5
Let k = -6973 - -6976. Let n(s) be the second derivative of 0 - 1/6*s**4 - 8*s + 1/5*s**k + 2/5*s**2. Solve n(v) = 0 for v.
-2/5, 1
Let t(z) be the second derivative of 1/36*z**6 + 14 + 1/252*z**7 - 1/4*z**2 - 1/36*z**4 + z + 1/20*z**5 - 7/36*z**3. Factor t(b).
(b - 1)*(b + 1)**3*(b + 3)/6
Suppose 0 = -433*o + 417*o - 1392. Let a be (-6)/o - 1296/(-3915). What is x in -2/5*x - 2/5 + 2/5*x**2 + a*x**3 = 0?
-1, 1
Let a be ((-84)/(-30))/(12/10). Let w be (-30)/(-16)*(51 + (-1804)/36). Solve 7/3*i**4 + 0 - a*i**2 - 2/3*i - i**3 + w*i**5 = 0.
-1, -2/5, 0, 1
Suppose 5 = -3*s + 9*a - 13*a, 3*s - 35 = 4*a. Suppose -2 = -k - 3. Let j(p) = p**2 + 1. Let x(l) = 2*l**2 - 9*l - 1. Let v(d) = k*x(d) + s*j(d). Factor v(o).
3*(o + 1)*(o + 2)
Suppose -57*y**2 + 47*y**3 - 200*y - 93*y**2 - 49*y**3 - 232*y = 0. What is y?
-72, -3, 0
Suppose 2*a = -4*j + 24, 0 = -2*a - a - j + 11. Find w such that 83*w**3 + 11*w**4 - 13 - 57*w**3 - 27*w + 4*w**4 - 8*w**a + w**5 + 6*w**2 = 0.
-13, -1, 1
Factor 6*k + 32/5 - 2/5*k**2.
-2*(k - 16)*(k + 1)/5
Let c(v) be the first derivative of -5*v**3/3 - 2180*v**2 - 950480*v + 4331. Factor c(d).
-5*(d + 436)**2
Let i(j) be the third derivative of 19/8*j**4 + 0*j + 9*j**3 + 1/20*j**5 - 140*j**2 + 0. Suppose i(h) = 0. Calculate h.
-18, -1
Factor -418*k + 10 - 142 - 93 - 63 - k**2 - 129.
-(k + 1)*(k + 417)
Suppose -4*c + 13 = -7. Suppose -c*t + r + 4 = -3*t, -t + 2 = -r. Factor 37*l**t - 39*l**2 + 3*l - l.
-2*l*(l - 1)
Let y(z) = -z**3 - 38*z**2 - 413*z - 17626. Let a be y(-39). Factor -27/2*h**5 - 117/2*h**3 + 135/2*h**4 + 0 + 37/2*h**2 - a*h.
-h*(h - 4)*(3*h - 1)**3/2
Solve 148/5*o + 2/5*o**3 - 38/5*o**2 - 112/5 = 0.
1, 4, 14
Let f(k) be the first derivative of -31*k**3/3 + 95*k**2/6 - 2*k/3 - 462. Factor f(d).
-(d - 1)*(93*d - 2)/3
Let u = -5518 - -5521. Let q(r) be the second derivative of -14*r + 0*r**u + 0*r**2 + 0 + 1/3*r**4. Suppose q(y) = 0. Calculate y.
0
Factor 14*v + 130*v - 52*v**2 - 1789*v**3 + 1793*v**3.
4*v*(v - 9)*(v - 4)
Let d = 385 - 372. Suppose 0 = -30*n + d + 47. Factor -2/9*c**n + 0 + 4/9*c.
-2*c*(c - 2)/9
Suppose 298/19*h**2 - 298/19 + 2/19*h - 2/19*h**3 = 0. What is h?
-1, 1, 149
Let p(a) = 5*a**3 + 75*a**2 + 285*a - 128. Let s(m) = -m**2 - m. Let y(x) = -x**3 + 33*x**2 - 32*x + 6. Let u be y(32). Let r(l) = u*s(l) - 2*p(l). Factor r(v).
-2*(v + 8)**2*(5*v - 2)
Let b be 0*(10 - 49)/(-1131). Factor -2/9*g**5 + b*g + 0*g**3 + 2/3*g**4 - 8/9*g**2 + 0.
-2*g**2*(g - 2)**2*(g + 1)/9
Let v(n) be the third derivative of n**6/40 - 5577*n**5/20 + 10367643*n**4/8 - 6424482779*n**3/2 + 5246*n**2 - 1. Factor v(i).
3*(i - 1859)**3
Let s(k) be the second derivative of -k**5/120 + 55*k**4/24 - 3025*k**3/12 + 37*k**2 - 81*k. Let y(m) be the first derivative of s(m). Factor y(r).
