et k(u) be the second derivative of -u**4/48 - 5*u**3/8 - 7*u**2/4 + 56*u. What is o in k(o) = 0?
-14, -1
Let -3/8*y**3 - 12*y**2 + 0 - 96*y = 0. What is y?
-16, 0
Factor 3*i**4 - 38359 - 4*i**4 - 36179*i**2 + 342*i**3 + 7282*i**2 + 8775 - 58824*i.
-(i - 172)**2*(i + 1)**2
Let n(t) be the second derivative of -3/20*t**5 + 0 - 1/2*t**4 + 0*t**2 - 11*t - 1/60*t**6 - 2/3*t**3. Solve n(r) = 0.
-2, 0
Find z such that -1184/9*z**3 - 1480/9*z**2 - 16/9*z**5 - 112/3*z - 28*z**4 + 196/9 = 0.
-7, -1, 1/4
Let m be 2/((-24)/9) - 1173/(-1380). Let r(n) be the second derivative of 0*n**2 + 4*n + m*n**6 + 3/20*n**5 + 0*n**3 + 0 - 1/2*n**4. Factor r(b).
3*b**2*(b - 1)*(b + 2)
Let w = 19606 - 117635/6. Factor -4/3 + w*f**3 + 1/3*f**2 - 2/3*f.
(f - 2)*(f + 2)**2/6
Let k(w) be the second derivative of w**5/40 + 5*w**4/24 - w**3/2 - 4*w + 3. Factor k(i).
i*(i - 1)*(i + 6)/2
Factor 0 + 1/5*i**3 + 3/5*i**2 - 4/5*i.
i*(i - 1)*(i + 4)/5
Let u(l) = l**2 - 18*l - 10. Let s(y) = -3*y + 1. Let k(h) = 6*s(h) - u(h). Factor k(b).
-(b - 4)*(b + 4)
Let t(l) = l**2 + 236*l + 2647. Let b(g) = g**2 - 239*g - 2648. Let r(p) = -2*b(p) - 3*t(p). Factor r(c).
-5*(c + 23)**2
Let 1134*t**2 + 92 + 138 + 41*t + 184*t - 1139*t**2 = 0. What is t?
-1, 46
Let o(h) be the second derivative of -h**6/10 + 27*h**5/20 - 6*h**4 + 8*h**3 - h - 50. Suppose o(z) = 0. Calculate z.
0, 1, 4
Let y(i) = -2*i**2 + 6 + 17*i**2 + 12*i + 1 - 11*i**3. Let t(m) = 6*m**3 - 8*m**2 - 6*m - 4. Let d(q) = 7*t(q) + 4*y(q). Factor d(h).
-2*h*(h - 3)*(h + 1)
Let f(c) be the second derivative of -1/140*c**5 + 1/7*c**4 + 0 - 6*c**2 + 8*c - 8/7*c**3. Let r(y) be the first derivative of f(y). What is k in r(k) = 0?
4
Suppose 12 = 3*y - 3*l, 6*l - 4 = -y + l. Suppose g = 0, -y*c + 9 = 4*g - 7. Factor -1 - 3*w + 7 - 36*w**2 + 6*w**c + 9*w**5 - 12*w**3 - 18*w**3.
3*(w - 2)*(w + 1)**3*(3*w - 1)
Let l(f) be the third derivative of f**7/525 + 8*f**6/75 + 63*f**5/25 + 162*f**4/5 + 243*f**3 + 252*f**2. Factor l(r).
2*(r + 5)*(r + 9)**3/5
Factor 3/4*o**2 + 117 + 60*o.
3*(o + 2)*(o + 78)/4
Let h be (-1 + 0/(-6))/(-2). Let c(b) be the first derivative of h*b**4 - 2 + 9*b**2 + 4*b**3 + 0*b. Factor c(z).
2*z*(z + 3)**2
Determine p, given that 0 - 4/7*p + 2/7*p**4 - 2/7*p**2 + 4/7*p**3 = 0.
-2, -1, 0, 1
Let n(r) be the second derivative of r**6/20 + 21*r**5/40 + 11*r**4/8 + 5*r**3/4 + 212*r. Factor n(j).
3*j*(j + 1)**2*(j + 5)/2
Suppose 174*r - 3*j - 10 = 169*r, 0 = -4*r + 5*j + 8. Suppose -768/5*m - 48/5*m**3 + 3/5*m**4 + 768/5 + 288/5*m**r = 0. What is m?
4
Let k be (320/(-35))/(-8) - (-1)/(-7). Let y be (((-3)/12)/k)/(2/(-2)). Factor 3/8*d - y - 1/8*d**2.
-(d - 2)*(d - 1)/8
Suppose 6 = -3*w + 6. Let z be w/2 + -1 - 330/(-275). Solve -z*n**5 + 3/5*n - 1/5 + 3/5*n**4 - 2/5*n**3 - 2/5*n**2 = 0 for n.
