for n.
1, 3
Let p(x) = -x**3 + 3*x**2 + 4. Let l(z) = -99*z**2 - 102*z**2 + 1 + 202*z**2. Let j = 29 - 49. Let b(a) = j*l(a) + 5*p(a). Determine t so that b(t) = 0.
-1, 0
Find f such that -54/13*f + 2/13*f**4 + 0 + 30/13*f**2 + 22/13*f**3 = 0.
-9, -3, 0, 1
Let m(u) be the third derivative of 17/80*u**6 - 11/560*u**7 + 0 + 307*u**2 - 111/160*u**5 - 1/2*u**3 + 0*u + 31/32*u**4. Solve m(i) = 0 for i.
2/11, 1, 4
Let v(t) be the third derivative of t**5/15 - 253*t**4/3 + 128018*t**3/3 + 2187*t**2. Factor v(h).
4*(h - 253)**2
Let b(w) be the third derivative of w**5/12 - 1165*w**4/24 + 575*w**3 - 17*w**2 - 76*w + 1. Suppose b(u) = 0. What is u?
3, 230
Let b(y) be the third derivative of -y**5/510 + 7*y**4/102 + 24*y**3/17 + 2*y**2 + 710*y. Factor b(s).
-2*(s - 18)*(s + 4)/17
Let y(t) be the first derivative of 19*t**4/14 - 52*t**3/7 + 12*t**2 - 16*t/7 - 805. Find u, given that y(u) = 0.
2/19, 2
Let j = -107087/10 + 53551/5. Solve j*m**3 + 21/2 + 57/4*m**2 + 111/4*m = 0 for m.
-7, -2, -1/2
Determine g so that -478/7*g**2 + 402*g + 2/7*g**3 - 4194/7 = 0.
3, 233
Let c be (-2)/(-7) - 126648/(-280). Let m = 453 - c. Factor 1/5*s**4 + 0 - m*s**3 - 1/5*s**2 + 2/5*s.
s*(s - 2)*(s - 1)*(s + 1)/5
Suppose -8*x + 307 = 323. Let o be (6/(-17))/(1/x*6). Find l, given that 0 + o*l**2 + 0*l = 0.
0
Let p(c) = c**3 + c. Let r(t) = 45*t**3 + 72*t**2 - 48*t - 75. Let f be (-51)/7 - -8 - 2/(-7). Let h(a) = f*r(a) + 3*p(a). Suppose h(o) = 0. Calculate o.
-5/4, 1
Let s = 18 + -13. Suppose 2*d + s*z = -3, -8*d - z = -3*d - 50. Suppose d - 9 + 12*w - 10 - 4*w**2 + 0 = 0. What is w?
1, 2
Factor -27/4 - 33/4*z + 1/4*z**3 - 5/4*z**2.
(z - 9)*(z + 1)*(z + 3)/4
Let q(y) be the first derivative of -2*y**5/105 - 67*y**4/42 - 1012*y**3/21 - 12100*y**2/21 - 21296*y/21 + 549. Factor q(z).
-2*(z + 1)*(z + 22)**3/21
Suppose -4*b = 2*z - 92, -2*z - 2*z = -3*b - 228. Let u = -46 + z. Find p such that 8*p**4 - p + 14*p**5 + 8 - p - 2*p + u*p**3 - 18*p**5 - 16*p**2 = 0.
-1, 1, 2
Let v(k) = -12*k**2 + 5*k**2 - 530*k - 4802 - k**2 + 135*k. Let x(h) = 40*h**2 + 1974*h + 24010. Let p(z) = 28*v(z) + 6*x(z). Factor p(o).
4*(2*o + 49)**2
Let z = -1370 + 1370. Let y be 3 + (-4 - -5) - z. Determine w, given that 2/11*w**y - 2/11*w**5 + 6/11*w**3 - 4/11*w + 0 - 2/11*w**2 = 0.
-1, 0, 1, 2
Let w = 4661/6 + -2329/3. Determine r so that 14*r**2 - 50*r - w*r**3 + 48 = 0.
2, 24
Let -3/7*g**2 + 411/7 + 408/7*g = 0. What is g?
-1, 137
Let d = 1189 + -1169. Let s(h) be the first derivative of -d*h + 2 + 25*h**4 + 9*h**5 - 25/3*h**3 - 50*h**2. Suppose s(z) = 0. Calculate z.
-2, -1, -2/9, 1
Let n(x) be the third derivative of -1/6*x**4 + 0*x - 1/40*x**6 - 1/8*x**5 + 0 - 100*x**2 + 1/420*x**7 + 0*x**3. Solve n(u) = 0 for u.
