivative of q**6/18 - q**5/3 + q**4/12 + 7*q**3/3 - 3*q**2 + 3129. Let u(v) = 0. Calculate v.
-2, 0, 1, 3
Suppose -w + 156 = 21*j - 24*j, -4*w + 666 = 2*j. Factor -120*h**2 - 168*h**2 + w + 323*h**2 - 205*h + 5*h**3.
5*(h - 3)*(h - 1)*(h + 11)
Let v(j) be the second derivative of j**6/15 + 31*j**5/10 - 86*j**4/3 + 284*j**3/3 - 144*j**2 + j + 1608. Let v(d) = 0. What is d?
-36, 1, 2
Let v = -5794 - -5796. Let h(q) be the first derivative of 0*q**3 + 1/8*q**4 + 0*q**v + 0*q - 29 - 1/20*q**5. Factor h(w).
-w**3*(w - 2)/4
Let c(d) be the second derivative of 1/20*d**5 + 2*d - 7/12*d**4 + 7/2*d**2 - 47 - 1/6*d**3. Determine a, given that c(a) = 0.
-1, 1, 7
Let o(g) be the third derivative of 1/210*g**7 + 0*g**3 + 3*g**2 - 1 + 1/30*g**6 + 1/12*g**5 + 1/12*g**4 + 0*g. Factor o(f).
f*(f + 1)**2*(f + 2)
Let r = -27 + 78. Let v = -45 + r. Let -20*i**3 - 504 + 504 + 5*i**4 + 26*i**2 - v*i**2 = 0. What is i?
0, 2
Let d(n) be the third derivative of n**8/504 + 13*n**7/315 + n**6/12 - 97*n**5/90 - 58*n**4/9 - 44*n**3/3 + n**2 - 7442*n. Let d(q) = 0. Calculate q.
-11, -2, -1, 3
Suppose -2*j = j - i - 104, -2*j + i = -68. Factor j*z**2 - 172/5*z - 68/5*z**3 + 4/5*z**4 + 56/5.
4*(z - 14)*(z - 1)**3/5
Let p(u) be the second derivative of -40*u**2 - 1/4*u**5 - 35*u - 15/4*u**4 - 20*u**3 + 0. Factor p(i).
-5*(i + 1)*(i + 4)**2
Let o be (-2 + 10 + -8)/5. Let k(x) be the second derivative of o + 5/6*x**3 - 5/12*x**4 + 5*x**2 + 17*x. Factor k(y).
-5*(y - 2)*(y + 1)
Determine c, given that -15/2*c**2 + 8*c - 1/2*c**3 + 0 = 0.
-16, 0, 1
Let u(g) be the first derivative of 2*g**3/15 - 2081*g**2/5 + 1891. Factor u(a).
2*a*(a - 2081)/5
Let f(k) = -266*k**2 + 524*k + 10102. Let w(v) = -83*v**2 + 174*v + 3367. Let m(