
0, 1, 3
Suppose 2*r = 11 - 3. Let k be (-1)/4 - (-13)/r. Factor -8*q**4 + 7*q**2 - 4*q**5 + k*q**2 + 12*q**2 + 4*q - 14*q**2.
-4*q*(q - 1)*(q + 1)**3
Factor -3112026/5*u**2 - 1058086804/5*u - 611*u**3 - 1054977832/5 - 1/5*u**4.
-(u + 1)*(u + 1018)**3/5
Let v(w) = -13*w**2 - 1742*w + 2013. Let r(d) = 55*d**2 + 7840*d - 9060. Let s(g) = -9*r(g) - 40*v(g). Find a, given that s(a) = 0.
6/5, 34
Let t(o) be the second derivative of -31*o**4/4 - 30*o**3 + 6*o**2 + 1989*o. Determine w so that t(w) = 0.
-2, 2/31
Factor 74 - 299/3*a + 26*a**2 - 1/3*a**3.
-(a - 74)*(a - 3)*(a - 1)/3
Let r(l) be the first derivative of 36*l + 12*l**2 + 4/3*l**3 + 20. Let r(t) = 0. Calculate t.
-3
Let j(b) be the second derivative of -b**5/120 - 239*b**4/8 + b**3/36 + 717*b**2/4 - 7020*b. Let j(f) = 0. What is f?
-2151, -1, 1
Factor 3/2*h**3 - 2096/3*h**2 + 54289/3 + 487669/6*h.
(h - 233)**2*(9*h + 2)/6
Let d be 49/88 + 330/34485*-19. Find m, given that 9/4 + d*m**3 + 33/8*m + 9/4*m**2 = 0.
-3, -2, -1
Solve 846/7 - 844/7*t + 2/7*t**4 + 844/7*t**3 - 848/7*t**2 = 0 for t.
-423, -1, 1
Let a = -4 + 3. Let b(p) = p**3. Let o(x) = -12*x**3 + 36*x**2 - 16*x. Let w(r) = -7*r + 3. Let c be w(1). Let g(z) = a*o(z) + c*b(z). Factor g(t).
4*t*(t - 4)*(2*t - 1)
Let q be (-9 + 7)/(2 - 10/4). Solve 135 + 7*f**4 + 40*f**3 - 4*f**4 - 14*f**4 + 6*f**q - 90*f**2 = 0.
-1, 3
Let f(k) be the first derivative of k**6/27 - 8*k**5/5 + 193*k**4/9 - 1040*k**3/27 - 2873*k**2/3 + 17576*k/9 - 3569. Suppose f(i) = 0. Calculate i.
-4, 1, 13
Let w be (-3)/2 - 6501/(-1182). Let j(c) be the second derivative of -2*c**2 + 0 - 5/9*c**3 - 1/18*c**w - 38*c. Factor j(g).
-2*(g + 2)*(g + 3)/3
Let d be 10/(-90) - (-171)/81. Let 6/17*w**5 + 0*w - 8/17*w**3 + 0 + 0*w**d - 8/17*w**4 = 0. What is w?
-2/3, 0, 2
Let n(v) be the third derivative of -v**5/20 + 97*v**4/4 + 591*v**3/2 - 2*v**2 - 2*v - 329. Determine p so that n(p) = 0.
-3, 197
Find s such that 1/2*s**4 + 11/2*s + 1/2*s**3 - 19/2*s**2 + 15 = 0.
-5, -1, 2, 3
Let d(t) be the second derivative of -t**4/15 + 1264*t**3/5 - 1797408*t**2/5 - 34*t + 44. Let d(k) = 0. What is k?
948
Let o(h) be the second derivative of h**8/420 + 4*h**7/105 + 7*h**6/90 - h**3/3 - h**2/2 - 2*h + 15. Let a(l) be the second derivative of o(l). Factor a(y).
4*y**2*(y + 1)*(y + 7)
Let s(k) be the second derivative of k**5/10 + 97*k**4/6 + 190*k**3/3 - 554*k. Find z, given that s(z) = 0.
-95, -2, 0
Suppose -73*x - 9504 = -361*x. Factor x*v - 63/2 - 3/2*v**2.
-3*(v - 21)*(v - 1)/2
Let x(a) = a**3 - 12*a**2 + 4*a - 26. Let m be -2*9/1*8/(-12). Let u be x(m). Factor -18*w + 3*w**2 + 28 + 9 - u.
3*(w - 5)*(w - 1)
Let l = 1831/3 - 609. Factor -2 + l*o**2 + 2/3*o**4 - 8/3*o + 8/3*o**3.
