+ 32)/3
Let n be (24/(-20))/(8/(-20)) - (-2 + 2). Let a(v) be the first derivative of 15/8*v**2 - n*v + 11/8*v**3 + 29 - 21/32*v**4. Factor a(j).
-3*(j - 2)*(j + 1)*(7*j - 4)/8
Let s(m) = 55*m**2 + 360*m + 355. Suppose -14*j + 26*j = -48. Let o(l) = 9*l**2 + 60*l + 59. Let v(y) = j*s(y) + 25*o(y). Factor v(k).
5*(k + 1)*(k + 11)
Let o(a) = 2*a**3 + 25*a**2 + 24*a - 149. Let g(d) = 10*d**3 + 124*d**2 + 120*d - 744. Let c(h) = 5*g(h) - 24*o(h). Determine l, given that c(l) = 0.
-6, 2
Let p(i) = i**3 + 2*i**2 - 6*i - 2. Let z be p(4). Let c be ((-2)/(-4))/(7/z). What is a in -5*a**5 - 5*a**5 - a**3 + 8*a**c - a**3 - 4*a**4 = 0?
-1, 0
Let z = -129019/42 - -18433/6. Find x, given that 6/7*x**5 - z*x - 20/7*x**3 - 24/7*x**2 + 4/7 + 4/7*x**4 = 0.
-1, 1/3, 2
Let z be (-1 - -2) + (-1113)/1590. Let g(a) be the first derivative of -3/20*a**4 - 27 + z*a**2 - 6/5*a + 2/5*a**3. Suppose g(o) = 0. What is o?
-1, 1, 2
Let i be 0/(16/192*-12). Factor 1/2*k**2 - 1/2*k**3 + i + k.
-k*(k - 2)*(k + 1)/2
Determine i, given that 40/3*i + 0 - 28*i**4 - 56*i**2 + 202/3*i**3 + 10/3*i**5 = 0.
0, 2/5, 1, 2, 5
Let g(x) = 4496*x - 8992. Let w be g(2). Factor w - b**2 - 11/6*b**3 + 1/6*b**5 - 2/3*b**4 + 0*b.
b**2*(b - 6)*(b + 1)**2/6
Let s(z) = z**3 + z**2 + 8*z. Let d(n) = 5 - 2 - 52*n**2 - 2 + 53*n**2. Let w(b) = -4*d(b) - s(b). What is t in w(t) = 0?
-2, -1
Solve -100 + 330/7*r + 652/7*r**2 - 328/7*r**3 - 2/7*r**5 + 48/7*r**4 = 0 for r.
-1, 1, 5, 14
Let n(l) be the second derivative of -3*l**5/5 + 5*l**4/3 - 2*l**3/3 - 2*l**2 - 4972*l. Factor n(v).
-4*(v - 1)**2*(3*v + 1)
Let r = 43/429 + 3989/3003. Find n, given that -12/7*n + 2/7*n**2 + r = 0.
1, 5
Suppose 12*k - 1155 + 1107 = 0. Let h(c) be the first derivative of 4/3*c**6 + k*c - 16/3*c**3 - 2*c**4 - 9 + 12/5*c**5 + 0*c**2. Solve h(z) = 0 for z.
-1, 1/2, 1
Let t(a) be the first derivative of 32*a**3/3 + 846*a**2 + 1660*a - 5882. Factor t(d).
4*(d + 1)*(8*d + 415)
Let k be 9 - ((-1508)/(-174) + (-2 - 2)/(-12)). Factor 0 + 8/11*j**2 - 2/11*j**5 + 4/11*j**4 + 14/11*j**3 + k*j.
-2*j**2*(j - 4)*(j + 1)**2/11
Let c(s) be the first derivative of s**3/30 + 531*s**2/20 - 3664. Suppose c(q) = 0. Calculate q.
-531, 0
Let v(p) be the second derivative of p**6/12 + 11*p**5/8 + 25*p**4/4 - 40*p**3/3 - 200*p**2 - 3*p + 246. Factor v(i).
5*(i - 2)*(i + 4)**2*(i + 5)/2
Let j(x) = -420*x**3 - 135*x**2 + 1055*x - 290. Let b(k) = -35*k**3 - 11*k**2 + 88*k - 24. Let c(p) = 35*b(p) - 3*j(p). Let c(g) = 0. Calculate g.
-2, 3/7, 1
Let d(v) = -6*v**3 + 782*v**2 - 8*v - 796. Let s(h) = 4*h**3 - 522*h**2 + 5*h + 531. Let t(o) = 9*d(o) + 14*s(o). Solve t(m) = 0.
-1, 1, 135
Suppose 126*i**2 - 3*i**4 + 60*i**3 + 24*i**3 - 39*i**2 = 0. What is i?
