 0.
0, 3
Let l(w) be the first derivative of -w**5/5 + 7*w**4/4 - 5*w**3/3 - 7*w**2/2 + 6*w - 87. Factor l(t).
-(t - 6)*(t - 1)**2*(t + 1)
Let v(o) = -o**3 + 11*o**2 - 11*o + 15. Let s be v(10). Factor -18*z**3 - s*z**4 - 5*z**4 - 12*z**2 + 6*z**4 + 2*z**3.
-4*z**2*(z + 1)*(z + 3)
Let w(l) be the third derivative of -l**7/945 - l**6/540 + l**5/90 + l**4/108 - 2*l**3/27 - 39*l**2 - l. Solve w(t) = 0 for t.
-2, -1, 1
Factor -9/4*i + 1/4*i**2 + 0.
i*(i - 9)/4
Let t(w) be the second derivative of -3/5*w**5 - 12*w + 0*w**3 + 2/3*w**4 + 0*w**2 + 2/15*w**6 + 0. Let t(r) = 0. Calculate r.
0, 1, 2
Let c(d) be the second derivative of 0*d**2 + 2/15*d**3 - 2/75*d**6 - 1/25*d**5 - 7*d + 1/15*d**4 + 0. Suppose c(x) = 0. Calculate x.
-1, 0, 1
Let f = 33547/89416 + -2/11177. Factor -3/2 - 3/8*u**3 + f*u + 3/2*u**2.
-3*(u - 4)*(u - 1)*(u + 1)/8
Let v(j) = j**3 - j**2 + j + 1. Let x(o) = -77*o**2 + 1 - 11*o + 67*o**2 - 4 + o**3 - 1. Let s(h) = -2*v(h) + x(h). Suppose s(k) = 0. What is k?
-6, -1
Let f be 42/(-189)*(-54)/36. Factor -f*b**2 + 0 - 4/3*b.
-b*(b + 4)/3
Let q = -193 - -195. Let k(g) be the third derivative of -1/225*g**5 + 7/180*g**4 - 7/900*g**6 + 0 + 2/45*g**3 + 0*g + 3*g**q. Determine p, given that k(p) = 0.
-1, -2/7, 1
Factor 0*t - 9/2*t**4 + 0*t**2 - 1/2*t**5 - 4*t**3 + 0.
-t**3*(t + 1)*(t + 8)/2
Let u(o) be the first derivative of 5*o**5 - 45*o**4/2 - 55*o**3 - 25*o**2 - 43. Factor u(a).
5*a*(a - 5)*(a + 1)*(5*a + 2)
Factor 5/4*b + 37/8*b**2 + 4*b**3 + 0 + 5/8*b**4.
b*(b + 1)*(b + 5)*(5*b + 2)/8
Let p(w) be the second derivative of -5/4*w**4 + 5/3*w**3 + 1/6*w**6 + 0*w**2 - 11*w + 0*w**5 + 0. Factor p(q).
5*q*(q - 1)**2*(q + 2)
Let o(w) be the third derivative of 11*w**6/24 + 25*w**5/4 + 65*w**4/6 - 10*w**3 + 377*w**2. Let o(a) = 0. Calculate a.
-6, -1, 2/11
Let q be (-9)/6 - 0 - (-15)/(-25). Let t = 43/10 - q. Find g, given that -18/5*g - t*g**2 - 28/5*g**3 - 12/5*g**4 - 4/5 - 2/5*g**5 = 0.
-2, -1
Let y(p) = 5*p - 3*p**2 + 2*p - 3 - 6*p**3 - 4*p. Let k(r) = -r**3 + r - 1. Let g(l) = 3*k(l) - y(l). Factor g(w).
3*w**2*(w + 1)
Suppose -19*r = -6 + 6. Let a(h) be the third derivative of -1/90*h**5 + 5/144*h**4 + 0*h + r - 1/18*h**3 + 7*h**2 + 1/720*h**6. Factor a(g).
(g - 2)*(g - 1)**2/6
Let i(x) be the second derivative of x**6/60 - x**5/40 - x**4/12 + 85*x. Factor i(m).
m**2*(m - 2)*(m + 1)/2
Let z(y) = -9*y**5 + 12*y**4 + 24*y**3 - 52*y**2 + 15*y + 5. Let h(f) = f**5 + f**4 + f**2 - f - 1. Let j(v) = -10*h(v) - 2*z(v). Determine t so that j(t) = 0.
-2, 0, 1/4, 1, 5
Let u be (0*3/18*3)/1. Let j(r) be the second derivative of r + 1/168*r**7 + 0 + u*r**2 + 1/24*r**4 - 1/60*r**6 - 1/24*r**3 + 0*r**5. Factor j(i).
i*(i - 1)**3*(i + 1)/4
Let x(h) be the first derivative of 3*h**2 + 10 + 1/5*h**3 + 15*h. Suppose x(t) = 0. What is t?