2*(o - 1)*(o + 1)**2*(o + 3)/3
Let k = 3/18616 - 27663391/93080. Let d = -294 - k. Factor 1/5*z**5 - d*z**2 - 2/5 - 6/5*z**4 + 14/5*z**3 + 9/5*z.
(z - 2)*(z - 1)**4/5
Let f(j) be the first derivative of -5*j**3 - 3141*j**2/2 - 1254*j + 5. Determine w, given that f(w) = 0.
-209, -2/5
Let y = -394565 - -394565. Factor 2/3*n**3 - 2/3*n**5 - 2/3*n**4 + y + 2/3*n**2 + 0*n.
-2*n**2*(n - 1)*(n + 1)**2/3
Determine r, given that -622/5*r**3 + 48/5*r**4 + 0 - 529/5*r - 1/5*r**5 + 1104/5*r**2 = 0.
0, 1, 23
Suppose 2*n - 2 = -3*p + 2, 5*n = 2*p + 48. Suppose -5*c + 7 = 2*z, 3*z + 9 = -9*c + n*c. Factor 4/5*x**2 + 0*x - 4/5*x**c + 0.
-4*x**2*(x - 1)/5
Let o(l) be the third derivative of 2*l + 16/3*l**3 + 8/3*l**4 + 8/15*l**5 + 10*l**2 - 1/15*l**6 + 0 - 1/21*l**7 - 1/168*l**8. Determine c so that o(c) = 0.
-2, -1, 2
Let g(x) = -x**3 - x**2 + 3*x - 2. Let s(q) = 4*q**3 - 301*q**2 - 225*q + 14. Let m(b) = -35*g(b) - 5*s(b). Determine o so that m(o) = 0.
-102, -2/3, 0
Let y(j) be the second derivative of 121*j**4/8 + 1463*j**3 + 53067*j**2 - 19*j - 69. Factor y(g).
3*(11*g + 266)**2/2
Suppose -6*d - 166 = 44*d - 121 - 1545. Factor 1350 + 1/6*i**2 + d*i.
(i + 90)**2/6
Let z = 0 + 1/3. Let g = 25301/37956 - -1/12652. Factor -g*b + z*b**2 + 0.
b*(b - 2)/3
Let q(t) be the first derivative of -t**7/28 - 3*t**6/20 + 3*t**5/10 + 7*t + 5. Let p(x) be the first derivative of q(x). Find f, given that p(f) = 0.
-4, 0, 1
Factor 2300*a - 405582*a**3 + 344 + 405583*a**3 - 94*a**2 - 4576.
(a - 46)**2*(a - 2)
Let c = 42700 - 42695. Let n(k) be the first derivative of 0*k**2 - 1/30*k**c - 1/6*k**3 + 0*k - 36 - 1/6*k**4. Solve n(a) = 0.
-3, -1, 0
Let n be (-31)/(-15) + 2/(-3). Let l = 1649862 - 8249301/5. Let -27/5*k**3 + l*k**2 - 27/5*k**4 - 2/5 + n*k = 0. Calculate k.
-1, -2/3, 1/3
Let x(j) = 1046*j + 85774. Let i be x(-82). Factor -8/3*l**i + 4/3*l**4 + 0*l + 0*l**3 + 4/3.
4*(l - 1)**2*(l + 1)**2/3
Let g = -3772 + 3772. Let c(h) be the first derivative of g*h**2 - 9 + 2/35*h**5 + 0*h + 0*h**3 + 5/14*h**4. Factor c(i).
2*i**3*(i + 5)/7
Let l(g) be the first derivative of -g**6/4 + 171*g**5/10 - 159*g**4/8 - 173*g**3/2 + 423*g**2/2 - 168*g - 1176. Solve l(w) = 0 for w.
-2, 1, 56
Suppose 2*d = -b - 1, b + 2*b + 8 = -d. Let n be -20 - -21 - (-14 - d). Factor -4*o + 16*o**4 + 4*o + 4*o - n*o**2 - 4*o**3.
4*o*(o - 1)*(o + 1)*(4*o - 1)
Let w(j) = 342*j**2 - 18*j + 18. Let r be w(1). Let c be r/36 + 1/2 - 6. Suppose 4/13*g**3 + 0*g - 2/13*g**2 + 0 - 2/13*g**c = 0. What is g?
0, 1
Suppose 195*z + 5*z**4 - 265/3*z**3 + 170/3 + 45*z**2 = 0. Calculate z.
-1, -1/3, 2, 17
Let r(d) be the second derivative of d**5/10 - 553*d**4/12 - 2215*d**3/48 - 277*d**2/16 - 2101*d. Factor r(b).
(b - 277)*(4*b + 1)**2/8
Let u = -112972/5 + 22612. Let -14/5*k**2 + 2/5*k**3 - u - 16*k = 0. What is k?