-1, 0, 29
Let t be (-11 - (-102)/12)*(-8)/10. Let 1906*o**t - 1313*o**3 + 1470*o**2 + 5593*o**3 + 100*o**4 + 672*o = 0. Calculate o.
-42, -2/5, 0
Let a(k) = -3*k**3 + k. Let m be a(-1). Factor 2*b**m - 15*b + 351*b + 3*b**2 + 10125 + 114*b.
5*(b + 45)**2
Suppose -2/11*r**5 - 186/11*r**2 + 76/11*r + 0 + 142/11*r**3 - 30/11*r**4 = 0. Calculate r.
-19, 0, 1, 2
Let o = -227 - -134. Let u = 156 + o. Factor -36*s**5 - 20*s**5 - 5*s**3 - 23*s**4 - 19*s**5 + u*s**4.
-5*s**3*(3*s - 1)*(5*s - 1)
Let k = -45 + 49. Suppose -4*t - 120 = -k*w + t, 5*t - 90 = -3*w. Solve w*a - 84*a**3 - 170 + 165 - 76*a**3 = 0.
-1/2, 1/4
Let m(s) be the first derivative of 54/5*s + 172 - 18/5*s**2 + 2/5*s**3. Factor m(a).
6*(a - 3)**2/5
Let c(b) be the first derivative of b**6/360 + 11*b**5/30 + 121*b**4/6 + b**3/3 + 7*b**2/2 - 20. Let f(v) be the third derivative of c(v). Factor f(a).
(a + 22)**2
Let b(f) be the third derivative of 239*f**6/40 - f**5/20 - 239*f**4/8 + f**3/2 - 7746*f**2. Determine n so that b(n) = 0.
-1, 1/239, 1
Find o, given that -3/8*o**2 - 27018003/8 - 9003/4*o = 0.
-3001
Let l = -68 + 100. Suppose -2*w + 0*w + z + 29 = 0, 2*w + 2*z = l. Factor -w*b**4 + 10*b**2 + 3*b**5 + 4*b**3 - 19*b**2 + 17*b**3.
3*b**2*(b - 3)*(b - 1)**2
Suppose -5*b - 171883*l - 70 = -171887*l, -3*b = -3*l + 54. Factor -2*y**3 - 5/2*y - 1 + 11/2*y**b.
-(y - 2)*(y - 1)*(4*y + 1)/2
Let j(q) = 10*q**4 + 1440*q**3 - 465*q**2 - 960*q + 5. Let k(n) = 11*n**4 + 1439*n**3 - 470*n**2 - 960*n + 4. Let f(u) = 4*j(u) - 5*k(u). Solve f(a) = 0.
-96, -2/3, 0, 1
Suppose 0*r = i - 3*r - 16, -4*r = -2*i + 24. Solve -74*v**3 - 30*v**i + 8 + 52*v - 74*v**3 + 36*v**2 + 94*v**4 - 12*v**3 = 0 for v.
-1/4, 1, 2
Suppose 27*k = 5849 - 5201. Factor 0*x**2 + 3/2*x**3 + k - 18*x.
3*(x - 2)**2*(x + 4)/2
Suppose w = s + 3, 4*s - 1 - 29 = -3*w. Let l(x) be the second derivative of -2/3*x**2 + 2/9*x**4 - 16*x - 7/9*x**s + 0. Factor l(o).
2*(o - 2)*(4*o + 1)/3
Let j(p) be the second derivative of -3*p**5/40 + 501*p**4/8 - 15750*p**3 + 46875*p**2 - 109*p - 2. Find x such that j(x) = 0.
1, 250
Let q(z) be the second derivative of -z**4/24 - 101*z**3/12 - 25*z**2 - 76*z + 7. Factor q(k).
-(k + 1)*(k + 100)/2
Let q(g) be the first derivative of 0*g + 3/2*g**2 + 0*g**3 - 3/4*g**4 + 15. Factor q(d).
-3*d*(d - 1)*(d + 1)
Let i(h) be the third derivative of h**5/240 - 59*h**4/96 - 5*h**3/2 + h**2 - 332. Factor i(o).
(o - 60)*(o + 1)/4
Suppose -25 = -22*j - 3. Let y be j*((-9)/3 + (-154)/(-28)). Factor 3/2*m**2 + 9/2*m - 1/2*m**3 + y.
-(m - 5)*(m + 1)**2/2
Let k(t) = 27*t - 16. Let i be (-90)/60*(8/(-2))/1. Let w be k(i). Factor 96*r + w*r**2 - 15 + 6*r**3 + 2*r**5 - 18*r**4 + 195*r - 99*r + 87.
2*(r - 6)**2*(r + 1)**3
Let l(w) = 2*w**3 - 9*w**2 - 18. Let r be l(5). Solve -4*j**2 + r*j**3 - 54*j + 54 - 8*j**2 - 9*j**3 + 30*j**2 = 0 for j.
