. Let k(a) = x(a) - 6*y(a). Let l be k(-17). Factor -30*c**2 + 64*c**2 + 21*c + 18 - 31*c**l.
3*(c + 1)*(c + 6)
Let s(t) = -69*t**2 - 4*t + 2. Let i be s(1). Let p = 79 + i. Factor 6 - 39*b**2 + p*b + 14*b**2 + 11*b**2 + 16*b**2.
2*(b + 1)*(b + 3)
Factor -18909*j**4 - 33*j**3 + j**5 + 18919*j**4 + 40*j**2 - 2*j**5 - 16*j.
-j*(j - 4)**2*(j - 1)**2
Let l = -3625 + 18127/5. Let n(i) be the first derivative of -11 + 0*i + 2/3*i**3 - 3/4*i**4 + 0*i**2 + 1/2*i**6 - l*i**5. Factor n(u).
u**2*(u - 1)*(u + 1)*(3*u - 2)
Suppose 296/7 + 267/7*r + r**2 = 0. Calculate r.
-37, -8/7
Suppose -19*m + 24 = -14. Determine n, given that 9408 + 5*n**2 + 12*n**2 - 19*n**2 + 5*n**m + 336*n = 0.
-56
Let s(y) = -5*y**4 - 132*y**3 + 806*y**2 + 628*y - 385. Let w(m) = -m**4 - m**3 - m - 11. Let g(r) = 3*s(r) - 24*w(r). Determine a, given that g(a) = 0.
-1, 1/3, 9, 33
Let o = 184882 + -541126/3. Factor 1040/3*b + 32/3 + 87880/3*b**3 + 285610/3*b**4 + o*b**2 + 371293/3*b**5.
(13*b + 2)**5/3
Let c be (236/6)/((-50)/(-825)). Let o be c/462 - (-5)/(-6). Solve 8/7*d**3 - 2/7*d**5 - 4/7 - 6/7*d + o*d**2 + 0*d**4 = 0.
-1, 1, 2
Let l(t) be the first derivative of 5/3*t**3 - 35/2*t**2 - 57 + 30*t. Solve l(p) = 0 for p.
1, 6
Let n(p) be the first derivative of 6*p**2 + 0*p + 27 + 8*p**3 - p**6 - 21/5*p**5 - 9/4*p**4. Find t such that n(t) = 0.
-2, -1/2, 0, 1
Suppose -6*b = -y - 21, 0 = b - 12*y + 14*y + 16. Factor -4/5*f**3 - 2/5 + 9/5*f - 3/5*f**b.
-(f - 1)*(f + 2)*(4*f - 1)/5
Factor 1/4*p**3 + 23*p + 22 + 13/2*p**2.
(p + 2)**2*(p + 22)/4
Factor -137*i - 92 + 1/2*i**3 - 89/2*i**2.
(i - 92)*(i + 1)*(i + 2)/2
Let u = -1961 + 13729/7. Suppose 2*w - d = -4*d + 3, 5 = 3*w + 5*d. Determine o, given that -u*o + w + 2/7*o**3 + 0*o**2 = 0.
-1, 0, 1
Let h(v) be the second derivative of -v**5/120 - v**4/4 - 5*v**3/12 + 17*v**2/6 - 15*v - 70. Find u such that h(u) = 0.
-17, -2, 1
Suppose -20 = d - z + 5*z, -3*z + 30 = -3*d. Let q be (d/18)/((-4)/18). Factor -q*m**4 + 3*m**3 - 8*m**2 + m**2 + 5*m**2 + 2*m**4.
-m**2*(m - 2)*(m - 1)
Let -456006*h - 4*h**2 - 469 + 4005 + 455786*h = 0. What is h?
-68, 13
What is n in 0 - 20/3*n**2 - 26*n + 2/3*n**3 = 0?
-3, 0, 13
Let o(n) = -n**2 + 1312*n - 6532. Let l be o(5). Suppose 2/3*f**2 + 0 + 0*f + 2/3*f**l = 0. What is f?
-1, 0
Let u be -188 + -9 - 15/3. Let i be -8 + 7 - (u - -1). Solve 156*b**2 - 394/3*b**3 - 152/3*b + i*b**5 - 430/3*b**4 + 16/3 = 0.
-1, 1/4, 2/5, 2/3
Let h(l) be the second derivative of -l**6/60 + 309*l**5/40 - 10609*l**4/8 + 1092727*l**3/12 + 3*l - 231. Solve h(c) = 0 for c.
0, 103
Let y = 18237/4 - 27297/20. Factor y*n**3 + 81/5 + 14641/5*n**4 + 1188/5*n + 6534/5*n**2.
(11*n + 3)**4/5
Factor b**3 + 433/5*b - 728/5*b**2 + 58.
