 139*q**5/40 - 141*q**4/8 + 425*q**3/12 - 71*q**2/2 + 619*q. Find n, given that y(n) = 0.
-142, 1
Let k = -21064 + 84257/4. Suppose -2*m - 5*j + 19 = 0, 1 = -4*m + 3*j - 0*j. Suppose 0 + k*f**m + 0*f = 0. Calculate f.
0
Let y(f) be the third derivative of f**7/420 + f**6/180 - f**5/12 + f**4/4 + 11*f**3/6 - 3*f**2. Let p(t) be the first derivative of y(t). Factor p(q).
2*(q - 1)**2*(q + 3)
Let p(u) be the second derivative of -1/66*u**4 + 0*u**3 + 0 - 3*u + 0*u**2 + 1/110*u**5. Factor p(b).
2*b**2*(b - 1)/11
Suppose -4*u - r - 11 = 10, -u - 6 = r. Let c be 12/(-6) + u/(-2). Factor -3/2*p**2 + c*p + 1 + 1/2*p**4 - 1/2*p**3.
(p - 2)*(p - 1)*(p + 1)**2/2
Suppose -2*o - 2*l - 40 = 3*o, 2*l - 40 = 5*o. Let p be (7/3 - 2)/((-8)/o). Solve p*b**2 + 0 + 0*b = 0.
0
Let k(j) be the third derivative of j**9/9072 + j**8/5040 - j**7/1260 - 11*j**3/3 - 26*j**2. Let x(p) be the first derivative of k(p). Factor x(g).
g**3*(g - 1)*(g + 2)/3
Let q(y) = -4*y - 1. Let d be q(-1). Solve 9*j - 10*j + 3*j**3 + 5*j**2 + d*j = 0 for j.
-1, -2/3, 0
Factor 0 - 12*o + 3/4*o**3 + 0*o**2.
3*o*(o - 4)*(o + 4)/4
Let x = -129 - -131. Let w(l) be the third derivative of 0 - 1/30*l**5 + 1/105*l**7 + 4*l**x + 1/12*l**4 - 1/60*l**6 + 0*l + 0*l**3. Let w(r) = 0. Calculate r.
-1, 0, 1
Let i(k) be the third derivative of k**8/168 - 13*k**7/210 - 3*k**6/40 + 13*k**5/60 + 7*k**4/24 - 8*k**2 - 3*k. Determine z so that i(z) = 0.
-1, -1/2, 0, 1, 7
Let t(h) = 2*h**3 + 5*h**2 + h - 8. Let c be t(-2). Let x be c/(-21) - 14/49. Find i such that 11/4*i**4 + 0*i - 3/4*i**3 + i**5 + x*i**2 + 0 = 0.
-3, 0, 1/4
Let j(y) be the second derivative of -y**5/8 - 14*y**4/3 - 11*y**3/3 - 846*y. Suppose j(m) = 0. Calculate m.
-22, -2/5, 0
Solve 36*g**2 + 39*g**2 + 6*g**2 - g**3 - 2*g**3 - 78*g = 0 for g.
0, 1, 26
Let b(q) = -80*q**3 + 85*q**2 + 9*q - 10. Let u(y) = 399*y**3 - 426*y**2 - 45*y + 51. Let k(t) = -21*b(t) - 4*u(t). Let k(v) = 0. What is v?
-2/7, 1/4, 1
Suppose -42*w = -53*w - 66. Let g be 20/11 + -2 + w/(-33). Factor 4/3*r + g + 0*r**2 - 4/3*r**3.
-4*r*(r - 1)*(r + 1)/3
Suppose 0 = -9*f - 116 + 431. Let p be (2 - 85/f)*(-4)/6. Factor 4/7*w**3 + 2/7 - 4/7*w - p*w**4 + 0*w**2.
-2*(w - 1)**3*(w + 1)/7
Let c = 32405/7602 - -25/1086. Determine s, given that -c*s**2 + 24/7 - 18/7*s**3 + 24/7*s = 0.
-2, -2/3, 1
Suppose 0 = -29*p + 40*p - 1529. Let j = -139 + p. Factor -1/3*b - b**2 + j - b**3 - 1/3*b**4.
-b*(b + 1)**3/3
Let k = 87011/70 + -1243. Let u(l) be the third derivative of -1/16*l**5 + 0*l**3 + 0 - k*l**7 + 0*l - 11/160*l**6 - 2*l**2 + 1/16*l**4. Solve u(m) = 0 for m.
-2, -1, 0, 1/4
Let w = 228 + -3647/16. Let g(a) be the second derivative of 1/24*a**3 - w*a**5 - 1/40*a**6 + 0*a**2 - 1/48*a**4 - 2*a + 0. What is d in g(d) = 0?