-5
Let s(g) be the first derivative of 9/4*g**2 + 1/2*g**3 - 6*g - 16. Find b, given that s(b) = 0.
-4, 1
Suppose 71*h = -69*h + 142*h. Let b(v) be the third derivative of 1/210*v**6 + 0*v + 0*v**5 + 0 + 0*v**3 + 0*v**7 + h*v**4 - 1/588*v**8 - 4*v**2. Factor b(z).
-4*z**3*(z - 1)*(z + 1)/7
Suppose 2 = 3*y + 2*a, a - 1 + 0 = 3*y. Suppose -3*b = -y*b - 6. Factor w**2 - b*w**4 + 4*w**4 - w**4 + 2*w**3.
w**2*(w + 1)**2
Factor -6*h**2 + 6 - 2/3*h**3 + 2/3*h.
-2*(h - 1)*(h + 1)*(h + 9)/3
Factor -2880*g**3 - 60*g - 5/3 - 720*g**2.
-5*(12*g + 1)**3/3
Let v(d) be the second derivative of -d**6/180 - 9*d**5/20 + 7*d**4/3 - 85*d**3/18 + 19*d**2/4 + 420*d. Determine c so that v(c) = 0.
-57, 1
Factor 98*y - 49*y**4 + 14*y**3 + 11*y**3 + 13*y**3 - 210*y**2 + 1372 + 47*y**4.
-2*(y - 7)**3*(y + 2)
Let u(o) be the third derivative of o**5/12 + o**4/3 - o**3/2 + 2*o**2 + 26. Let f(k) = k**2 + k - 1. Let m(a) = 6*f(a) - u(a). Solve m(w) = 0.
-1, 3
Determine u so that 8/9 + 8/9*u + 2/9*u**2 = 0.
-2
Let v = 40 - 35. Let y be (-57)/(-36) + v/30. Let y*g**5 + 29/4*g**3 - 2 - 9*g + 15/2*g**4 - 11/2*g**2 = 0. Calculate g.
-2, -1, -2/7, 1
Let q(i) be the third derivative of 0*i**4 + 0 + 4/9*i**3 + 0*i - i**2 - 1/90*i**5. Factor q(r).
-2*(r - 2)*(r + 2)/3
Let y(f) be the first derivative of f**5/12 + 5*f**4/6 + 10*f**3/3 + 12*f**2 + 14. Let d(p) be the second derivative of y(p). Factor d(t).
5*(t + 2)**2
Let b(z) be the second derivative of 0*z**2 + 1/5*z**5 + 2/3*z**3 - 2/3*z**4 + 0 + 10*z. Factor b(p).
4*p*(p - 1)**2
Let j(l) be the first derivative of -l**4 - 68*l**3 - 1350*l**2 - 2500*l - 176. Factor j(b).
-4*(b + 1)*(b + 25)**2
Let c(z) = -3*z - 11. Let k be c(-5). Suppose k*g + 18 = 18. Factor -2/7*w**4 - 4/7*w**3 + 0*w - 2/7*w**2 + g.
-2*w**2*(w + 1)**2/7
Let o be (0 + -3)/18 + 750/180. Let a(y) be the second derivative of -1/21*y**o + 2/105*y**6 - 2/35*y**5 + 4/21*y**3 + 0*y**2 - 9*y + 0. Solve a(b) = 0 for b.
-1, 0, 1, 2
Suppose 0 = -s + 2*d - 6, -s + 2*d - 6*d = -24. Let g be (-76)/(-36) + s/(-36) - 0. Let -3/2*k - 1/2*k**g - 1 = 0. Calculate k.
-2, -1
Factor -3*l**3 - 7*l**2 - 80 + 63*l + 15 - 20*l**2 + 32.
-3*(l - 1)**2*(l + 11)
Let t(k) be the first derivative of 5*k**3/3 - 5*k**2 + 5*k - 81. Suppose t(a) = 0. Calculate a.
1
Suppose 976 = -12*x + 1000. Factor -1/4*u**x + 1/4*u**4 + 0 + 1/4*u**3 - 1/4*u.
u*(u - 1)*(u + 1)**2/4
Let b = -18 - -130. Let y = -112 + b. Factor 0 - 1/3*d**3 + 0*d**2 + y*d - 1/6*d**4.
-d**3*(d + 2)/6
Suppose 23*o = 20*o. Let l(u) be the second derivative of o*u**2 + 0 + 1/30*u**5 - 1/6*u**4 + 2/9*u**3 + 4*u. Factor l(n).
2*n*(n - 2)*(n - 1)/3
Let h(c) be the second derivative of -c**7/105 - 4*c**6/75 - 3*c**5/50 - 97*c. Factor h(l).
