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Let s be ((-24)/30)/(-35 - -27). Let h(p) be the first derivative of 21 + s*p**4 + 2/5*p**2 + 0*p - 2/5*p**3. Factor h(a).
2*a*(a - 2)*(a - 1)/5
Determine w, given that 1/2*w**2 + 67 - 69/2*w = 0.
2, 67
Let c = -645543 + 1291087/2. Factor -c*t - 5/6*t**2 + 3/2 - 1/6*t**3.
-(t - 1)*(t + 3)**2/6
Let z(c) be the second derivative of -2*c + 0 - 1/150*c**5 + 9*c**2 + 8/15*c**3 + 7/60*c**4. Let j(h) be the first derivative of z(h). Factor j(f).
-2*(f - 8)*(f + 1)/5
Let b(m) be the second derivative of -25/54*m**4 - 1/90*m**5 - 68/27*m**3 - m - 44/9*m**2 + 195. Factor b(f).
-2*(f + 1)*(f + 2)*(f + 22)/9
Let q(i) be the first derivative of -3*i**5/5 + 183*i**4/4 - 174*i**3 - 13069. Factor q(j).
-3*j**2*(j - 58)*(j - 3)
Suppose 10 = 4*a - 6. Let h be 5*(-4)/(-4)*a/(-5). Let u(m) = 11*m**2 - 35*m - 26. Let b(r) = -r**2 + 1. Let x(i) = h*b(i) + u(i). Find y such that x(y) = 0.
-2/3, 3
Let t(m) be the second derivative of m**5/10 + 13*m**4/3 + 13*m**3/3 - 300*m**2 + m + 420. Let t(f) = 0. Calculate f.
-25, -4, 3
Let x be (-2)/8*40/45 + (-80)/(-36). Factor 44/3*h**x + 0 - 104/3*h + 4/3*h**3.
4*h*(h - 2)*(h + 13)/3
Let 324 - 19772*r + 9806*r - 4*r**2 + 9870*r = 0. What is r?
-27, 3
Let t(k) be the first derivative of 0*k**5 + 6*k**4 - 32/3*k**3 + 22 + 6*k**2 - 2/3*k**6 + 0*k. Find u, given that t(u) = 0.
-3, 0, 1
Let b = -374792/5 - -74971. Suppose -3/5*a**2 + 27 - b*a + 3/5*a**3 = 0. What is a?
-5, 3
Let f(n) be the second derivative of n**5/105 + n**4/42 - 3*n**2 - 28*n - 1. Let d(t) be the first derivative of f(t). Factor d(v).
4*v*(v + 1)/7
Let o be (-149245)/(-285) + 4/(-6). Let l = o - 2606/5. Let -6/5 + 0*p**2 + l*p - 3/5*p**3 = 0. What is p?
-2, 1
Let q(c) be the first derivative of -4*c**3/21 - 5804*c**2/7 - 8421604*c/7 - 31. Factor q(t).
-4*(t + 1451)**2/7
Suppose 27*t = -77 + 131. Let w(v) be the second derivative of -2/3*v**3 + 0 + v**t + 1/6*v**4 - 11*v. Factor w(r).
2*(r - 1)**2
Let n(b) be the first derivative of 3*b**6/4 - 53*b**5/4 - 671*b**4/16 - 147*b**3/4 - 19*b**2/8 + 17*b/2 - 14492. Let n(f) = 0. Calculate f.
-1, -1/2, 2/9, 17
Let t be (-32 + (-3791)/(-119))*-1*28. Let v(y) be the second derivative of 3/80*y**5 - 1/16*y**t + 0*y**2 + 10*y - 1/120*y**6 + 0 + 1/24*y**3. Factor v(x).
-x*(x - 1)**3/4
Let b(n) be the second derivative of 0 + 0*n**3 + 49*n - 1/15*n**6 + 0*n**5 + 5/6*n**4 - 4*n**2. Determine c so that b(c) = 0.
-2, -1, 1, 2
Suppose -7*l = 12*l - 57. Factor -208 + 86 + 240*r + 75*r**2 + 5*r**l - 198.
5*(r - 1)*(r + 8)**2
Suppose g = -2*q + 6, -g - 52 = -3*q - 48. Let a(y) = 24*y**3 + 445*y**2 - 114*y. Let j(r) = 12*r**3 + 223*r**2 - 57*r. Let b(m) = g*a(m) - 5*j(m). Factor b(s).
-3*s*(s + 19)*(4*s - 1)
Let t(i) be the first derivative of i**4/12 + 10*i**3/9 - 23*i**2/6 + 4*i + 1133. Suppose t(r) = 0. What is r?