-2, 11
Let t(d) be the first derivative of 605*d**6/2 + 3707*d**5 + 9810*d**4 - 70280*d**3/3 - 80040*d**2 - 67280*d - 6318. Suppose t(w) = 0. What is w?
-58/11, -1, -2/3, 2
Let k(a) be the second derivative of 8*a + 4*a**3 + 1/30*a**6 + 0 - 4/15*a**5 - 12*a**2 + 1/6*a**4. Let f(n) be the first derivative of k(n). Factor f(m).
4*(m - 3)*(m - 2)*(m + 1)
Let t(j) be the third derivative of -1/75*j**6 - 3/50*j**5 + 0*j**3 + j**2 + 34*j - 1/30*j**4 + 0. Factor t(h).
-2*h*(h + 2)*(4*h + 1)/5
Suppose 22*i - 40 = 48. Factor -4*y**i - 1 + 231*y - 30*y**3 - 38*y**2 - 472*y + 229*y + 1.
-2*y*(y + 1)*(y + 6)*(2*y + 1)
Let i be ((-27)/(-15) - 1)*30. Suppose 15*k - 138 = -31*k. Find o such that -20*o**k + 11*o**2 + i*o**4 - 23*o**2 + 28*o - 20*o = 0.
-2/3, 0, 1/2, 1
Suppose -13*n + 117 = -318 + 162. Let n*l - 3/2*l**2 + 45/2 = 0. What is l?
-1, 15
Let p(b) = b**3 + 5*b**2 + 18*b + 60. Let d be p(-4). Let i be 28/14 - (-1)/(12/21). Factor -2*r**2 + i*r + 9/4 - d*r**3.
-(r - 1)*(4*r + 3)**2/4
Suppose -39 = 8*h - 183. Determine u so that -h - 5 - 24*u + 2 + 9*u**2 - 12*u**2 = 0.
-7, -1
Let c be (50/((-15200)/532))/(7*1/(-8)). Suppose 60*g**c - 56/3*g**3 - 28/3*g - 8 = 0. Calculate g.
-2/7, 1/2, 3
Factor -5/4*t**3 + 4430*t + 4415/4*t**2 + 4435.
-5*(t - 887)*(t + 2)**2/4
Let i(o) be the second derivative of -o**4/4 + 19*o**3 + 945*o**2/2 - 26*o - 68. Let i(u) = 0. What is u?
-7, 45
Determine y so that -1110/7*y**2 - 4/7*y**3 - 160 + 2796/7*y = 0.
-280, 1/2, 2
Suppose 2 = -4*g + 5*m - 11, -4*m + 35 = 5*g. Let 11*l**g + 111*l**4 - 12 + 13*l**3 - 107*l**4 + 8*l**2 - 16*l - 8*l**3 = 0. Calculate l.
-3, -1, 1
Suppose -7842625*d + 32 = -7842609*d. Factor -2662/3 + 3*x**4 - 295/3*x**3 - 3751*x + 1067*x**d.
(x - 11)**3*(9*x + 2)/3
Let h(w) be the third derivative of w**8/1512 - 32*w**7/945 + 11*w**6/54 + 34*w**5/135 - 109*w**4/36 - 28*w**3/3 + 1238*w**2. Solve h(d) = 0 for d.
-1, 3, 28
Suppose n = -10*n + 55. Suppose 24 = 3*k - n*g, k + 4*g - 6 = 5*g. Suppose -2 - 5*d**3 + 14*d**3 + 6*d**2 + d**k - 5*d**3 - 9*d = 0. What is d?
-2, -1/5, 1
Factor 3/8*g**2 + 855/8 + 51/4*g.
3*(g + 15)*(g + 19)/8
Factor 104 - 2/3*y**2 - 152/3*y.
-2*(y - 2)*(y + 78)/3
Find w such that 495/2 + 615/4*w - 5/4*w**3 + 20*w**2 = 0.
-3, 22
Let y = -2938/3 + 980. Let q(m) be the second derivative of 0 - y*m**3 - 9*m - 2/15*m**6 - 2/21*m**7 + 2/3*m**4 + 2/5*m**5 - 2*m**2. What is j in q(j) = 0?
-1, 1
Let t(x) = 3*x**3 - 2*x**2 - 11*x - 35. Let s be t(7). Let u = -819 + s. Suppose u + 4/13*l**4 + 2/13*l**5 + 0*l**3 - 4/13*l**2 - 2/13*l = 0. Calculate l.
-1, 0, 1
Factor -3023*t**2 - 65536 + 10*t - 522*t + 3022*t**2.
-(t + 256)**2
Let s(p) = -p**2 + 13*p - 20. Let b be s(11). Let -1080*o + 972 + 229*o**3 - 120*o**3 - 112*o**3 + 0*o*