-1, 0, 8
Let m = -988 + 994. Let b(v) be the third derivative of 0*v - 6*v**2 - 1/3*v**3 - 13/24*v**4 + 0 - 2/5*v**5 - 17/120*v**m - 2/105*v**7. Factor b(l).
-(l + 1)**2*(l + 2)*(4*l + 1)
Let n = 5249263451/819 + -6409356. Let f = 7/117 + n. Find y, given that -4/7*y**3 + 3/7*y - 9/7 + f*y**2 = 0.
-1, 3/2
Let b(u) = -50*u - 32 - 3*u**2 + 82*u - 24*u. Let v(z) = -4*z**2 + 10*z - 31. Let t(s) = -5*b(s) + 4*v(s). Factor t(c).
-(c - 6)*(c + 6)
Suppose a = 3*a - v - 20, 24 = 5*a + 4*v. Let y(m) = -m**3 + 9*m**2 - 7*m - 5. Let g be y(a). Let 15*j**2 + 10*j**2 + 5*j**g + 11 + 4 + 35*j = 0. Calculate j.
-3, -1
Let o(q) be the third derivative of q**7/420 - 17*q**6/240 + 11*q**5/20 + 415*q**2. Determine y so that o(y) = 0.
0, 6, 11
Let u = -34/729 - -358/729. Factor 1/9*x**3 - u*x + 1/9*x**2 - 4/9.
(x - 2)*(x + 1)*(x + 2)/9
Let s(p) = 45*p**2 + 337*p - 180. Let d be s(-8). Suppose -5/6*l**2 + 0 + 3/2*l**3 - 1/6*l**5 + 0*l - 1/2*l**d = 0. What is l?
-5, 0, 1
Let m(y) be the second derivative of -170*y + 1/12*y**4 - 1/2*y**3 + 0 - 9*y**2. Find u, given that m(u) = 0.
-3, 6
Suppose 327 = 6*j - 153. Let r be 20/j - (-1)/(-4)*-7. Suppose -10*b**3 - 2*b - 2*b**3 + 0*b**5 - 8*b**2 - r*b**5 - 8*b**4 = 0. Calculate b.
-1, 0
Factor 138401*d + 2245*d**2 - 1342149 + 53924 + 107894*d + 5*d**3.
5*(d - 5)*(d + 227)**2
Let x be (-2)/14 + 35/(2205/19422). Let o = x - 306. Factor 3*l**2 - 6/7 + o*l.
3*(l + 1)*(7*l - 2)/7
Let y(u) be the second derivative of -u**6/270 - 4*u**5/45 - 7*u**4/18 + 65*u**3/3 - 2*u + 23. Let r(b) be the second derivative of y(b). Solve r(q) = 0.
-7, -1
Let u(w) be the third derivative of 23*w**5/20 + 185*w**4/8 + 4*w**3 - 2*w**2 + 518. Find a, given that u(a) = 0.
-8, -1/23
Let l(a) = 5*a - 147. Let x be l(30). Factor u**4 + 47*u**x + 48*u**2 - 3*u**3 + 436*u**2.
u**2*(u + 22)**2
Let k(m) be the first derivative of -73 - 1/6*m**3 - 3*m - 5/4*m**2. Factor k(b).
-(b + 2)*(b + 3)/2
Let u = 455 - -164. Let y = u - 586. Factor 21/2*t**4 + 39/2*t + 3/2*t**5 + 9/2 + 27*t**3 + y*t**2.
3*(t + 1)**4*(t + 3)/2
Suppose 2332/3*g + 2/3*g**4 + 226592*g**2 - 679778/3 - 2332/3*g**3 = 0. What is g?
-1, 1, 583
Let p(y) be the second derivative of 0 - 11/24*y**4 - y**2 + 50*y - 2*y**3. Factor p(g).
-(g + 2)*(11*g + 2)/2
Let j = -600304 - -1800913/3. Find g such that 7/3*g**2 + j*g**3 - 25 - 5/3*g = 0.
-5, 3
Let o(p) be the third derivative of -p**7/210 + 5*p**6/12 - 4*p**5/5 - 25*p**4/12 + 49*p**3/6 + 2*p**2 - 27*p + 46. Let o(r) = 0. Calculate r.
-1, 1, 49
Suppose -i + 388 = -2*f, -5*i = -3*f - 2151 + 204. Factor 233 - 352*g + g**2 + i*g + 128.
(g + 19)**2
Let o = 3221 - 3218. Factor -9/5 + 1/5*s**o - 9/5*s + 1/5*s**2.
(s - 3)*(s + 1)*(s + 3)/5
Let i(o) = 2*o + 11. Let z be i(12). Let j = z + -44. Let r(s) = -5*s**2 + 15*s - 10. Let l(t) = 21*t**2 - 60*t + 39. Let m(y) = j*r(y) - 2*l(y). Factor m(p).