-12, 1
Let m(c) = -15*c**3 + 184*c**2 + 11. Let s(x) = 3*x**3 - 37*x**2 - 2. Suppose -5*i = -27 - 28. Let t(j) = i*s(j) + 2*m(j). Let t(d) = 0. What is d?
0, 13
Let s(n) = -144*n**2 - 837*n + 306. Let y(a) = 9*a**2 + 52*a - 19. Let d(b) = 2*s(b) + 33*y(b). Factor d(q).
3*(q + 5)*(3*q - 1)
Let c = -2056497/100 - -20565. Let b(a) be the second derivative of 1/10*a**3 + 41*a + 3/10*a**2 + 0 - 1/20*a**4 - c*a**5. Factor b(j).
-3*(j - 1)*(j + 1)**2/5
Let b be 5 + 9 + -4 + -6. Suppose -6*l + l - 20 = n, 12 = -3*n - 3*l. Let n*x + 6/5*x**b - 2/5*x**5 + 0 + 0*x**2 - 4/5*x**3 = 0. What is x?
0, 1, 2
Factor 1064/9*o**2 - 141512/9*o + 0 - 2/9*o**3.
-2*o*(o - 266)**2/9
Let g(d) be the second derivative of d**4/54 - 382*d**3/27 - 256*d**2/3 - 1263*d. Factor g(b).
2*(b - 384)*(b + 2)/9
Let j(c) = c**3 + 17*c**2 - 39*c - 13. Let x be j(-19). Factor -x*h**3 + 9*h**2 + 10*h + 12*h - 14 - 3*h**4 + 2 - 10*h.
-3*(h - 1)**2*(h + 2)**2
Suppose 6*c - 7 = 5. Suppose c*a - 2*q = -6, -a + 3*q - 13 = -0*q. Factor 0*n + a*n + n**3 - 2*n**2 - 5*n + 0*n**3.
n*(n - 3)*(n + 1)
Let l(c) be the third derivative of c**8/840 - 22*c**7/525 - 2*c**6/25 + 11*c**5/75 + 23*c**4/60 - 251*c**2. Let l(b) = 0. Calculate b.
-1, 0, 1, 23
Let l(v) = -v**2 + 8*v + 13. Let a be l(9). Let z = -60 - -64. Let -6*x**3 + x**z - x**5 + 4*x**a + 7*x - 95 - 2*x**2 + 92 = 0. What is x?
-1, 1, 3
Let r(t) = 52*t - 50. Let v be r(1). Let j(g) be the first derivative of -6 - 3/2*g - 9/4*g**v - g**3. Factor j(y).
-3*(y + 1)*(2*y + 1)/2
Determine m so that 128/3*m**3 + 27 + 112/3*m**2 - 165/2*m = 0.
-2, 9/16
Let p(u) = -61*u + 126. Let s be p(2). What is t in -4514*t**2 + 4354*t**2 - 84*t**3 - 5*t**5 - 60*t**s - 96*t**3 = 0?
-8, -2, 0
Let n be (0 - (-2630)/322) + -8. Let r = 17/23 - n. Factor r*o**3 + 8/7*o**2 + 0*o - 4/7*o**4 + 0.
-4*o**2*(o - 2)*(o + 1)/7
Let p be 372/(14/7) - -5. Suppose 177*o = p*o - 56. Factor 2/9*y**5 + 2/9*y**2 + 0 + 2/3*y**3 + 0*y + 2/3*y**o.
2*y**2*(y + 1)**3/9
Let a(k) be the third derivative of 0*k - 1/85*k**5 + 0 + 0*k**3 + 1/1785*k**7 + 8*k**2 + 1/340*k**6 - 2/51*k**4. What is w in a(w) = 0?
-4, -1, 0, 2
Suppose 2*j + 3*n = 6*j - 89, 0 = j - 4*n - 19. Suppose j*p - 11 = 35. Factor 0 - 3*b**4 - 3*b**p - 3/4*b**5 - 9/2*b**3 - 3/4*b.
-3*b*(b + 1)**4/4
Let d(r) = -r**3 + 15*r**2 + 17*r - 3. Let v be d(16). Factor v*j**2 - 72*j - 25*j**2 + 15*j**3 + 20*j**2 - 73*j**2 - 109*j**2.
3*j*(j - 12)*(5*j + 2)
Suppose 0 = 10*n + 24*n - 136. Let -131*x**2 + 2*x**4 - 29*x**3 - 24*x**n - 48*x - 8*x**4 + 11*x**2 - 3*x**5 - 70*x**3 = 0. What is x?
-4, -1, 0
Let x = -16 + 10. Let r(j) = -4*j**2 - 26*j - 4. Let w be r(x). Solve -w*d + 35*d + 14*d**3 - 14*d**4 + 26*d**4 - 6*d**2 - 41*d**3 - 6 = 0.
