
Let s(w) be the first derivative of -1/6*w**3 + 110 + 5/2*w**2 - 9/2*w. Factor s(x).
-(x - 9)*(x - 1)/2
Suppose 0 = 2*s + g - 326, 3*g = 4*s - 2*g - 666. Suppose 2*n = -136 + s. Factor 10*i**4 - 15*i**5 - 8*i**4 - 2*i**2 + n*i**5 + i.
-i*(i - 1)**3*(i + 1)
Let w(b) be the second derivative of -b**4/2 - 1571*b**3/2 - 2355*b**2/2 - 3035*b + 2. Determine f so that w(f) = 0.
-785, -1/2
Let g = -6572/3 + 2192. Suppose 2*f = 3*y + 19, -5*f - 2*y - 16 = -8*f. Factor -g*j**3 + 0 + 0*j - 8/3*j**f + 4/3*j**4.
4*j**2*(j - 2)*(j + 1)/3
Let x be (-58)/(-145) + -2 + 7623/4755. Let r = 955/1268 - x. Determine t so that r*t**5 - 5/4*t**4 - 1/2*t**3 - 1/4 - 1/4*t + 3/2*t**2 = 0.
-1, -1/3, 1
Let a(t) be the second derivative of t**6/80 - 3*t**5/32 - 7*t**4/2 + 44*t**3 - 11*t - 24. Find o, given that a(o) = 0.
-11, 0, 8
Factor -112/25 + 52/25*k + 2/25*k**2.
2*(k - 2)*(k + 28)/25
Suppose 4*c + 31265*f - 14 = 31270*f, -2*c = -f - 22. Solve 10/3*p + 2/3*p**2 - c = 0.
-8, 3
Find t such that 1944*t**2 + 100*t**5 + 592*t**3 - 1308*t**3 - 78 - 179*t**4 - 18 - 552*t - 488*t - 13*t**4 = 0.
-3, -2/25, 1, 2
Find i, given that 119 + 7*i - 141*i + 5*i**4 - 156*i + 81 - 25*i**2 - 25137*i**5 + 25132*i**5 + 115*i**3 = 0.
-4, -2, 1, 5
What is c in -179361*c**2 + 4*c**5 + 256*c**4 + 194613*c**2 - 9856 - 6048*c - 3366 - 2330 + 44*c**4 + 6044*c**3 = 0?
-36, -3, -1, 1
Let v be 3 - (0 + 3) - (9 + -14). Factor v + 2 + 1 - 4256*a**2 + 4254*a**2.
-2*(a - 2)*(a + 2)
Let y(w) = 10*w**2 + 7*w - 11*w**2 + 8*w + 8. Let l(v) = -v + 1. Let o(p) = 4*l(p) + y(p). Suppose o(k) = 0. Calculate k.
-1, 12
Suppose 8*u - 7*u = 0. Suppose u = -203*i + 202*i + 4. Solve 1/3*m**i - 1/3*m**3 - 2/3*m**2 + 0 + 0*m = 0.
-1, 0, 2
Let h be (((-9)/(-315))/((-29)/232))/(0 - (-4)/(-10)). Suppose 8/7*y**2 + 12/7 - 26/7*y + 12/7*y**3 - h*y**4 - 2/7*y**5 = 0. What is y?
-3, -2, 1
Let z(x) be the first derivative of -x**6/75 + x**4/6 - 4*x**2/5 - 24*x - 27. Let w(l) be the first derivative of z(l). Suppose w(a) = 0. What is a?
-2, -1, 1, 2
Let y be 15/((-4)/(-120)*25). Let n be y/(-7) + 3 + 99/945. Factor n*j - 2/5 - 2/15*j**2.
-2*(j - 3)*(j - 1)/15
Let q(h) be the first derivative of -h**5/40 - h**4/24 + h**3/12 + 10*h**2 - h - 2. Let k(x) be the second derivative of q(x). Determine a, given that k(a) = 0.
-1, 1/3
Let b(s) be the first derivative of 77*s**3 - 3/4*s**4 + 237*s + 471/2*s**2 + 255. Find h such that b(h) = 0.
-1, 79
Let 548800/9 + 37408/9*l**2 + 124/9*l**4 + 227360/9*l + 2/9*l**5 + 3056/9*l**3 = 0. What is l?
-14, -10
Suppose -4*k + 43 = 31. Suppose -2*y = -k*g + 1, 6*g - 1 = 11*g - 4*y. What is b in 0*b**2 - 2/7*b**g + 2/7*b + 0 = 0?
-1, 0, 1
Suppose -9451 = -52*s + 6461. Let t be (-4)/26 + s/468. Factor 3/2*o**2 - 1/2*o**4 - t*o + 1/2*o**3 - 1.