(b - 145)*(b - 1)*(5*b + 2)/5
Suppose -3*v - 2*x = -28, v = 4*x + 255 - 283. Let m(b) be the first derivative of -20/3*b**3 - 1/2*b**v - 9*b**2 + 0*b - 36. Factor m(n).
-2*n*(n + 1)*(n + 9)
Let w(o) be the third derivative of -o**5/300 + 7*o**4/30 - 13*o**3/2 + 5756*o**2. Factor w(p).
-(p - 15)*(p - 13)/5
Solve -2152/5*r**3 + 386*r**2 + 128/5*r**5 + 1420*r + 800 - 160*r**4 = 0 for r.
-5/4, 2, 8
Let x(s) = -72*s + 8. Let t(d) = -d**2 + d + 2. Let a(j) = 4*t(j) - x(j). Solve a(g) = 0.
0, 19
Factor -21*l**2 + 3/7*l**3 + 2145/7*l - 9801/7.
3*(l - 27)*(l - 11)**2/7
Suppose -12 = -3*p, 2*m = 6*m + p - 4. Let s be 130/(-195) + -1*(-32)/30. Solve s*z**3 + 0*z**2 + m - 2/5*z = 0 for z.
-1, 0, 1
Let v(k) = 13894415*k**2 - 16676*k + 17. Let n(p) = -5*p**2 - p + 2. Let g(z) = -6*n(z) + v(z). Factor g(m).
5*(1667*m - 1)**2
Suppose 96 = -206*l + 202*l - 2*r, 70 = -3*l - r. Let x be (l/(-198))/(2/((-192)/(-20))). Factor -6/5*c - x*c**2 - 4/15.
-2*(c + 2)*(4*c + 1)/15
Let v(u) be the first derivative of 32*u**2 - 1/3*u**3 - 154 - 1024*u. Factor v(c).
-(c - 32)**2
Let i(v) be the third derivative of -v**8/5040 + v**7/140 - 2*v**6/45 + v**5/30 + 19*v**4/24 - 64*v**2. Let b(p) be the third derivative of i(p). Factor b(j).
-4*(j - 8)*(j - 1)
Factor 10*g**3 + 23*g**4 + 14*g**4 + 15*g**4 - 64*g**4 - 24*g**2 + 13*g**4.
g**2*(g - 2)*(g + 12)
Suppose -327*l + 348*l = -2058. Let h be (-130)/(-92) - l/1127. Factor 0 - 2*g**2 - h*g - 1/2*g**3.
-g*(g + 1)*(g + 3)/2
Let l(g) be the second derivative of -7*g - 3/13*g**4 + 2/273*g**7 - 8/65*g**5 - 27/13*g**2 + 18/13*g**3 + 1/39*g**6 + 6. Determine k so that l(k) = 0.
-3, 1, 3/2
Factor 20*y - 1/7*y**2 - 411/7.
-(y - 137)*(y - 3)/7
Determine r, given that 64 + 464*r**3 - 118*r**5 + 3355*r + 18*r**5 - 20*r**4 + 64*r**2 - 3611*r = 0.
-2, -1, 2/5, 2
Let i be (-12)/(-15) + ((-224)/20)/(-1). Let t be 39/(-26)*2/i*-2. Suppose -7/2*w - 2 - w**2 + t*w**3 = 0. Calculate w.
-1, 4
Let i(l) be the second derivative of -l**5/30 - 31*l**4/9 + 12*l. Factor i(s).
-2*s**2*(s + 62)/3
Let f = 9398 + -9394. Let z(t) be the second derivative of -16*t + 0 + 0*t**2 + 1/45*t**f + 1/45*t**3 + 1/150*t**5. Suppose z(y) = 0. Calculate y.
-1, 0
Let c(z) be the third derivative of z**6/30 - 6*z**5/5 + 16*z**4 - 320*z**3/3 + 618*z**2. Factor c(t).
4*(t - 10)*(t - 4)**2
Suppose t + 398 - 328 = -4*f, -10*t + 3*f + 74 = 0. Factor 0 - 2/5*o**4 - 14/5*o**2 - t*o**3 - 6/5*o.
-2*o*(o + 1)**2*(o + 3)/5
Let f(d) be the first derivative of 8/3*d**2 + 7 - 7/9*d**3 - 1/18*d**4 + 28*d. Let y(i) be the first derivative of f(i). Let y(n) = 0. What is n?
-8, 1
Suppose -2*w - 23 + 27 = 0. Let 17*j**w + 26*j**2 - 6*j - 46*j**2 = 0. What is j?
-2, 0
Let f(c) = 12*c**3 + 274*c**2 + 17. Let s be 51/(-15)*3*(-10)/3. Let x(k) = -2*k**3 - 46*k**2 - 3. Let o(i) = s*x(i) + 6*f(i). Let o(a) = 0. What is a?