-(r - 55)**2/2
Factor 177*r - 351/2 - 3/2*r**2.
-3*(r - 117)*(r - 1)/2
Let m(d) = 53*d**3 + 28*d**2 - 56*d + 17. Let q(j) = -15*j**3 - 9*j**2 + 18*j - 6. Let a(l) = -4*m(l) - 14*q(l). Factor a(y).
-2*(y - 4)*(y - 2)*(y - 1)
Let a = -24 + 26. Suppose 6*r - 16 = a*r. Find s such that 8*s**3 + 18*s**2 - 4*s - r*s**5 - 1 - 25*s**2 - s**4 + 9*s**2 = 0.
-1, -1/4, 1
Let r(k) be the third derivative of -1/140*k**7 + 9*k - 1/120*k**5 + 2*k**2 + 1/672*k**8 + 1/80*k**6 + 0*k**4 + 0 + 0*k**3. Factor r(s).
s**2*(s - 1)**3/2
Let w(u) = -8*u - 302. Let c be (1 + 56)*20/(-210)*7. Let i be w(c). Suppose -2/3*s**2 + i*s + 8/3 = 0. What is s?
-1, 4
Factor 26*h**5 + 42192/13*h**3 - 492*h**4 - 15552/13 - 108000/13*h**2 + 75168/13*h.
2*(h - 6)**3*(13*h - 6)**2/13
Let j be 20979/4221 + 8/268. Factor 1/6*m**4 - 1/2*m**3 - 1/3*m - 5/6*m**2 + 1/6*m**j + 0.
m*(m - 2)*(m + 1)**3/6
Find c, given that -257*c - 2173*c - 1450*c - 632*c - 4*c**2 + 7*c**2 + 1696512 = 0.
752
Let 0 + 0*f - 2/13*f**3 - 2/13*f**4 + 0*f**2 = 0. What is f?
-1, 0
Let m(y) = -y**2 + 17*y + 40. Let c be m(19). Let u be (-432)/(-32)*54/243. Let 2*b**c - 16/3*b + 4/3*b**u - 2/3*b**4 + 8/3 = 0. What is b?
-2, 1, 2
Let i(p) be the third derivative of 0*p + 37 + 15/2*p**4 + 5/4*p**5 - p**2 + 18*p**3. Suppose i(f) = 0. What is f?
-6/5
Let y(x) = -x**2 - 81*x + 10. Let g(s) = -s**2 - 41*s + 6. Let d(a) = 32*a + 69. Let o be d(-2). Let l(m) = o*g(m) - 3*y(m). Factor l(p).
-2*p*(p - 19)
Let j = -972 + 537. Let c = j + 754. Factor c*z + 2*z**2 - 315*z + 2 - 3 - 5.
2*(z - 1)*(z + 3)
Let n(w) = 65*w**2 - 168*w - 17. Let l(h) = 11*h - 1. Let t(i) = -2*l(i) + n(i). Suppose t(c) = 0. Calculate c.
-1/13, 3
Let s = -174530/459 + 10276/27. Factor 0 - 4/17*c**2 - s*c**3 + 0*c - 2/17*c**4.
-2*c**2*(c + 1)*(c + 2)/17
Suppose 61*x = -82*x. Let n(y) be the third derivative of 1/540*y**5 - 1/216*y**4 + 4*y**2 - 1/27*y**3 + 0*y + x. Suppose n(k) = 0. What is k?
-1, 2
Let k(f) be the second derivative of 0*f**3 - 10*f + 2/57*f**4 + 0*f**2 + 1/285*f**6 - 2/95*f**5 + 0. Suppose k(q) = 0. What is q?
0, 2
Let z(q) be the third derivative of -1/8*q**6 - 39*q**2 + 0*q - 13/6*q**5 + 15/8*q**4 + 0 + 0*q**3. Solve z(a) = 0.
-9, 0, 1/3
Let y(o) be the first derivative of -o**4/24 + o**3/6 - o**2/4 + o/6 + 69. Suppose y(g) = 0. Calculate g.
1
Let g = -10580 - -74061/7. Let v(m) be the first derivative of 0*m + g*m**2 - 3 + 0*m**3 - 1/14*m**4. Factor v(n).
-2*n*(n - 1)*(n + 1)/7
Let d be -15*(3 - 50/15) - (-48)/(-16). Let z(r) be the second derivative of 3/2*r**d - 7*r + 5/4*r**3 + 0 + 1/2*r**4 + 3/40*r**5. Factor z(y).