-(o - 2)*(o - 1)*(o + 1)**2/2
Let v(s) be the second derivative of -s**6/90 - s**5/30 + 4*s**4/3 + 112*s**3/9 + 128*s**2/3 - 168*s + 3. Determine u so that v(u) = 0.
-4, -2, 8
Let k = 429 - 430. Let x be 0 - (k/3 + 170/(-102)). Find j, given that -9/4*j + 5/4*j**x + 1 = 0.
4/5, 1
Let x = 230 - 216. Solve 3*t**3 - 79*t**2 + x*t + 67*t**2 - 2*t = 0 for t.
0, 2
Let q = 735 + -739. Let y(a) = -3*a**4 - 39*a**3 - 132*a**2 - 87*a. Let f(w) = w**4 + 19*w**3 + 66*w**2 + 44*w. Let h(x) = q*y(x) - 9*f(x). Factor h(u).
3*u*(u - 8)*(u + 1)*(u + 2)
Let j(a) be the first derivative of -a**4/30 - 814*a**3/15 + 163*a**2 - 2446*a/15 + 3754. Find x such that j(x) = 0.
-1223, 1
Let i(k) = 33*k**2 - 313*k + 698. Let u(f) = 2*f**2 + 2*f. Let o(p) = -3*i(p) + 51*u(p). Factor o(g).
3*(g - 2)*(g + 349)
Suppose -109*k = -16*k - 186. Let r(q) be the third derivative of -1/60*q**5 + 0*q + 0 + 0*q**4 + 0*q**3 - q**k + 1/120*q**6. Factor r(a).
a**2*(a - 1)
Let c(g) be the first derivative of -g**5/120 + g**4/24 + g**2 + 16*g - 60. Let i(o) be the second derivative of c(o). Factor i(p).
-p*(p - 2)/2
Find t, given that -32*t**3 + 1001157*t**4 - 1001157*t**4 + 30*t**2 - 30 + 31*t + t**5 = 0.
-6, -1, 1, 5
Find o, given that 57/7*o**2 + 12/7*o - 12/7*o**5 + 24/7*o**4 + 81/7*o**3 + 0 = 0.
-1, -1/2, 0, 4
Let o be (-7)/84 + (0 - (9 + 185/(-20))). Determine i, given that 0*i + o*i**2 + 0 = 0.
0
Let v(r) = -22*r**4 + 188*r**3 - 488*r**2 - 78*r - 60. Let g(x) = -x**4 + x**3 + x**2 + x - 6. Let i(f) = -10*g(f) + v(f). Let i(j) = 0. Calculate j.
-1/6, 0, 4, 11
Let z = 1854431 + -9272107/5. Suppose 5*m + 2*s + 2 = 16, -3*m + s + 4 = 0. Suppose -2/5*n**3 - z*n**m - 2/5*n**5 + 0 - 32/5*n + 12/5*n**4 = 0. What is n?
-1, 0, 4
Let w(t) be the first derivative of 1/30*t**6 + 3*t**4 + 10/3*t**3 + 0*t - 25/2*t**2 + 60 + 14/25*t**5. Solve w(g) = 0 for g.
-5, 0, 1
Suppose 191 = 72*n - 169. Determine g, given that 0 + 10*g**3 - 2*g**4 - 34/3*g**2 - 2/3*g**n + 4*g = 0.
-6, 0, 1
Let x = 17735/11 - 124035/77. Factor 12/7*b + 2/7*b**2 + x.
2*(b + 1)*(b + 5)/7
Let t = 120286/55121 - 2/5011. Let c = 173/44 - t. Suppose c*q + 3/2 - 3/4*q**2 = 0. Calculate q.
-2/3, 3
Let s be (-2)/4*(-13)/(39/6). Let q be 1/(-3) + 8/15*s. Suppose -2/5 + 1/5*y**2 - q*y = 0. What is y?
-1, 2
Let d(z) = 5*z**3 + 11*z**2 + 2*z. Let h be d(0). Determine i so that h + 1/5*i**4 + 0*i**2 + 0*i + 1/5*i**3 = 0.
-1, 0
Let a = 7468204/5 + -1493631. Factor 14/5*k + 1/5*k**2 + a.
(k + 7)**2/5
Let -8 - 32/5*b**2 - 76/5*b + 4/5*b**3 = 0. Calculate b.
-1, 10
Suppose 16 = 8*u - 0*u. Suppose 180 + 28 + 375*h + 92 - 9*h**2 + 4*h**u + 80 = 0. Calculate h.
-1, 76
Suppose -17 = -12*c + 13*c + 5*n, -7 = -c + n. Determine f, given that 23*f + f**4 - 7*f - 10*f**3 - c*f**4 - 4*f**2 = 0.