-20, 0
Let x(z) be the third derivative of z**6/120 + 11*z**5/60 - 15*z**4/2 + 23*z**2 + 38*z. Factor x(s).
s*(s - 9)*(s + 20)
Let a = 212 - 210. Factor -g**3 - 11966 + 11962 - 9*g - 8*g**a + 2*g**2.
-(g + 1)**2*(g + 4)
Let g(o) = -6*o**3 - 12*o**2 + 48*o + 195. Let i = -271 - -274. Let q(m) = -17*m**3 - 36*m**2 + 144*m + 584. Let h(p) = i*q(p) - 8*g(p). Factor h(w).
-3*(w - 4)*(w + 4)**2
Find r, given that -802/11*r**3 + 1158/11*r**4 + 816/11*r + 328/11 - 1486/11*r**2 - 14/11*r**5 = 0.
-1, -2/7, 1, 82
Let o(h) = h**3 - 203*h**2 + 621*h - 4000. Let l be o(200). Factor -1/8 - l*q**2 - 10*q.
-(40*q + 1)**2/8
Let t = 4934806/5 + -986961. Factor 8/5*q - 3 - t*q**2.
-(q - 5)*(q - 3)/5
Let g(k) = k**4 - 2*k**2 + 5*k. Let s(y) = 6*y**4 - 462*y**3 - 9806*y**2 + 42295*y + 18432. Let j(i) = 44*g(i) - 4*s(i). Let j(a) = 0. What is a?
-48, -2/5, 4
Suppose -831 = -71*o + 873. Suppose 14 = o*g - 17*g. Suppose -8/3 + 0*h + 2/3*h**g = 0. Calculate h.
-2, 2
Factor 102/5*n**2 + 0 + 4/5*n.
2*n*(51*n + 2)/5
Let x(t) be the second derivative of t**6/60 - 3*t**5/40 - 13*t**4/24 + 5*t**3/4 - 862*t. Factor x(q).
q*(q - 5)*(q - 1)*(q + 3)/2
Let c(s) = 4*s**4 + 36*s**3 - 100*s**2 + 39*s - 3. Let r(a) = -a**4 - 5*a**2 - a - 1. Let y(u) = -c(u) + 3*r(u). Factor y(x).
-x*(x - 1)*(x + 7)*(7*x - 6)
Let n(a) be the first derivative of -2*a**3/3 - 267*a**2 + 1076*a - 252. Let n(f) = 0. What is f?
-269, 2
Let q(v) = -v**3 - 16*v**2 + 559*v - 56. Let y be q(-33). Solve 9/2*u + y + 1/2*u**2 = 0.
-5, -4
Suppose 53 = -51*s + 16 + 394. Let d(n) be the second derivative of 4/21*n**2 + 1/126*n**4 + 0 + s*n + 5/63*n**3. Factor d(r).
2*(r + 1)*(r + 4)/21
Let z(f) = 172*f**2 + 331*f + 19. Let p(h) = -87*h**2 - 165*h - 9. Let d(i) = 5*p(i) + 3*z(i). Let d(c) = 0. What is c?
-2, -2/27
Let z(p) = 5*p**3 - 90*p**2 + 135*p + 205. Let q(o) = -5*o**3 + 88*o**2 - 133*o - 206. Let a(c) = 5*q(c) + 4*z(c). Suppose a(u) = 0. Calculate u.
-1, 3, 14
Let r = -25167 - -25170. Let a(h) be the third derivative of 1/30*h**6 - 1/5*h**5 + 0*h**r + 0*h - 30*h**2 + 0 + 1/3*h**4. Find p such that a(p) = 0.
0, 1, 2
Let c(l) be the second derivative of -l**6/345 + 20*l**5/23 + 239*l**4/23 + 1032*l**3/23 + 81*l**2 - 3424*l. Suppose c(q) = 0. Calculate q.
-3, -1, 207
Let a(p) = p**2 + 61*p + 802. Let m be a(-19). Let z(v) be the second derivative of 0*v**3 + 1/9*v**m + 39*v + 1/30*v**5 + 0 + 0*v**2. Factor z(o).
2*o**2*(o + 2)/3
Let i = -409 - -416. Let r be (-4 + i)/((-216)/(-32)). Suppose -2/9*s**2 + 2/3*s - r = 0. What is s?
1, 2
Let v(a) be the third derivative of -a**7/420 - 17*a**6/120 + 187*a**5/120 - 77*a**4/12 + 13*a**3 + 1650*a**2. Factor v(g).
-(g - 2)**2*(g - 1)*(g + 39)/2
Suppose 0 = -3*s, -2*s - 29 - 3