-1, 1
Let u(q) = -14*q**3 + 3*q**2 - 7*q - 6. Let w(b) = -33*b**3 + 7*b**2 - 14*b - 12. Let i(x) = -7*u(x) + 3*w(x). Determine l so that i(l) = 0.
-2, -1, 3
Suppose 217*y + 9 = 220*y - 3*w, -w = -2*y + 3. Let v(o) be the third derivative of y - 5/24*o**4 + 25/12*o**3 + 8*o**2 + 1/120*o**5 + 0*o. Solve v(u) = 0.
5
Let l be 1 - ((-4)/2 - -1). Factor 11 - j**5 - j**3 - l*j**2 - j**3 + 3*j**4 + 3*j - 12.
-(j - 1)**4*(j + 1)
Let u = 4943 - 24713/5. Let m = 2 + -2. Let -2/5*g + 2/5*g**3 - 2/5*g**4 + u*g**2 + m = 0. Calculate g.
-1, 0, 1
Let v(w) be the first derivative of -w**7/42 + w**6/30 + w**5/20 - w**4/12 - 7*w - 2. Let j(u) be the first derivative of v(u). Factor j(p).
-p**2*(p - 1)**2*(p + 1)
Suppose 0*h**2 + 1/4*h**5 + 0*h + 1/2*h**4 + 1/4*h**3 + 0 = 0. Calculate h.
-1, 0
Let z(h) = 9*h**2 + 60*h + 36. Let v be z(-6). Let q(f) be the second derivative of v*f**2 + 0 + 4/3*f**3 - 1/3*f**4 - 12*f. What is i in q(i) = 0?
0, 2
Let m(l) = 5*l - 80. Let k = 77 + -61. Let x be m(k). Suppose x*b - 3/2 + 3/2*b**2 = 0. What is b?
-1, 1
Suppose 2*m = -3*z - 26, -4*z + 0*z + m - 42 = 0. Let i be ((-2)/8*z)/((-18)/(-36)). Solve -4*a**3 - 2*a**4 - 2/5 - 2/5*a**i - 4*a**2 - 2*a = 0.
-1
Let i(j) be the third derivative of 1/60*j**6 + 6*j**2 + 9*j**4 + 0 - 72*j**3 + 0*j - 3/5*j**5. Suppose i(t) = 0. What is t?
6
Let x = 28698 - 28695. Factor 0 + 4/3*y**x + 0*y - 4/3*y**4 + 0*y**2.
-4*y**3*(y - 1)/3
Let w(v) be the third derivative of -5*v**5/12 + 5*v**4/12 + 5*v**3/2 + v**2 + 12. Find u such that w(u) = 0.
-3/5, 1
Suppose 581 + 239 = 66*j + 226. Factor -3*a - 1/4*a**2 - j.
-(a + 6)**2/4
Suppose -35*b = -30*b - j, 15 = 5*b + 2*j. Factor 7/2*t - b - t**4 + 25/8*t**3 + 1/8*t**5 - 19/4*t**2.
(t - 2)**3*(t - 1)**2/8
Let n(w) be the first derivative of 0*w + 3*w**4 + 16/3*w**3 - 20 - 8*w**2 - 2/3*w**6 - 8/5*w**5. Factor n(s).
-4*s*(s - 1)**2*(s + 2)**2
Solve -180 + 148*b + 2*b**3 + 3*b**3 - 135*b - 68*b - 25*b**2 - 105*b = 0.
-2, 9
Factor 87/4*f + 3/4*f**3 - 21/2 - 12*f**2.
3*(f - 14)*(f - 1)**2/4
Let y be ((-228)/532)/(36/(-56)). Factor 0 + y*b**5 - 2/3*b**3 - 2/3*b**4 + 2/3*b**2 + 0*b.
2*b**2*(b - 1)**2*(b + 1)/3
Let b(l) be the second derivative of 0 + 0*l**4 - 1/18*l**3 + 1/60*l**5 + 0*l**2 - 12*l. Factor b(f).
f*(f - 1)*(f + 1)/3
Let g(s) = -13*s**4 - 61*s**3 + 60*s**2 + 14*s. Let h(l) = 4*l**4 + 20*l**3 - 20*l**2 - 4*l. Let z(j) = 2*g(j) + 7*h(j). Factor z(p).
2*p**2*(p - 1)*(p + 10)
Let t(q) be the first derivative of 1/2*q + 1/2*q**3 - 18 + 3/4*q**2 + 1/8*q**4. Suppose t(p) = 0. Calculate p.
-1
Factor 0 - 2/9*j - 2/9*j**3 - 4/9*j**2.