3*(y + 1)**2*(y + 2)/2
Suppose 15*s - 26 = 14*s - 3*k, 0 = 4*s + 3*k - 86. Solve -22*o**2 + 7*o - 4*o + 0*o**4 + s - 3*o - 6*o + 2*o**4 + 6*o**3 = 0.
-5, -1, 1, 2
Let a(x) be the second derivative of 6*x - 4 - 3/2*x**4 - 63*x**3 - 1323*x**2 - 1/70*x**5. Find i, given that a(i) = 0.
-21
Let p(m) be the second derivative of 1/2*m**2 - 1/120*m**6 + 60*m - 1/16*m**4 - 1/20*m**5 + 0 + 1/6*m**3. What is v in p(v) = 0?
-2, -1, 1
Let j(q) be the first derivative of 4*q**5/5 + 11*q**4 + 40*q**3/3 + 2914. Factor j(u).
4*u**2*(u + 1)*(u + 10)
Let n(j) be the third derivative of -j**6/240 + j**5/8 - 3*j**4/8 - 18*j**3 + 639*j**2. Find c, given that n(c) = 0.
-3, 6, 12
Let b = -13466 + 13469. Let h(a) be the third derivative of 0*a**b - 37*a**2 - 1/30*a**6 + 0*a**4 - 2/105*a**7 + 0 + 0*a + 0*a**5. Factor h(z).
-4*z**3*(z + 1)
Let y(b) = -b**3 + 6*b**2 + 71*b + 16. Let j be y(12). Suppose 10*t - 5*t - 3*q = 22, j*q = -16. Factor 8/3*z + 0 - 2/3*z**t.
-2*z*(z - 4)/3
Let c(y) be the second derivative of -y**6/120 + 3*y**5/80 + 3*y**4/16 + 5*y**3/24 - 927*y - 1. Let c(p) = 0. What is p?
-1, 0, 5
Let o(t) be the third derivative of -t**5/60 + 2909*t**4/24 + t**2 + 19*t - 18. Factor o(s).
-s*(s - 2909)
Suppose -150*q**2 - 308*q**3 - 104 - 476*q - 213*q**2 - 297*q**2 - 20*q**4 = 0. What is q?
-13, -1, -2/5
Let g = 177113/102 - 10249/6. Factor 188/17*m**3 - 32/17*m**4 - g*m**2 + 0 + 450/17*m + 2/17*m**5.
2*m*(m - 5)**2*(m - 3)**2/17
Let i(f) be the first derivative of f**5/35 - 358*f**4/7 + 171362*f**3/7 - 511940*f**2/7 + 511225*f/7 - 1638. Solve i(a) = 0.
1, 715
Let m(i) be the first derivative of -i**4/4 + 76*i**3/3 - 640*i**2 - 6400*i + 2000. Solve m(j) = 0 for j.
-4, 40
Let l be ((-16942)/387 - -45) + 31. Factor 14/9*w**3 + l*w**2 + 196/9*w - 80/9.
2*(w + 1)*(w + 20)*(7*w - 2)/9
Let n = 115039 + -115036. Factor -10/3*f - 1 + n*f**2 + 4/3*f**3.
(f - 1)*(f + 3)*(4*f + 1)/3
Let i be (24/(-3) + 6)/(-3) + 0. Let x(c) be the second derivative of -10*c - i*c**3 - 1/15*c**4 + 0*c**2 - 4. Determine s, given that x(s) = 0.
-5, 0
Suppose 1134 = 16*g + 5*g. Suppose -23*s + g = 4*s. Find z, given that 0 - 2/13*z**s - 4/13*z = 0.
-2, 0
Let w(s) be the first derivative of s**4/12 - 29*s**3/6 - 8*s + 58. Let z(x) be the first derivative of w(x). Suppose z(g) = 0. Calculate g.
0, 29
Suppose 8*l - 4*l + 1 = -r, 5*r = -5*l + 10. Factor 10*s**2 + 163*s**4 + r*s - 173*s**4 + 2*s - 3*s**5 - 2*s**5.
-5*s*(s - 1)*(s + 1)**3
Let o(t) = -11*t**2 - 112*t - 18. Let g be o(-10). Factor 308*s**g - 32*s**3 - 57*s**3 - 368*s - s**4 + s**3 + 5*s**4 + 144.
4*(s - 18)*(s - 2)*(s - 1)**2
Let w = 18256/187 + -1638/17. Determine q so that -4/11*q**4 + 30/11*q**3 - 10/11*q**2 - 30/11*q + w = 0.
-1, 1/2, 1, 7
Let x(v) be the third derivative of -v**8/560 - v**7/70 + v**6/200 + v**5/20 - 5*v**2 - 109*v. Solve x(r) = 0.
-5, -1, 0, 1
Let f = 147 + -142. Suppose -355*r**3 - 50*r**f - 209