2/15 + 2/15*t**n - 4/15*t**3 = 0.
-1, 1
Let p(m) be the third derivative of 5*m**6/8 + 89*m**5/4 + 273*m**4 + 882*m**3 + 9*m**2 - 103. Factor p(q).
3*(q + 1)*(5*q + 42)**2
Factor 52*c - 1/4*c**3 + 112 + 5*c**2.
-(c - 28)*(c + 4)**2/4
Let h(f) = 439*f - 8339. Let y be h(19). Factor 10 + 16/3*o + 2/3*o**y.
2*(o + 3)*(o + 5)/3
Let h(i) be the first derivative of -2*i**3/9 - 126*i**2 + 762*i - 8471. Factor h(u).
-2*(u - 3)*(u + 381)/3
Factor 242172 - 744*o + 4/7*o**2.
4*(o - 651)**2/7
Let p(m) = -20*m + 445. Let j be p(22). Let r(i) be the first derivative of 24*i**2 - 588*i**j + 504*i**4 + 343/2*i**6 - 15 + 0*i - 176*i**3. Factor r(c).
3*c*(c - 2)*(7*c - 2)**3
Let p = 258 + -252. Let h(j) = 3*j**2 + 210*j - 3267. Let g(z) = 5*z**2 + 418*z - 6534. Let l(v) = p*g(v) - 11*h(v). Factor l(b).
-3*(b - 33)**2
Find a such that -844*a + 203 - 12*a**2 + 495 + 1088 - 1476*a - 234 = 0.
-194, 2/3
Factor -1/3*c**2 - 16834609/3 - 8206/3*c.
-(c + 4103)**2/3
Factor 617 + 21123216*b - 1232 + 4*b**3 - 239*b**2 - 18145*b**2 + 615.
4*b*(b - 2298)**2
Suppose -4*l = -p - 5, -p = 4*p - 15. Let c = 108238 - 541188/5. Factor c*q**l + 6/5*q + 0.
2*q*(q + 3)/5
Let z = 427 - 435. Let k be (10 + -6)*(-4)/z. Suppose -2/11*j**3 - 216/11*j + 432/11 + 36/11*j**k = 0. Calculate j.
6
Suppose -11*o + 10*o + 15 = 0. Let u(m) = 2*m - 27. Let a be u(o). Factor 9*g**3 - 15*g - 4 + 4*g**2 + 2*g**3 + g + 3*g**a.
2*(g - 1)*(g + 1)*(7*g + 2)
Suppose 60 = 2*n + 3*k + 26, -5*k + 54 = 2*n. Let -3/2*t**n - 75/2 + 15*t = 0. What is t?
5
Let u = 2/1945 + 377/11670. Let k(f) be the second derivative of -1/6*f**4 - 12*f + 0*f**5 + 0 + 1/2*f**2 + 0*f**3 + u*f**6. Factor k(q).
(q - 1)**2*(q + 1)**2
Let n(v) be the third derivative of 1/210*v**7 + 0*v - 1/30*v**6 + 3/2*v**3 - 1/30*v**5 + 22*v**2 + 1/2*v**4 + 0. Solve n(k) = 0.
-1, 3
Let s(v) = 23 + 43*v + 50 - 5*v**2 + 0*v**2 - 103. Let x(n) = -3*n**2 + 28*n - 20. Let y(i) = -5*s(i) + 8*x(i). Factor y(f).
(f - 1)*(f + 10)
Factor 1/3*b**3 + 7/3 + 5*b + 3*b**2.
(b + 1)**2*(b + 7)/3
Determine v so that 0 + 0*v**3 - 4/7*v**2 + 2/7*v**5 + 4/7*v**4 - 2/7*v = 0.
-1, 0, 1
Suppose -43*i - 5*j + 2 = -39*i, -11 = -5*i - 2*j. Factor 7*v**2 + 3330 - 2979 + 2829 - 312*v - i*v**2 + 2904.
4*(v - 39)**2
Let t(f) = 8*f**3 + 48*f**2 + 156*f + 44. Let u(h) = 7*h**3 + 49*h**2 + 147*h + 45. Let s(a) = 5*t(a) - 6*u(a). Factor s(j).
-2*(j + 1)**2*(j + 25)
Let w(u) = -u**2 + 5. Let i(p) = 5510*p - 1518030. Let l(s) = i(s) + 5*w(s). Solve l(x) = 0.
551
Let o(y) be the first derivative of -y**8/2520 - y**7/630 + y**3 + 25*y**2/2 + 118. Let v(z) be the third derivative of o(z). Factor v(g).
-2*g**3*(g + 2)/3
Determine b so that 38 + 22 + 925*b**3 + 32*b + 3*b**4 - 476*b**3 - 479*b**3 + 99*b**2 - 164*b = 0.