-4, -2, 0, 1
Let c(b) = -69*b**2 - 701*b - 46. Let i(a) = -11*a**2 - a + 2. Let d(z) = c(z) - i(z). Factor d(p).
-2*(p + 12)*(29*p + 2)
Let g(w) be the first derivative of -w**6/6 - w**5/4 + 5*w**4/4 + 5*w**3/6 - 5*w**2 - 112*w - 271. Let n(r) be the first derivative of g(r). Solve n(h) = 0.
-2, -1, 1
Let q(h) be the second derivative of -h**7/14 + 38*h**6 + 9879*h. Factor q(i).
-3*i**4*(i - 380)
Suppose 46*m = -49*m. Let c(f) be the third derivative of 0*f**6 - f**2 + 0*f**4 + 0*f + 0*f**3 - 1/1365*f**7 + 0 + m*f**5. Factor c(u).
-2*u**4/13
Suppose 71*u + 2 = 70*u. Let b be 3634/(-632) - 12/u. Factor 0 + 3*f**2 - 13/4*f**3 + 3/2*f**4 - f - b*f**5.
-f*(f - 2)**2*(f - 1)**2/4
Suppose 0 = 6*x - 5*x, 0 = 3*k + 4*x - 1356. Find y, given that -640*y**2 - 360*y**5 + 1125*y**4 - 80 - 265*y**5 + 248*y**3 + k*y**3 + 32*y - 512*y = 0.
-2/5, 1, 2
Factor -6*b**2 + 6*b**2 - 6*b**2 + 1320 + 757*b + 2*b**2 + 559*b.
-4*(b - 330)*(b + 1)
Let o be 76/133*322/920. Factor -o*b**2 - 2/5*b + 0.
-b*(b + 2)/5
Let h(n) be the second derivative of 0*n**3 - 4/15*n**6 - 1 + 3*n**4 - 15*n + 0*n**2 + 3/10*n**5 - 1/21*n**7. What is y in h(y) = 0?
-3, 0, 2
Let z(s) be the second derivative of 11/42*s**4 - 9 + 1/10*s**5 + 2/21*s**3 - 11/105*s**6 - 3/49*s**7 + s + 0*s**2. Solve z(m) = 0.
-1, -2/9, 0, 1
Let x = -4124 + 11897. Let s = x - 54168/7. Factor -s*u**5 + 12/7*u**2 + 0 - 120/7*u**3 + 0*u + 351/7*u**4.
-3*u**2*(u - 1)*(9*u - 2)**2/7
Suppose -13*c + 8*c = -6*c + 4. Let f(w) be the third derivative of 0 + 0*w**3 - 1/300*w**6 + 0*w**5 - 10*w**2 + 0*w**c + 0*w. Find o, given that f(o) = 0.
0
Let p be (-1)/3*(-126)/(-12). Let d = 95/26 + p. Find f such that d*f + 2/13*f**3 + 4/13*f**2 + 0 = 0.
-1, 0
Let a(b) = 3*b - 44. Let k(h) = -5*h + 89. Let g(f) = -5*a(f) - 2*k(f). Let s be g(8). Determine r so that 4*r**s + 16 - 9*r - 25*r + 0*r + 14*r = 0.
1, 4
Let j be 6/8 + 30/16*6/9. Let o(y) be the first derivative of -39/16*y**4 - 9/20*y**5 - 13/4*y**3 - 9/8*y**j - 2 + 0*y. Let o(q) = 0. Calculate q.
-3, -1, -1/3, 0
Let v be (48/40)/(4/(-1022)*1). Let w = v + 307. Factor 0 - w*d**4 - 2/5*d**3 + 2/5*d + 2/5*d**2.
-2*d*(d - 1)*(d + 1)**2/5
Let i(z) be the second derivative of z**4/42 - 40*z**3/21 - 129*z**2/7 + 1482*z - 2. Solve i(w) = 0 for w.
-3, 43
Find a, given that -4594/5 + 4596/5*a - 2/5*a**2 = 0.
1, 2297
Suppose 6*i + 12 = -0*i. Let o be (-49)/i - ((-5)/2)/5. Find w such that 4 + 5*w**3 + 4*w**2 - o*w + 6 + w**2 + 5 = 0.
-3, 1
Let m be 141/12 - ((-477)/(-9) - 43). Let m*j**4 + 1/4*j**5 + 7/4*j**3 - 19/4*j**2 + 5 - 4*j = 0. Calculate j.
-5, -2, 1
Let v(t) be the second derivative of -49*t**4/2 + 3*t**3/2 + 2*t - 9650. Find x, given that v(x) = 0.
0, 3/98
Let y(d) = -132*d**2 + 117*d - 84. Let x(c) = c**3 - 133