-1, 0, 1/3
Let n(l) be the third derivative of -l**8/3360 + l**7/700 - l**6/600 - l**5/300 - 7*l**4/12 - 2*l**2. Let m(c) be the second derivative of n(c). Factor m(i).
-2*(i - 1)**2*(5*i + 1)/5
Let t(h) = 13*h**3 + 288*h**2 + 4615*h + 24576. Let z(b) = -9*b**3 - 192*b**2 - 3077*b - 16384. Let v(i) = 5*t(i) + 7*z(i). Let v(a) = 0. What is a?
-16
Let m be (-104)/156*-1*(-6)/(-16). Factor -m*x**2 + 1 + 0*x.
-(x - 2)*(x + 2)/4
Let s = -41515 - -41518. Factor -90/7*b**2 - 6*b**4 - 6/7*b + 12/7 - 114/7*b**s.
-6*(b + 1)**3*(7*b - 2)/7
Suppose w**5 - w**4 - 6*w**3 - w**3 + 2*w**4 + 5*w**3 - 3*w**3 + 3*w**2 = 0. Calculate w.
-3, 0, 1
Let l(h) = -14*h**3 + 24*h**2 + 11*h - 3. Let w = -13 + 11. Let r = -3 - w. Let u(g) = -g + 1. Let p(c) = r*l(c) - 3*u(c). Determine o, given that p(o) = 0.
-2/7, 0, 2
Suppose i = 5*i - 40. Factor -2*c - 4 - 6*c + 0*c + i*c**2 + 2*c.
2*(c - 1)*(5*c + 2)
Let n be (-2)/30 - (30/200)/((-9)/24). Factor -1/6*r**3 + n*r**2 + 0 + 1/2*r.
-r*(r - 3)*(r + 1)/6
Suppose -11*g**3 - 4*g + 12*g**3 - 5*g - 12*g**2 - 9*g + 5*g = 0. Calculate g.
-1, 0, 13
Let v(s) be the first derivative of -5/3*s**4 + 0*s**2 - 14 + 1/4*s**5 + 10/3*s**3 - 14*s. Let g(u) be the first derivative of v(u). Find l such that g(l) = 0.
0, 2
Suppose f - 13 = -2*d - 0*f, 5*d - 15 = f. Factor -179*o**d - o**3 + 4*o**2 + 191*o**4 - 15*o**3.
4*o**2*(o - 1)*(3*o - 1)
Let k(p) be the first derivative of p**6/1980 - p**5/132 + p**4/22 + 34*p**3/3 - 23. Let q(j) be the third derivative of k(j). Factor q(c).
2*(c - 3)*(c - 2)/11
Suppose 0 = 4*c - 4*d - 20, 129*c + 4*d = 127*c - 2. Factor -1/2*k**2 + 1/2 - 1/2*k + 1/2*k**c.
(k - 1)**2*(k + 1)/2
Let 110/3 + 15*h - 5/3*h**2 = 0. Calculate h.
-2, 11
Let i be 1/(-3)*(-21 - -20). Let r(z) be the second derivative of 2*z + 5/6*z**3 + 0 + z**2 + i*z**4 + 1/20*z**5. Determine q so that r(q) = 0.
-2, -1
Let m(g) be the second derivative of 0*g**3 + 10*g + 0*g**2 + 0 + 1/60*g**4 - 1/200*g**5. Factor m(x).
-x**2*(x - 2)/10
Let p(b) be the third derivative of -b**7/385 + b**6/660 + b**5/66 - b**4/132 - 2*b**3/33 - 161*b**2. Let p(y) = 0. Calculate y.
-1, -2/3, 1
Let o(h) = -h**5 + 3*h**4 + 2*h**3 - h - 1. Let v(b) = -b**4 - b**2 + 1. Let n(p) = -p**2 - 26*p + 54. Let q be n(-28). Let s(g) = q*v(g) - o(g). Factor s(k).
(k - 1)**3*(k + 1)**2
Factor -645*j**3 + 88*j**2 - 154*j**4 - 99*j + 89*j - 346*j**4 - 255*j**3 + 107*j**2.
-5*j*(j + 2)*(10*j - 1)**2
Let k(u) be the second derivative of 32*u**3 + 13/3*u**4 + 5*u + 0 + 72*u**2 + 1/5*u**5. Let k(n) = 0. What is n?
-6, -1
Let w(v) be the first derivative of 0*v + 4/65*v**5 - 4/39*v**3 + 1/39*v**6 + 0*v**4 + 22 - 1/13*v**2. Factor w(y).