3
Let c be ((-17)/(-51))/((-2)/(-12)). What is l in 4*l - 20*l**2 + 12*l**2 + 4*l**3 + 16*l**c = 0?
-1, 0
Let p(v) be the third derivative of v**5/30 + 67*v**4/6 + 4489*v**3/3 + 6797*v**2. Factor p(c).
2*(c + 67)**2
Let k(j) be the second derivative of -35*j - 8/63*j**7 + 24*j**2 - 32/45*j**6 - 1/3*j**5 + 56/3*j**3 + 55/9*j**4 - 1. Suppose k(r) = 0. Calculate r.
-2, -3/2, -1, 2
Suppose 0 = 4*f - 14 + 2. Factor 5*o**3 - 24*o**2 + o - 7*o - f*o - 14*o**3 + 6*o**4.
3*o*(o - 3)*(o + 1)*(2*o + 1)
Let b(c) = 15*c + 5. Let v be b(-1). Let f be ((-4)/10*-3)/((-4)/v). Factor 9 - 12*a**2 + f*a - 3 + 9*a**2.
-3*(a - 2)*(a + 1)
Let n = 419/5 - 1537/15. Let x = n - -20. Solve 0*r**2 + 0*r + 2/3*r**3 - x*r**4 + 2/3*r**5 + 0 = 0.
0, 1
Suppose -p + 196 = 3*p + 2*y, 4*y = 2*p - 98. Let d = 52 - p. Factor 13*f**2 - 5*f**3 + f**d - 6*f**2 + 8*f - 11*f**2.
-4*f*(f - 1)*(f + 2)
Suppose 5*m - q - 37 = 473, 5*q = 4*m - 387. Let f = -308/3 + m. Find z such that -1/3 + 1/3*z**2 - f*z**3 + 1/3*z = 0.
-1, 1
Let w(q) = -17*q**3 - q**2 + q. Suppose 7*m = 2*m - 5. Let h be w(m). Factor -5 - 4 - 3*x**2 - 3 + h*x.
-3*(x - 4)*(x - 1)
Suppose 4*g = -5*s + 8, -3*g + 6 = 22*s - 20*s. Let t(h) be the first derivative of -1 - 3/4*h**4 + 4*h**3 - 9/2*h**2 + s*h. Factor t(i).
-3*i*(i - 3)*(i - 1)
Factor 4/17*q**3 + 42848/17*q + 21632/17 - 830/17*q**2.
2*(q - 104)**2*(2*q + 1)/17
Let z be (56/(-70))/(3/((-1155)/(-2))). Let a = 156 + z. Factor -10/13*b - 20/13*b**3 + 20/13*b**a + 2/13 - 2/13*b**5 + 10/13*b**4.
-2*(b - 1)**5/13
Let a be (6 + 1 - 1)*(-896)/(-168). Factor -a - 390*z - 4*z**2 + 174*z + 180*z.
-4*(z + 1)*(z + 8)
Let c(p) be the second derivative of 5*p**4/12 - 175*p**3/2 - 1090*p**2 + p + 914. Determine d so that c(d) = 0.
-4, 109
Let v be 0/((-1)/1) + 8/4. Let p(y) = -2*y**4 + 16*y**3 - 20*y**2. Let s(d) = -d**2. Let f(g) = v*p(g) - 12*s(g). Factor f(n).
-4*n**2*(n - 7)*(n - 1)
Suppose -34579*x = -34638*x + 1652. Factor 392 + 1/2*o**2 - x*o.
(o - 28)**2/2
Suppose -150 = r - 74. Let s = r + 78. Factor q - 5/4 + 1/4*q**s.
(q - 1)*(q + 5)/4
Let t be (-1219)/(-184)*-1 + (-1)/(-2)*14. Suppose 3/8*c**3 + 3/8*c - 1/4*c**5 + 0 - 7/8*c**2 + t*c**4 = 0. Calculate c.
-3/2, 0, 1
Let l(g) be the first derivative of -g**3/9 - 3295*g**2/3 - 10857025*g/3 + 9248. Suppose l(q) = 0. What is q?
-3295
Let c(a) = a**2 + 12*a + 29. Let z be c(-9). Suppose 116*b - 72*b = 0. Factor -2/3*k + b - k**z - 1/3*k**3.
-k*(k + 1)*(k + 2)/3
Let q(b) = 2*b**2 - 17*b + 39. Let a be q(4). Suppose -3 = -r - 2*k + a, -2*k = 4*r - 6. Factor 2*w**3 - 5/4*w**4 + 0*w - w**2 + r + 1/4*w**5.
w**2*(w - 2)**2*(w - 1)/4
Let b(k) be the first derivative of -k**3/9 - 376*k**2/3 - 3609. Factor b(a).
-a*(a + 752)/3
Solve -12*