 687. Find t such that 2*t**2 + 1/2*t**4 + b*t - 5/2*t**3 + 0 = 0.
0, 1, 4
Suppose 6/7*x**2 - 2484/7*x + 354 = 0. What is x?
1, 413
Let c(y) be the first derivative of -y**4/16 + 9*y**3/4 - 13*y**2/4 + 1291. Let c(a) = 0. Calculate a.
0, 1, 26
Solve 2/5*x**3 - 2048/5 + 126/5*x**2 + 384*x = 0.
-32, 1
Let s = 1061342/3 - 353780. Suppose -1/3*j**3 + s*j**2 + 7/3*j + 4/3 = 0. What is j?
-1, 4
Let h(b) be the second derivative of -14/5*b**2 + 1/10*b**3 - 27 + 1/60*b**4 + 2*b. Find n such that h(n) = 0.
-7, 4
Let y(j) = -65*j**2 + 17965*j - 686465. Let g(f) = -3*f**2 + 816*f - 31203. Let r(l) = -45*g(l) + 2*y(l). Factor r(v).
5*(v - 79)**2
Let k = 695 - 691. Suppose 118 = k*y + 98. Find g such that -1/2*g**2 + 0*g + 3/2*g**3 + 1/2*g**y - 3/2*g**4 + 0 = 0.
0, 1
Let g(u) = u**2 - 1. Let z = -719 + 718. Let h = -15 - -11. Let r(o) = o**3 - 4*o**2 - o + 4. Let a(j) = h*g(j) + z*r(j). Factor a(m).
-m*(m - 1)*(m + 1)
Let a(m) be the third derivative of -m**5/330 + 113*m**4/44 - 338*m**3/33 + 878*m**2 + m - 2. Factor a(d).
-2*(d - 338)*(d - 1)/11
Let k = 33 + -6. Suppose -6*n + k = 3*j - n, -2*n = 5*j - 26. Suppose -15*a**2 - 4*a**3 + 34*a + 3*a**5 - 40*a - 5*a**3 + 3*a**j = 0. What is a?
-1, 0, 2
Let v be (-2)/(-9) - (-11 + 3832/(-104))/9. Suppose 32/13 + v*n + 18/13*n**3 + 56/13*n**2 + 2/13*n**4 = 0. Calculate n.
-4, -2, -1
Let l = 1124 - 1126. Let f be (-1332)/296*l/3. Factor 0 + 0*u + 3/2*u**f + u**2.
u**2*(3*u + 2)/2
Let t be (-2)/((-41)/(-86) + 3/(-6)). Suppose -134*l**3 + 90*l**2 - 41*l**3 + t*l**4 + 96*l**2 - 68*l - 37*l**4 + 8 = 0. Calculate l.
2/7, 1, 2
Let q(l) = -56*l**4 + 11*l**3 - 22*l + 11. Let p(n) = -20*n**4 + 4*n**3 - 8*n + 4. Let w(y) = 11*p(y) - 4*q(y). Factor w(v).
4*v**4
Let x(c) be the third derivative of -23*c**8/4032 + c**7/48 + c**6/72 + c**5/30 - 2*c**4 - 12*c**2 + 4*c. Let s(z) be the third derivative of x(z). Factor s(k).
-5*(k - 1)*(23*k + 2)
Suppose 4/7*d**2 - 2/7*d**4 + 0 + 2/7*d**3 + 0*d = 0. What is d?
-1, 0, 2
Suppose 27*l + 2666 = -4*l. Let f = -83 - l. Factor 5/3*b**5 + 2/3*b - 11/3*b**2 + 0 + 7*b**f - 17/3*b**4.
b*(b - 1)**3*(5*b - 2)/3
Let z(q) = -8*q**2 + 40*q + 3. Suppose -4*v - 18 + 38 = 0. Let y be z(v). Factor 9/4*g**2 + 0*g - 3/4*g**y + 0.
-3*g**2*(g - 3)/4
Let m be 2*(8 + (-26)/4). Suppose 5*i + 2*j - 20 = 0, m*j + 8 = 2*i - 2*j. Factor -1/2*p**2 - 3/2*p**3 + 1/2*p**5 + 1/2*p**i + p + 0.
p*(p - 1)**2*(p + 1)*(p + 2)/2
Suppose -2*q + o + 57 + 76 = 0, -q - o + 65 = 0. Determine c, given that 0*c**3 + 70304 - q*c**2 + 378*c**2 + 4*c**3 + 8112*c = 0.
-26
Find p such that p**2 + 3*p**2 - 110 + 4*p + 12 + 18 = 0.
-5, 4
Let l(i) be the first derivative of 5*i**4/4 - 680*i**3/3 + 11560*i**2 - 1519. Factor l(w).
