37796 = 0. Determine p, given that 4/9*p + 2/9*p**5 - 2/3*p**3 - 2/9*p**b + 0 + 2/9*p**4 = 0.
-2, -1, 0, 1
Let z = -3601 - -3604. Let y be (70/(-4))/((-3)/6). Factor 1 + 33*p**3 - 1 + y*p**2 - 38*p**z.
-5*p**2*(p - 7)
Suppose -42*t = -44*t + 2064. Factor -496*r**3 + 16 + 48*r + t*r**3 + 4*r**4 - 512*r**3 + 52*r**2.
4*(r + 1)**2*(r + 2)**2
Suppose -n = 3*i + 46, -2*n = -i - 4736 + 4716. Find o, given that -58/11*o + 20/11 - 6/11*o**n = 0.
-10, 1/3
Let p be (2/(32/465396))/(204/16). Let g = p + -2281. Let -g + 2/17*b - 2/17*b**3 + 6/17*b**2 = 0. Calculate b.
-1, 1, 3
Let d = -21 + -38. Let i = 69 + d. Solve 3*t + 2*t + i*t**3 + t - 12*t**2 - 3*t**4 - 1 = 0 for t.
1/3, 1
Suppose -3*k - 22 = -7, 0 = 4*w + k - 19. Let l(t) be the second derivative of 6*t + 1/105*t**w + 0*t**2 + 0*t**5 + 0*t**3 + 0 + 0*t**4. Factor l(p).
2*p**4/7
Let a(f) be the second derivative of -8*f**6/15 + 14*f**5/15 - f**4/27 - f**3/3 - f**2/9 + 4*f - 457. Find p such that a(p) = 0.
-1/6, 1/2, 1
Let v(g) = g**3 - 2*g**2 + 2*g. Let q(k) = 4*k**3 - 18*k**2 - 5*k. Let f(c) = -q(c) + 5*v(c). Find l such that f(l) = 0.
-5, -3, 0
Let a(p) be the first derivative of -p**3/4 - 39*p**2/8 + 21*p/2 + 710. Solve a(j) = 0.
-14, 1
Suppose 2*q = 4*g + 24, 5*q - 22*g + 24*g = 108. What is c in 142*c**3 - q*c + 2*c**5 - 14*c**4 - 305*c**3 + 109*c**3 - 58*c**2 = 0?
-1, 0, 10
Let c = 2230 + -2295. Let m(i) = i**2 + 60*i - 320. Let n be m(c). Factor 2/5*y**2 + 3/5*y**4 - 1 + 2*y**3 - 9/5*y - 1/5*y**n.
-(y - 5)*(y - 1)*(y + 1)**3/5
Determine h so that -656/13*h - 2/13*h**2 + 0 = 0.
-328, 0
Factor 401/6 - 67*k + 1/6*k**2.
(k - 401)*(k - 1)/6
Let j(c) = -c**2 - 19*c - 14. Suppose 16 = -3*m - 38. Let d be j(m). Let -24*s + 18*s**2 + 7*s**4 - 25*s**d + 12*s + 3*s**5 - 3*s + 12*s**3 = 0. Calculate s.
-1, 0, 1, 5
Let t(y) be the first derivative of -2*y**3/15 - 63*y**2/5 + 536*y/5 - 1786. Find n such that t(n) = 0.
-67, 4
Solve 1761/4*n + 759/4*n**3 - 567*n**2 - 9/2*n**4 - 117/2 = 0.
1/6, 1, 2, 39
Determine v so that -20/3*v**4 + 0*v**2 + 0*v + 0 + 2/3*v**5 - 22/3*v**3 = 0.
-1, 0, 11
Let n(p) be the second derivative of p**4/6 + 116*p**3/3 + 228*p**2 + 727*p - 3. Factor n(o).
2*(o + 2)*(o + 114)
Let x = -623245 - -623345. Factor x*t**2 + 0 + 0*t - 10*t**3 + 1/4*t**4.
t**2*(t - 20)**2/4
Let -208/5*q - 92/5*q**2 + 768/5 + 2/5*q**3 = 0. What is q?
-4, 2, 48
Let g(h) = -161*h - 81. Let f be g(-9). Let p be f/1404 - 6/9. Suppose p*n**2 - 2/13*n - 2/13*n**3 + 0 = 0. What is n?
0, 1
Let k(g) be the first derivative of -g**8/336 + g**7/42 - g**6/24 - g**3/3 + 21*g**2/2 - 71. Let t(y) be the third derivative of k(y). Factor t(p).
-5*p**2*(p - 3)*(p - 1)
Let a(z) be the third derivative of -z**7/1680 - 277*z**6/480 - 69*z**5/20 - 827*z**4/96 - 551*z**3/48 - 2753*z**2. Let a(x) = 0. What is x?