1, 2, 5
Let j(w) = -31*w**3 + 63*w**2 + 72*w. Let g(o) = o**4 + 32*o**3 - 63*o**2 - 102*o. Let z(d) = -3*g(d) - 4*j(d). Factor z(v).
-v*(v - 6)*(v - 3)*(3*v - 1)
Let o(p) be the third derivative of -p**6/480 + p**5/40 + p**4/96 - p**3/4 - 30*p**2 - 5*p. Solve o(c) = 0.
-1, 1, 6
Suppose 5*g + 12 = -23. Let w(k) = -k**2 - 6*k + 9. Let o be w(g). Solve -c**5 + 4*c**2 - 2*c**4 - 2*c**o + 0*c**2 + c**3 + 0*c**3 = 0 for c.
-2, -1, 0, 1
Let b = 2881/590 - 998/295. Determine d, given that 1/2*d**3 - 1/2*d - 1/2*d**4 + b*d**2 - 1 = 0.
-1, 1, 2
Suppose 0 = -10*y - 12 + 22. Factor y + u**4 - 1 + 496*u**3 - 495*u**3.
u**3*(u + 1)
Let s be (-87)/45 - -2 - -518*(-5)/(-1650). Factor 2/11*f**3 + s*f**2 - 18/11 - 2/11*f.
2*(f - 1)*(f + 1)*(f + 9)/11
Suppose -8478*b + 258 = -8349*b. Solve -3/2*z**b - 78 + 42*z = 0 for z.
2, 26
Let i(b) = -35*b**2 + 4490*b - 82115. Let a(c) = 3*c**2 - 374*c + 6843. Let t = -48 + 50. Let g(o) = t*i(o) + 25*a(o). Determine j, given that g(j) = 0.
37
Let g = 69121 - 69119. Factor -4/3 - 2/3*u + u**g + 1/6*u**4 + 5/6*u**3.
(u - 1)*(u + 2)**3/6
Let d(w) be the second derivative of w**4/6 - 307*w**3/3 - 308*w**2 - 1089*w - 2. Factor d(l).
2*(l - 308)*(l + 1)
Let g be 2/4*3 - (29/(-46) - 4299/(-32959)). Factor 100/3*f - 2500/3 - 1/3*f**g.
-(f - 50)**2/3
Let d(o) be the second derivative of 1/2*o**4 + 25/2*o**2 - 2/5*o**5 + 20/3*o**3 - 2 - 153*o + 1/30*o**6. Solve d(z) = 0.
-1, 5
Let h(r) be the first derivative of -5/2*r**4 + 1/4*r**5 - 15*r**2 + 8*r + 26 + 55/6*r**3. Let v(w) be the first derivative of h(w). Factor v(q).
5*(q - 3)*(q - 2)*(q - 1)
Let i(x) be the third derivative of -x + 37/54*x**4 + 22*x**2 - 1369/27*x**3 - 1/270*x**5 + 0. Suppose i(b) = 0. What is b?
37
Let u be 11 + ((-21583)/3955 - (-24)/(-21)). Solve -4*t - 2/5*t**3 - u*t**2 + 0 = 0.
-10, -1, 0
Let d(s) be the first derivative of -s**7/420 + 13*s**6/60 - 6*s**5 - 100*s**4/3 + 53*s**3/3 + 2*s + 74. Let k(h) be the third derivative of d(h). Factor k(o).
-2*(o - 20)**2*(o + 1)
Let a(x) = 9*x**2 + 22*x - 7. Let i be a(-4). Find l, given that -32*l - i*l - 16 + 29*l - 12*l**2 = 0.
-4, -1/3
Let d(r) be the first derivative of -4*r**3 + 17/10*r**4 + 12/5*r**2 - 107 - 6/25*r**5 + 16/5*r. Factor d(n).
-2*(n - 2)**3*(3*n + 1)/5
Let w = 8929/18010 - -38/9005. Factor w - 1/4*u**3 - 1/2*u**2 + 1/4*u.
-(u - 1)*(u + 1)*(u + 2)/4
Let t(l) = -675*l**3 - 5*l - 24. Let u be t(-4). Factor 4*c**3 + 20*c**2 + 0*c**3 - 4*c + 43176 - u.
4*(c - 1)*(c + 1)*(c + 5)
Let x(i) be the third derivative of i**7/840 + i**6/160 - i**5/24 - 5572*i**2. Solve x(f) = 0.
-5, 0, 2
Let y(w) be the first derivative of 1/2*w**4 - 2/3*w**3 - 40*w + 127 - 16*w**2. Factor y(i).