-2*j*(j + 1)**2/9
Let n(z) be the third derivative of z**8/840 + 23*z**7/525 + 19*z**6/30 + 329*z**5/75 + 833*z**4/60 + 343*z**3/15 + z**2 + 43*z. Solve n(x) = 0 for x.
-7, -1
Let 72/23 - 24/23*h + 2/23*h**2 = 0. What is h?
6
Let d = 807 - 803. Solve d*t - 8 - 1/2*t**2 = 0.
4
Let a(x) = -x**3 - 6*x**2 + 7*x + 5. Let j be a(-7). Suppose 4*y + 4 = j*y. Factor 6*o**3 - 3*o**y - 3*o**3 + 6*o**4.
3*o**3*(o + 1)
Let y(z) be the second derivative of -z**8/2688 + z**7/1680 + z**6/960 - z**5/480 + 2*z**2 + 3*z + 2. Let b(g) be the first derivative of y(g). Factor b(u).
-u**2*(u - 1)**2*(u + 1)/8
Let u(c) be the second derivative of c**5/80 + 211*c**4/48 + 1378*c**3/3 - 2809*c**2/2 - 419*c - 2. Suppose u(r) = 0. Calculate r.
-106, 1
Suppose -20*g - 30046 = -30086. Factor 27 - 9*p + 3/4*p**g.
3*(p - 6)**2/4
Suppose -4*z = 5*i - 49, -5*z + 7 = i - 28. Let c be 1 - 2 - (z + (-183)/21). Factor -18/7*s - 2/7*s**3 - c*s**2 + 0.
-2*s*(s + 3)**2/7
Let c = -8641/2 + 4323. Factor -c*b + 0 - 5/2*b**2.
-5*b*(b + 1)/2
Solve -3/5*q**2 - 102/5*q + 0 = 0 for q.
-34, 0
Let c(p) be the first derivative of -8/9*p - 1/18*p**4 - 2/15*p**5 - 29 + 1/27*p**6 + 14/27*p**3 + 0*p**2. Let c(r) = 0. Calculate r.
-1, 1, 2
Let b(n) = n**3 - n**2. Let d be b(2). Let z be d/(-6) + (-148)/(-6). Factor 3*k**2 + 4*k - 3*k**2 + z*k**3 - 16*k**4 - 16*k**2 + 4*k**5.
4*k*(k - 1)**4
Let f = -32/599 - 146563/3594. Let w = f - -41. Factor 1/2 + w*c**2 - 2/3*c.
(c - 3)*(c - 1)/6
Let g(r) be the second derivative of -r**6/18 - 71*r**5/120 + 5*r**4/12 + 625*r**3/36 - 125*r**2/6 - 16*r + 5. Let g(u) = 0. What is u?
-5, 2/5, 5/2
Let p(j) be the third derivative of -j**5/360 - 23*j**4/144 - 11*j**3/18 + 111*j**2. Factor p(r).
-(r + 1)*(r + 22)/6
Let r = -25933/3 + 8645. Solve -150 - r*h**2 - 20*h = 0.
-15
Let v(j) be the third derivative of j**7/5880 - j**6/2520 - j**5/840 + j**4/168 + 13*j**3/6 - 18*j**2. Let b(g) be the first derivative of v(g). Factor b(l).
(l - 1)**2*(l + 1)/7
Factor 0*m + 0 - 1/5*m**5 - 216/5*m**2 - 18/5*m**4 - 108/5*m**3.
-m**2*(m + 6)**3/5
Let i(s) be the second derivative of 5/12*s**4 + 0 + 0*s**2 + 5/6*s**3 - 8*s. Find u, given that i(u) = 0.
-1, 0
Let p(k) be the second derivative of k**4/78 - 4*k**3/13 - k**2 + 42*k. Find h, given that p(h) = 0.
-1, 13
Suppose -3*p = -5*p - 32. Let o be -1 + -1 + p/(-5). Determine j, given that 0 + 2/5*j**2 + o*j = 0.
-3, 0
Let d(z) be the second derivative of 7/45*z**5 + 10/27*z**3 + 17*z + 11/27*z**4 + 2/135*z**6 + 0*z**2 + 0. Suppose d(t) = 0. Calculate t.
-5, -1, 0
Let d = -78701/8 + 9838. Factor d*q**3 - 1/2*q + 1/8*q**4 + 0*q**2 + 0.
q*(q - 1)*(q + 2)**2/8
Let f = -80 + 112. Let f*u + 3*u**2 + 192 + 10*u - 21*u + 27*u = 0. Calculate u.
-8
Let a(w) be the first derivative of -w**5/10 + 13*w**4/8 + 32*w**3/3 + 17*w**2 - 480. Find v, given that a(v) = 0.
-2, 0, 17
Suppose 4 = -120*h + 122*h + 5*u, 0 = 5*u. Deter