-551, -1
Let g(f) be the first derivative of -44*f**3/27 - 58*f**2/3 + 32*f/9 + 3366. Let g(l) = 0. Calculate l.
-8, 1/11
Let t(g) be the first derivative of -g**5/40 + 7*g**4/8 - 13*g**3/4 + 44*g**2 - 29. Let r(f) be the second derivative of t(f). Let r(s) = 0. What is s?
1, 13
Factor 17*f + 72*f**2 - 86*f**3 + 343 - 73 + 133*f**3 - 50*f**3 - 356*f.
-3*(f - 18)*(f - 5)*(f - 1)
Determine v, given that 332*v**2 + 822 - 2*v**3 + 1641*v + 115*v**2 + 369*v**2 - v**3 = 0.
-1, 274
Suppose -l - 4*l = 2*u - 915, -4*l - 477 = -u. Factor -909 + u*n - 243 - 561*n - 2*n**2.
-2*(n + 24)**2
Let h be (-14)/6*((-220)/273 - (-456)/(-8892)). Suppose 19*d = 21*d. Factor 1/5*b**h + 0*b - 1/5*b**3 + d.
-b**2*(b - 1)/5
Let p be (12 - 4) + 84/(-12). Let t be 8/(-8)*-1 + p. Factor 0 + 1/2*c**4 - 3*c**3 + 4*c - t*c**2 + 1/2*c**5.
c*(c - 2)*(c - 1)*(c + 2)**2/2
Let q(i) be the second derivative of -i**6/30 - 41*i**5/4 + 207*i**4/4 - 623*i**3/6 + 104*i**2 + 890*i - 1. Factor q(k).
-(k - 1)**3*(k + 208)
Let i be 21/6*(-16)/(-7). What is z in -8*z**3 - 4*z**4 + 2 + i*z**2 + 12*z**3 - 2 = 0?
-1, 0, 2
Let p be 15/40 + 203/(-8). Let m be ((-24)/(-15))/((-10)/p). Solve m*z**3 + 5*z + 10*z**2 - 18*z + 8*z**2 + 9*z**5 - 20*z**4 + 2 = 0.
-1, 2/9, 1
Let d be (-18 - 702/(-130)) + 45. Determine i so that -d + 32*i**2 + 2/5*i**4 - 36/5*i + 36/5*i**3 = 0.
-9, -1, 1
Let y(c) be the second derivative of c**4/12 + 28*c**3 + 12070*c. Determine d, given that y(d) = 0.
-168, 0
Let h be (-576)/23*(17 - ((-8 - -3) + 2448/108)). Factor 0 + 32/23*c**3 - h*c**2 + 2/23*c**5 + 26/23*c**4 + 0*c.
2*c**2*(c - 3)*(c + 8)**2/23
Suppose 145*q + 2*n = 151*q - 36, -3*q - 5*n - 18 = 0. Suppose 32/11*b**5 + 178/11*b**2 - 58/11*b + 6/11 + 16/11*b**q - 174/11*b**3 = 0. What is b?
-3, 1/4, 1
Let y(c) = -12*c - 10. Let t be y(-12). Let h = t + -130. What is q in -8*q**h + 8*q**3 - 55*q**2 + 3*q**4 + 137*q - 167*q - 38*q**3 = 0?
-3, -2, -1, 0
Determine o so that 0 + 12*o**2 + 0*o + 2*o**3 - 1/4*o**5 - 5/4*o**4 = 0.
-4, 0, 3
Determine v, given that 1642 + 2*v**3 + 2*v**3 - 4791 + 112*v**2 + 2509 - 303*v - 229*v = 0.
-32, -1, 5
Let w(o) be the second derivative of 3*o**5/10 - 143*o**4/3 + 928*o**3/3 - 736*o**2 - 237*o + 11. Find b such that w(b) = 0.
4/3, 2, 92
Let n(l) be the first derivative of -l**4/7 - 20*l**3/21 - 2*l**2 - 12*l/7 - 2032. Factor n(f).
-4*(f + 1)**2*(f + 3)/7
Let v(z) be the second derivative of z**6/2 - 237*z**5/20 + 309*z**4/4 - 185*z**3/2 - 75*z**2 - 57*z + 27. Determine j, given that v(j) = 0.
-1/5, 1, 5, 10
Let f(w) be the third derivative of 0 + 0*w + 1/2*w**4 - 64*w**2 - 20/3*w**3 + 1/15*w**5. Let f(c) = 0. What is c?