-1, 1/4, 1, 2
Let w = 12465 - 12465. Let q(c) be the third derivative of 3*c**2 + 0*c**4 - 1/350*c**7 + 0*c**3 + w*c - 1/50*c**5 - 3/200*c**6 + 0. Let q(b) = 0. Calculate b.
-2, -1, 0
Solve 25*a**4 - 3*a**5 - 57*a**2 + 2*a**4 - 139*a**2 + 2*a**5 - 168*a**3 = 0.
-1, 0, 14
Factor 23/2*u + 24 - 49/4*u**2 + 1/4*u**3.
(u - 48)*(u - 2)*(u + 1)/4
Let s(a) be the second derivative of -41*a + 1/36*a**3 - 1/9*a**4 + 2 + 1/24*a**5 + 1/6*a**2. Factor s(v).
(v - 1)**2*(5*v + 2)/6
Suppose -4*c + 4*g = 2*g + 36, -3*g = -5*c - 47. Let i be ((-6)/(-9))/(c/(-21)). Factor 300 + 5*s**2 - 61*s - 4*s**i + 2*s**2 + s.
3*(s - 10)**2
Let v(n) be the second derivative of n**5/240 + n**4/24 + n**3/6 + 38*n**2 - 61*n. Let w(x) be the first derivative of v(x). Let w(z) = 0. Calculate z.
-2
Suppose 1391*f = -522*f - 253*f + 4332. Factor 23/2 + 21/4*z - 1/4*z**f.
-(z - 23)*(z + 2)/4
Let c be (-270)/27 + -31 + 44. Factor 0*k - 2/9*k**5 - 16/9*k**c + 0 + 10/9*k**4 + 8/9*k**2.
-2*k**2*(k - 2)**2*(k - 1)/9
Factor 1058/5*l - 1057/5 - 1/5*l**2.
-(l - 1057)*(l - 1)/5
Suppose 0 = -7*y - 14, -24*o + 21*o - 4*y = -7. Let n(f) be the third derivative of 0*f + 28*f**2 - 1/60*f**6 - 2/15*f**o + 0 + 6*f**3 + 1/4*f**4. Factor n(h).
-2*(h - 2)*(h + 3)**2
Factor 0 - 2*b**2 + 1/10*b**3 + 10*b.
b*(b - 10)**2/10
Let k = -2/3 + 71/12. Suppose -3*h - s = -5, 14*s - 13*s = 4*h - 9. Factor -k*y - 3/8*y**h - 147/8.
-3*(y + 7)**2/8
Let v = 11459/2451 - 7/817. Suppose 1/3*r + v*r**3 + 17/3*r**2 - 2/3 = 0. What is r?
-1, -1/2, 2/7
Let m(k) be the first derivative of 2*k**6/15 - k**5 + k**4/3 + 14*k**3 - 36*k**2 + 23*k - 115. Let s(g) be the first derivative of m(g). Factor s(x).
4*(x - 3)**2*(x - 1)*(x + 2)
Let q(h) = h**3 + 11*h**2 + 22*h + 44. Let y be q(-9). Suppose -2*f - f + 27 = 0. Factor y + f*z**3 + 2*z**4 + 18*z**4 + 3*z**3 - 28*z**2 - 12*z.
4*(z - 1)*(z + 1)**2*(5*z - 2)
Let z = -51909 + 51909. Determine u, given that 0 + 1/5*u**4 + z*u**2 - 2/5*u**5 + 0*u + 1/5*u**3 = 0.
-1/2, 0, 1
Let i = 1047 - 1037. Suppose -i*n + 12*n = 14*n. Factor 2/9*g**3 + 0*g - 4/9*g**2 + n.
2*g**2*(g - 2)/9
Let q(l) be the first derivative of 4*l**5/45 - 59*l**4/18 - 256*l**3/27 + 59*l**2/9 + 28*l - 122. Determine d, given that q(d) = 0.
-2, -1, 1, 63/2
Let a(k) = 3*k**4 - 9*k**3. Let l(o) = 2*o**4 - 5*o**3. Let s be (0 - 15/12)*(-8)/(-2). Let y(v) = s*l(v) + 3*a(v). Determine r, given that y(r) = 0.
-2, 0
Solve 1066*t + 4*t**2 + 12620160 - 9827*t - 5487*t + 67684 = 0 for t.
1781
Factor -2794248/5 + 557904*s + 2/5*s**3 + 4726/5*s**2.
2*(s - 1)*(s + 1182)**2/5
Suppose 502/9*y**2 - 596/9*y + 16/3 + 46/9*y**3 = 0. Calculate y.
-12, 2/23, 1
Let s = -16 - -16. Suppose -m - 1 + 5 = s. Determine v so that 10*v**2 - 4*v + 23*v**3 - 8*v**m - 2*v**2 + 4*v*