5*w*(w - 68)**2
Suppose -3*k + 2*g - 6*g + 26 = 0, -3 = -4*k + g. Factor 8*r - 15*r + r**3 - 12 + r**k - 2*r**3 + 15*r.
-(r - 2)**2*(r + 3)
Let x(n) be the third derivative of n**8/3360 + 29*n**7/1050 - n**6/400 - 43*n**5/150 + 29*n**4/60 - 1513*n**2. Suppose x(b) = 0. Calculate b.
-58, -2, 0, 1
Let j be 83/(37433/8692) + (-3)/11. Let g(y) be the second derivative of -j*y + 0 + 3*y**2 + 1/6*y**4 + 4/3*y**3. Find o such that g(o) = 0.
-3, -1
Let t = 3/29438 - -58861/147190. Let t*n**3 + 0 + 6/5*n - 8/5*n**2 = 0. What is n?
0, 1, 3
Let n be 7 + (1092/(-539) - -2 - (-18)/(-42)). Factor n - 70/11*t - 2/11*t**2.
-2*(t - 1)*(t + 36)/11
Suppose 21 = 4*a + 3*a. Factor -5*u**2 + 4*u**2 - 5*u**a - 74*u**2.
-5*u**2*(u + 15)
Let i(k) be the first derivative of -k**7/1785 - k**6/510 + k**4/102 + k**3/51 - k**2/2 + k + 23. Let q(l) be the second derivative of i(l). Factor q(o).
-2*(o - 1)*(o + 1)**3/17
Suppose 2*a = y - 17, 0 = -23*y + 27*y + 3*a + 9. Let f(l) be the first derivative of 1/5*l**2 - 1/5*l + y - 1/15*l**3. Factor f(c).
-(c - 1)**2/5
Suppose 0*h - 32 = -2*h - 4*f, 67 = 5*h - 3*f. Let w = h - 9. Find a, given that 8*a**4 + a**4 - 6*a**3 + 79*a**w - 82*a**5 = 0.
0, 1, 2
Factor -10*j - 1/6*j**2 + 61/6.
-(j - 1)*(j + 61)/6
Let b be (-30)/(6 + -11) - 4. Suppose -b*c - 2*c + 5 = -3*x, -5*x + 15 = 5*c. Find j such that 4/15*j**3 + 2/5*j**4 + 0 + 0*j + 0*j**c = 0.
-2/3, 0
Let b(y) be the first derivative of y**4/20 - 7*y**3/5 + 3*y**2 + 152*y/5 + 7636. Determine k, given that b(k) = 0.
-2, 4, 19
Let q = -369795 - -369805. Factor q + 1/3*o**2 + 31/3*o.
(o + 1)*(o + 30)/3
Suppose -5*x = 2 + 73. Let r = 17 + x. Factor 98*m**3 - 11*m**r - 16 - 24*m - m**2 - 100*m**3.
-2*(m + 2)**3
Let w(s) be the first derivative of -s**6/35 + s**5/35 - s**4/84 - s**3/3 - 2*s + 9. Let y(l) be the third derivative of w(l). Factor y(g).
-2*(6*g - 1)**2/7
Suppose -13*i = -0*i. Let 17*b**3 - b + i*b**3 - 6*b**2 + 3 - 15*b**3 - b**5 + 3*b**4 = 0. Calculate b.
-1, 1, 3
Factor -2*g**4 + 1009*g + 67*g**2 - 2757*g - 498*g**2 - 1061 + 168*g**3 + 101 - 187*g**2.
-2*(g - 80)*(g - 6)*(g + 1)**2
Let w(u) = -228*u**3 - 3*u**2 - 8*u - 4. Let o be w(-2). Let v be o/152 - 2*5. Factor 0 - 2/5*b**v - 16/5*b.
-2*b*(b + 8)/5
What is w in -18/5*w**4 - 104/5*w**3 - 66/5*w**2 + 236/5*w - 48/5 = 0?
-4, -3, 2/9, 1
Let m be -19 - (-13)/((-403)/(-651)). Factor 0 + 5/4*x**3 - 5/4*x + 0*x**m.
5*x*(x - 1)*(x + 1)/4
Let a(n) be the third derivative of -n**8/16 - 13*n**7/35 + 11*n**6/20 + 4*n**5 - 87*n**4/8 + 9*n**3 + 31*n**2 - 16*n. Determine u, given that a(u) = 0.
-3, 2/7, 1
Find y, given that -1152*y**2 - 341*y + 1007*y - 4*y**5 - 200*y**3 + 96*y**4 + 594*y = 0.