-5, 2
Let g = -194591/2 + 98657251/1014. Let m = -8/169 - g. Factor 0*i**3 + 0 + m*i**5 + 0*i + 1/3*i**4 + 0*i**2.
i**4*(i + 1)/3
Suppose -q - 19*g + 24*g + 24 = 0, 8 = 3*q + g. Determine u so that -8/3*u + 4 - 16/3*u**2 + 4/3*u**q + 8/3*u**3 = 0.
-3, -1, 1
Let p be (2412/48)/67 - ((-159)/12 - 2). Factor 1/4*j**2 - 4*j + p.
(j - 8)**2/4
Let d(v) = 2*v**2 - 252*v + 3524. Let t be d(16). Solve -4*o**3 + 0 - 4/9*o**5 + 0*o + 8/3*o**t + 0*o**2 = 0.
0, 3
Let w be (9/(-24))/((-6)/(-4)) - 27/(-12). Factor -3/2 - 1/4*v**w - 5/4*v.
-(v + 2)*(v + 3)/4
Factor -125*i**2 + 23*i**3 - 42*i**3 + 191*i**2 + 16*i**3 - 63*i.
-3*i*(i - 21)*(i - 1)
Let k(f) be the third derivative of -f**5/120 - 137*f**4/8 + 412*f**3/3 - 1447*f**2. Let k(g) = 0. Calculate g.
-824, 2
Find c, given that -8/3*c**5 - 56/3 - 314/3*c**2 + 52/3*c**3 - 304/3*c + 110/3*c**4 = 0.
-1, -1/4, 2, 14
Let k(m) be the second derivative of 6/25*m**5 + 0*m**3 - 2/75*m**6 - 1/3*m**4 - m + 1 + 0*m**2. Factor k(q).
-4*q**2*(q - 5)*(q - 1)/5
Suppose 348*p + 3 - 3 = 379*p. Let x(k) be the second derivative of p*k**2 - 23*k + 0*k**5 + 0 + 1/10*k**6 + 0*k**3 + 0*k**4 + 1/14*k**7. Factor x(y).
3*y**4*(y + 1)
Let b be 6/(-42) - 17/(-21). Let q = -305057/3 - -101686. Solve q*s**2 + b*s + 0 = 0.
-2, 0
Let c(w) be the first derivative of 2*w**3/21 - 28*w**2 - 394*w/7 + 687. Determine t so that c(t) = 0.
-1, 197
Let l(a) = 15*a + 2 + 3*a**2 - 2 - 2*a**2 - 16*a. Let k(q) = 12*q**2 - 64*q + 160. Let x(n) = -k(n) + 8*l(n). Factor x(u).
-4*(u - 10)*(u - 4)
Let d(j) be the first derivative of -11/18*j**4 + 100/9*j - 2/45*j**5 - 23 - 5/9*j**2 - 22/9*j**3. Determine v so that d(v) = 0.
-5, -2, 1
Suppose -6*g + 390 = 2004. Let i = g - -270. Solve 5/2*u - 7/2*u**2 + i = 0 for u.
-2/7, 1
Let o = 1013 - 1006. Determine s, given that -41*s**4 - 2*s**4 + 25*s**2 + 10*s**3 + o*s - 17*s + 17*s**4 + s**4 = 0.
-1, 0, 2/5, 1
Let k(p) = 81*p**3 + 938*p**2 + 3091*p - 960. Let z(q) = -41*q**3 - 468*q**2 - 1546*q + 480. Let n(t) = -6*k(t) - 11*z(t). Determine m so that n(m) = 0.
-8, -6, 2/7
Factor -12*n + 304 - 148 - n**2 - 7*n - 140 + 4*n.
-(n - 1)*(n + 16)
Let o be (20 - 20)*(-6)/24. Factor -3/2*d**3 + o*d + 6*d**2 + 0.
-3*d**2*(d - 4)/2
Solve 1/3*w**2 + 172225/3 + 830/3*w = 0 for w.
-415
Let o(x) be the first derivative of 2*x**3/3 - 77*x**2 - 910. Suppose o(f) = 0. Calculate f.
0, 77
Let c = 112293/280720 + -1/56144. Factor 4/5*k**2 - c*k**3 + 8/5*k - 16/5.
-2*(k - 2)**2*(k + 2)/5
Let p(y) be the third derivative of -1/40*y**4 + y**2 - 66*y + 1/100*y**5 + 1/30*y**3 + 0 - 1/600*y**6. Let p(n) = 0. Calculate n.
1
Let o be (0 + (-70)/4)*84/(-315). Let n = 10537 + -10537. What is t in -16/3 + 8*t - o*t**3 + 2/3*t**5 + 4/3*t**2 + n*t**4 = 0?
-2, 1, 2
Let c(u) be the third derivative of 1/210*u**5 + 0*u + 529/21*u**3 + 0 + 23/42*u**4 - 2*u*