-2*l**3*(l + 1)*(l + 3)/5
Let r = -4 + 4. Suppose 3*u - 9 + 0 = r. Find s such that -5*s**4 - 2*s**5 - 6*s**4 - s**2 + 6*s**4 - 4*s**u = 0.
-1, -1/2, 0
Let d(o) be the first derivative of -30*o**3 - 38 - 40*o + 35/4*o**4 + 50*o**2 - o**5. Factor d(r).
-5*(r - 2)**3*(r - 1)
Let w(l) be the second derivative of -l**5/140 + 7*l - 3. Factor w(m).
-m**3/7
Let z(h) = 9*h**3 - 10*h**2 - 9*h + 10. Let j(x) = -10*x**3 + 10*x**2 + 10*x - 10. Suppose -30 = -5*l - l. Let b(v) = l*z(v) + 4*j(v). Solve b(q) = 0.
-1, 1, 2
Let f(c) be the first derivative of 0*c - 2*c**2 - 1/40*c**6 - 1/2*c**4 - 1/5*c**5 - 3 + 0*c**3. Let w(d) be the second derivative of f(d). Factor w(a).
-3*a*(a + 2)**2
Determine o so that 24*o + 4 + 31*o**2 + 30*o**2 - 64*o**2 + 23*o**2 = 0.
-1, -1/5
Let w(z) be the third derivative of z**8/1512 + 2*z**7/315 + z**6/270 - 8*z**5/135 - z**4/36 + 10*z**3/27 - 8*z**2 + 4*z. Suppose w(k) = 0. What is k?
-5, -2, -1, 1
Let d be 9*(-56)/(-24)*2/(-19). Let q = d - -187/76. Factor 1/4*r**3 - 1/4*r**2 + q - 1/4*r.
(r - 1)**2*(r + 1)/4
Suppose 0 - 12/5*u**3 + 8/5*u - 4/5*u**4 + 4/5*u**2 + 4/5*u**5 = 0. Calculate u.
-1, 0, 1, 2
Factor 12/5*j + 16/5 + 2/5*j**2.
2*(j + 2)*(j + 4)/5
What is q in -95/3*q**3 + 5/3*q**4 - 35*q + 0 - 205/3*q**2 = 0?
-1, 0, 21
Let z be (12/(-10) - (-180)/150)/5. Factor z + 5/6*h**3 + 0*h + 5/6*h**2.
5*h**2*(h + 1)/6
Suppose 4*h = 5*n - 35, 3*n + 5*h = -0*n - 16. Suppose n*u = 5*w - 3, 2*u + 1 = 9. Suppose 0*d**2 + 1/2*d**w + 0 + 0*d = 0. What is d?
0
Suppose -k + 2*i + 394 = -5*k, 202 = -2*k - 2*i. Let s = 98 + k. Factor -54/7 + 54/7*n + 2/7*n**3 - 18/7*n**s.
2*(n - 3)**3/7
Suppose 160 - 1/5*n**3 - 64*n - 38/5*n**2 = 0. Calculate n.
-20, 2
Let i be (-2 + ((-2)/1 - -3))*-3. Solve -2*w**2 + w**i + 12*w**2 - 4*w**2 + 4 + 9*w = 0 for w.
-4, -1
Factor 0*z**2 + 0*z - 1/2*z**3 - 2/5*z**5 - 9/10*z**4 + 0.
-z**3*(z + 1)*(4*z + 5)/10
Let b(a) = -2*a + 20. Let p be b(-10). Determine z, given that -p*z - 13 + 2*z**2 - 4*z + 2*z**2 + 53 = 0.
1, 10
Let t(n) be the third derivative of n**5/30 + n**4/6 - 5*n**3 - 8*n**2. Factor t(a).
2*(a - 3)*(a + 5)
Suppose 0 = 36*a - 33*a. Let g = 475/2 - 237. Factor a + 1/2*w - g*w**2.
-w*(w - 1)/2
Let k(z) be the third derivative of 0*z + 1/15*z**4 + 0*z**3 - z**2 - 1/25*z**5 + 0 + 1/150*z**6. Solve k(o) = 0.
0, 1, 2
Factor -81/11*t**2 + 2187/11*t + 1/11*t**3 - 19683/11.
(t - 27)**3/11
Let q(j) be the second derivative of -j**5/15 - 266*j**4/9 - 35378*j**3/9 - 67*j. Let q(r) = 0. What is r?
-133, 0
Let u(c) be the first derivative of -3/22*c**4 + 14/33*c**3 + 0*c**2 - 3 - 8/11*c. Find t, given that u(t) = 0.
-2/3, 1, 2
Let z be (-84)/5292*(-6)/4. Let p(b) be the second derivative of -z*b**4 - 9*b + 0*b**2 + 0*b**3 + 0. Factor p(g).
-2*g**