3*(p - 4)*(p - 1)
Let a(b) = -329*b + 21060. Let u be a(64). Factor 3/7*p**u + 53/7*p**2 - 37/7*p**3 + 4/7*p**5 - 27/7*p + 4/7.
(p - 1)**3*(p + 4)*(4*p - 1)/7
Let r(s) = 7*s**2 - s + 3. Let f(l) = 3*l**2 + 1. Let g(o) = -5*f(o) + 2*r(o). Let d(p) = 3*p. Let w(k) = 2*d(k) + 3*g(k). Factor w(i).
-3*(i - 1)*(i + 1)
Let f be 12/(-19) + 226722/123785. Suppose 180*b**2 + 42*b**3 + 0*b - f*b**5 + 0 - 24/5*b**4 = 0. What is b?
-5, 0, 6
Suppose 14 + 20 = -28*n + 45*n. Suppose 0 - 2/23*i**3 - 2/23*i**n + 0*i = 0. What is i?
-1, 0
Let m(z) = -4*z - 26 + 4*z + 2 + 8*z**2 + 4*z. Let v(l) = 7*l**2 + 5*l - 22. Let a(s) = 5*m(s) - 6*v(s). What is t in a(t) = 0?
-6, 1
Let j be 12/(-18)*6*-1. Suppose 3*o - 169 - 221 = 0. Determine v so that -o*v**j - 9*v**3 + 65*v**4 + 68*v**4 = 0.
0, 3
Factor 0 + 1/2*i**3 + 27*i**2 - 56*i.
i*(i - 2)*(i + 56)/2
Let x be (2172/8)/(99/66). Suppose 2*m = x - 177. Suppose 2/9*o**4 - 4/9 + 10/9*o + 4/3*o**5 - 38/9*o**3 + m*o**2 = 0. What is o?
-2, -1/2, 1/3, 1
Let y(n) = 8*n**3 + 19379*n**2 + 11751474*n + 13. Let k(t) = -4*t**3 - 9690*t**2 - 5875740*t - 6. Let d(j) = 13*k(j) + 6*y(j). Factor d(w).
-4*w*(w + 1212)**2
Let o(z) be the first derivative of 155 - 2/9*z**6 + 0*z - 512/3*z**2 + 640/3*z**3 - 8*z**5 - 193/3*z**4. Let o(r) = 0. What is r?
-16, 0, 1
Let r(x) be the first derivative of 0*x**4 + 0*x + 4/9*x**2 - 4/9*x**3 + 4/45*x**5 - 25. Determine v so that r(v) = 0.
-2, 0, 1
Suppose 0 - 4*x + 26/3*x**2 - 4/3*x**5 - 14/3*x**4 + 4/3*x**3 = 0. What is x?
-3, -2, 0, 1/2, 1
Let c(r) be the third derivative of -1/15*r**5 + r**2 + 0 - 1350*r**3 + 15*r**4 - 32*r. Factor c(v).
-4*(v - 45)**2
Let b(k) be the first derivative of k**5/5 + 11*k**4/4 - 55*k**3 + 325*k**2/2 + 500*k + 5929. Factor b(m).
(m - 5)**2*(m + 1)*(m + 20)
Let a = -5838 - -29211/5. Factor 54/5 - 3/5*z**2 + a*z.
-3*(z - 9)*(z + 2)/5
Let j = 233 + -218. Let h be (-20)/(-9) - (j - (-1596)/(-108)). Solve 1/2*u + 0 - 1/2*u**h = 0.
0, 1
Factor 0 - 2*g**4 + 0*g - 3*g**3 - 4/3*g**2 - 1/3*g**5.
-g**2*(g + 1)**2*(g + 4)/3
Let g(v) be the second derivative of v**4/12 - 107*v**3/3 - 215*v**2/2 - 1632*v. Determine n so that g(n) = 0.
-1, 215
Suppose 4*m + 45 = 5*c, -10*m = 5*c - 7*m - 10. Let y(o) be the first derivative of 33*o**4 - 24*o + 9 + 28/5*o**c + 14*o**2 + 52*o**3. Factor y(x).
4*(x + 1)**2*(x + 3)*(7*x - 2)
Let s(n) be the second derivative of -n**6/6 + n**5/4 + 5*n**4/3 - 10*n**3/3 - 1529*n. Factor s(u).
-5*u*(u - 2)*(u - 1)*(u + 2)
Suppose 5*z = -3*r + 27, 4*z - 32 = -24*r + 19*r. Let f = 64 - -76. Factor -3*n**z + 0*n**2 + f*n - 9*n**2 - 113*n - 15.
-3*(n - 1)**2*(n + 5)
Let m = -834341/7 - -119192. Determine o so that -12/7 + 9/7*o 