2*y*(y - 1)*(y + 1)**3/13
Let p(m) be the first derivative of 2*m**5 + 0*m + 9 - 5/4*m**4 - 5/6*m**6 + 0*m**2 + 0*m**3. Factor p(k).
-5*k**3*(k - 1)**2
Determine u so that 15*u**3 - 3*u**5 + 26*u**2 - 16*u**2 - 10*u**2 - 12*u = 0.
-2, -1, 0, 1, 2
Let p = -3328 - -3330. Factor 1/5*n**4 + 0*n + 0*n**p - 1/5*n**3 + 0.
n**3*(n - 1)/5
Solve 4/7*x**2 + 18496/7 - 544/7*x = 0 for x.
68
Let l(n) = 19*n - 126. Let u be l(7). Let b(t) be the first derivative of -2 - 4/5*t**5 + 4*t + t**4 - 1/3*t**6 + u*t**2 + 16/3*t**3. Find k such that b(k) = 0.
-1, 2
Let i(x) be the first derivative of -4*x**5/5 + 10*x**4 - 64*x**3/3 - 600. Factor i(y).
-4*y**2*(y - 8)*(y - 2)
Let f = -1430 - -2863/2. Suppose -1/6*t**2 - f - t = 0. What is t?
-3
Let k = -294 - -296. Let r(u) be the first derivative of 1/4*u + 1/4*u**k + 1 + 1/12*u**3. Determine h, given that r(h) = 0.
-1
Let q(w) = -15*w**3 + 25*w**2 + 5*w + 5. Let u(k) = 2*k**3 - k**2 + k. Let b(o) = q(o) + 10*u(o). Let b(g) = 0. What is g?
-1
Let -21*h**2 + 38 - 9*h**3 + 3*h**4 + 16 - h**3 + 12*h**3 + 45*h - 11*h**3 = 0. What is h?
-2, -1, 3
Let m(z) = 3*z**3 - 72*z**2 - 588*z - 864. Let i(t) = 2*t**3 - 73*t**2 - 586*t - 864. Let x(v) = -6*i(v) + 5*m(v). Factor x(h).
3*(h + 2)*(h + 12)**2
Let u(v) be the first derivative of 27*v**4/22 + 2*v**3 - 48*v**2/11 - 24*v/11 + 118. Suppose u(q) = 0. Calculate q.
-2, -2/9, 1
Let u(l) be the third derivative of 0*l**3 + 0*l + 0*l**4 + 1/2016*l**8 + 22*l**2 + 0 + 0*l**5 + 0*l**6 + 0*l**7. Solve u(r) = 0.
0
Let p(t) be the third derivative of -t**3 - 1/4*t**4 + 0*t - 3/40*t**5 + 0 - 1/120*t**6 - 2*t**2. Let m(w) be the first derivative of p(w). Factor m(i).
-3*(i + 1)*(i + 2)
Let f(p) be the second derivative of 49*p**5/90 + 133*p**4/54 + 40*p**3/9 + 4*p**2 - 3*p - 1. Factor f(t).
2*(t + 1)*(7*t + 6)**2/9
Let f(o) be the first derivative of -o**3/15 + 172*o**2/5 - 29584*o/5 - 92. Factor f(n).
-(n - 172)**2/5
Let s be 6/9 + (-3 - (-9 - -6)). Let y = -169/3 + 57. Factor -s*q + y*q**3 - 4/3 + 4/3*q**2.
2*(q - 1)*(q + 1)*(q + 2)/3
Let p(w) be the first derivative of -w**3/12 + 25*w**2/8 - 33*w/2 - 846. Factor p(y).
-(y - 22)*(y - 3)/4
Let f(k) be the second derivative of k**6/75 + k**5/25 - k**4/30 - 2*k**3/15 - 3*k - 1. Factor f(g).
2*g*(g - 1)*(g + 1)*(g + 2)/5
Let m(a) be the first derivative of a**7/280 - 3*a**5/40 - a**4/4 - 20*a**3/3 - 21. Let b(d) be the third derivative of m(d). Factor b(z).
3*(z - 2)*(z + 1)**2
Let n(y) = -y. Let r be n(-4). Suppose -7 + 3 = -2*l - c, -l = -c + r. Factor -17*q**5 + 2*q**3 - 3*q**4 + 18*q**5 + l*q**3.
q**3*(q - 2)*(q - 1)
Let k = 30404/75985 - 2/15197. Factor 0*m + 8/5 - k*m**2.
-2*(m - 2)*(m + 2)/5
Suppose -37*o**4 + 41*o**4 - 12*o**2 - 8*o - 2 + 2 = 0. What is o?
-1, 0, 2
Let f(b) be the second derivative of -1/66*b**4 + 0 + 0*b**2 - 13*b + 0*b**3. Find w such that f(w) = 0.