-3, 0, 1, 5, 21
Let u(q) be the second derivative of 267/5*q**5 + 85*q**3 + 36*q**2 + 207*q + q**7 + 123/10*q**6 + 1 + 393/4*q**4. Find b, given that u(b) = 0.
-4, -3, -1, -1/2, -2/7
Let o(s) be the second derivative of -s**6/1200 - s**5/600 + s**4/240 + s**3/60 - 91*s**2/2 + 2*s - 4. Let x(f) be the first derivative of o(f). Factor x(m).
-(m - 1)*(m + 1)**2/10
Let q = -174605 + 698425/4. Suppose 3/4*j**3 - 7/2 + q*j + 11/2*j**2 = 0. Calculate j.
-7, -1, 2/3
Let u = 141 + -80. Suppose -2*f + u = 53. Find t, given that 0*t**2 - 2*t**2 + 4*t + 3*t**2 - 4*t**3 - 3*t - f*t**4 = 0.
-1, -1/2, 0, 1/2
Let -208845/4*o + 207025/2 + 228*o**2 - 1/4*o**3 = 0. Calculate o.
2, 455
Factor 0*x + 0 - 2*x**4 + 1/8*x**5 + 69/8*x**3 - 27/4*x**2.
x**2*(x - 9)*(x - 6)*(x - 1)/8
Let n = 4635/7 + -3566/7. Let k = n - 152. Solve -6/7 + 1/7*y**2 + k*y = 0.
-6, 1
Factor 3071 - 17*p**2 - 441*p + 177*p + 31*p**2 + 2737 - 11*p**2.
3*(p - 44)**2
Suppose 64 = -8*c + 96. Let -21*n - 435*n**3 - 30*n**2 + 432*n**3 - 3*n + 3*n**c = 0. What is n?
-2, -1, 0, 4
Let r be ((-715)/3575)/((-2)/4). Factor -r*b**2 - 48/5*b + 10.
-2*(b - 1)*(b + 25)/5
Let j(b) be the second derivative of b**5/10 + 361*b**4/2 + 130321*b**3 + 47045881*b**2 + 473*b - 1. Factor j(m).
2*(m + 361)**3
Let t(z) = 1003*z - 5009. Let b be t(5). Let g(a) be the second derivative of 0 + b*a + 1/90*a**4 - 1/15*a**3 - 2/3*a**2. Factor g(o).
2*(o - 5)*(o + 2)/15
Factor 77*g**2 + 2008835*g - 31*g**2 - 32 - 2008849*g.
2*(g - 1)*(23*g + 16)
Let f(x) be the first derivative of x**5/5 + 11*x**4/4 - x**3 - 35*x**2/2 - 22*x + 864. Factor f(k).
(k - 2)*(k + 1)**2*(k + 11)
Suppose -49 = -13*x - 94 + 45. Let m(n) be the third derivative of 0 + 1/660*n**6 + 3/44*n**4 - 4/33*n**3 + 33*n**2 + x*n - 1/55*n**5. Factor m(t).
2*(t - 4)*(t - 1)**2/11
Let o be 960/336*5075/174. Factor -2/3*r**3 + 50/3*r + o - 10/3*r**2.
-2*(r - 5)*(r + 5)**2/3
Let x(q) be the first derivative of -3*q**4/20 + 29*q**3/5 - 84*q**2 + 540*q - 87. Factor x(z).
-3*(z - 10)**2*(z - 9)/5
Let t(h) be the first derivative of 14*h**6/3 + 3816*h**5/5 + 30673*h**4 - 167432*h**3 + 129080*h**2 + 117600*h + 3994. Find c such that t(c) = 0.
-70, -2/7, 1, 3
Let v(r) be the first derivative of -2*r**3/21 - 15*r**2 + 212*r/7 - 1176. Factor v(w).
-2*(w - 1)*(w + 106)/7
Let z be 14 + 6/((9/108)/((-6)/36)). Suppose -4*l + 16/9 - 10/9*l**z = 0. Calculate l.
-4, 2/5
Suppose 588 = -21*b + 714. Let o(t) be the third derivative of -1/56*t**4 + b*t**2 + 1/140*t**5 + 0*t - 1/7*t**3 + 0. Suppose o(i) = 0. What is i?
-1, 2
Let z(v) = 2*v + 99. Let u be z(-38). Suppose -d - 12 = -4*p, -5*d = -3*p + u + 3. Factor 3/7*q**p + 6/7*q + 0.
3*q*(q + 2)/7
Let h(l) be the first derivative of l**8/5880 - l**7/420 - 2*l**3 + 7*l**2/2 - 16. Let g(d) be the third derivative of h(d). Solve g(u) = 0.
0, 7
Factor 0 + 7*u + 39/4*u**2 + 3*u**3 + 1/4*u**4.
u*(u + 1)*(u + 4