2*(i - 5)*(i + 2)**2
Let t be 3/(-16)*(-472)/177. Let w(d) be the second derivative of 0 - 2*d - 1/30*d**6 - 1/10*d**5 - t*d**2 + 1/6*d**4 + 1/42*d**7 + 1/6*d**3. Factor w(a).
(a - 1)**3*(a + 1)**2
Let t be (-106)/(-6) + (-3 - -2). Let p = -1202380 - -1202384. Determine n so that 0 - 4*n - t*n**p + 38/3*n**3 - 50/3*n**5 + 26/3*n**2 = 0.
-1, 0, 2/5, 3/5
Let m(s) be the first derivative of -s**4/4 - 4*s**3 + 4*s**2 - 10*s + 61. Let t(a) = -6*a**2 + 4*a - 4. Let v(j) = -2*m(j) + 5*t(j). Let v(i) = 0. Calculate i.
0, 1, 2
Factor -207/5*o + 108/5*o**2 - 3/5*o**3 + 102/5.
-3*(o - 34)*(o - 1)**2/5
Let b(d) be the second derivative of 8/5*d**2 - 1/50*d**5 - 4*d + 21 + d**3 + 1/5*d**4. Factor b(h).
-2*(h - 8)*(h + 1)**2/5
Suppose -18 = 3*n - 300. Suppose 3*r - 70 = -y + n, -2*y = r - 58. Factor 21*g**2 + 4 - g**3 - r*g**2 + 4*g + 18*g**2 + 14*g**2.
-(g - 2)*(g + 1)*(g + 2)
Suppose 2*c - 6 = 0, -4*h - 5*c - 952 = 1061. Let f = -507 - h. Let 0 - 3/4*n**5 + f*n**2 + 3/2*n**3 + 0*n - 3/4*n**4 = 0. Calculate n.
-2, 0, 1
Let h = 54451/9 - 6050. Let o(k) be the first derivative of -1/3*k**2 - h*k**3 - 24 - 1/3*k. Let o(w) = 0. Calculate w.
-1
Suppose -5*s = -s + 3*f - 23, 5*s + 3*f = 25. Suppose x - 7 = -i - s*i, 3*x = -15. What is z in 2*z**i + 0*z + 0 + 2/3*z**3 + 0*z**2 = 0?
-1/3, 0
Let d = 7109/17385 - 31/3477. Let w be ((1 - -1) + -2)/1. Solve 0*t**3 + 3/5*t**2 + w + d*t - 1/5*t**4 = 0 for t.
-1, 0, 2
Find r, given that -3594/5 + 3/5*r**2 - 1791/5*r = 0.
-2, 599
Let b(q) be the second derivative of q**4/4 - 173*q**3 - 3141*q**2/2 - 6*q + 188. Factor b(x).
3*(x - 349)*(x + 3)
Let o(s) be the third derivative of s**8/168 + s**7/15 + 13*s**6/60 - s**5/10 - 3*s**4/2 - 3*s**2 + 34. Factor o(c).
2*c*(c - 1)*(c + 2)*(c + 3)**2
Let p(j) be the first derivative of -5*j**3/6 + 525*j**2/4 + 1090*j - 1342. Factor p(w).
-5*(w - 109)*(w + 4)/2
Let o(n) = 6*n + 50. Let t be o(-8). Factor -33*j**2 + 8 + 116*j**2 - 79*j**t - 12*j.
4*(j - 2)*(j - 1)
Suppose -786 = -m - n, -5*m - 4*n + 0*n = -3935. Let p = m - 3953/5. Solve -4/5 + 2/5*i + p*i**2 = 0.
-2, 1
Let u = 67924 - 475452/7. Factor -4/7*s - u + 2/7*s**2.
2*(s - 4)*(s + 2)/7
Let u be 337 + (-1 + 19/10)/((11277/42)/(-179)). Determine n, given that -1566/5*n + 114/5*n**2 - u - 2/5*n**3 = 0.
-1, 29
Let w(p) be the third derivative of p**6/120 + p**5/4 - 17*p**4/12 - 4921*p**2. Suppose w(f) = 0. What is f?
-17, 0, 2
Solve 6455*z**2 - 2 + 2 + 4*z**3 - 6607*z**2 = 0.
0, 38
Solve 1/4*o**2 + 47 - 51/4*o = 0.
4, 47
Solve 183*s**2 - 702*s + 1/3*s**4 - 44/3*s**3 + 0 = 0.
0, 9, 26
Let m(p) be the third derivative of -p**9/105840 + p**5/30 - 13*p**3/3 + 62*p**2. Let r(z) be the third derivative of m(z). Solve r(o) = 0.
0
Let p(g) be the first derivative of g**3/2 - 129*g**2 + 513*g/2 - 826. Factor p(k).
3*(k - 171)*(k - 1)/2
Let q be 59/(5310/440)*30/