
Let d(z) be the first derivative of -z**4/14 + 18*z**3/7 + 266. Determine m, given that d(m) = 0.
0, 27
Let u(q) be the third derivative of 0*q - 2/105*q**7 + 1/10*q**6 + 0*q**4 - 21*q**2 + 0 + 0*q**3 + 4/15*q**5. Factor u(d).
-4*d**2*(d - 4)*(d + 1)
Let w(k) = 2*k**3 - 14*k**2 + 18*k + 10. Let t be w(5). Factor 6/19*s**3 + 0 + t*s - 4/19*s**4 + 4/19*s**2.
-2*s**2*(s - 2)*(2*s + 1)/19
Let k(d) be the first derivative of -5*d**4/4 - 5*d**3/3 + 25*d**2/2 - 15*d + 122. Solve k(y) = 0.
-3, 1
Factor -1/3*w**2 + 40/3 - w.
-(w - 5)*(w + 8)/3
Suppose 30*f + 9 = 33*f. Let z(m) = m**2 + 5*m + 4. Let r(w) = 4*w - w - 2*w + 1. Let y(i) = f*z(i) - 15*r(i). Factor y(a).
3*(a - 1)*(a + 1)
Factor 35041*f**4 + 2*f + 37*f**3 - 18*f - 35036*f**4 - 26*f**2.
f*(f - 1)*(f + 8)*(5*f + 2)
Let d(b) be the second derivative of -3*b**5/10 - 43*b**4/30 - 8*b**3/5 + 4*b**2/5 + 40*b + 2. Find n such that d(n) = 0.
-2, -1, 2/15
Suppose -3*a = -9*a - 372. Let z = a + 65. Factor 0 + z*d**5 + 3/5*d**3 - 6/5*d**2 + 24/5*d**4 + 0*d.
3*d**2*(d + 1)**2*(5*d - 2)/5
Let b(m) be the second derivative of -m**5/60 - 29*m**4/12 - 841*m**3/6 - 24389*m**2/6 - 115*m. Find w such that b(w) = 0.
-29
Let y(j) be the third derivative of j**8/2016 - j**7/315 - j**6/120 + j**5/90 + 5*j**4/144 + 31*j**2. What is k in y(k) = 0?
-1, 0, 1, 5
Let t(z) = -25*z + 41. Let l be t(7). Let h = 942/7 + l. Factor h + 0*u**2 + 6/7*u - 2/7*u**3.
-2*(u - 2)*(u + 1)**2/7
Let t = 15 - 6. Let -18*k - 2*k**4 - 7*k + 10*k + 3*k**3 - 6 - t*k**2 + 5*k**4 = 0. What is k?
-1, 2
Let q be -2 - 3/(-3) - -3. Let l**q - 52 + 52 + l = 0. What is l?
-1, 0
Let d(p) = p**3 + 9*p**2 + 7*p - 6. Let o be d(-8). Suppose -o*m + 10*m - 7*m**3 + 2*m**4 + m**3 = 0. What is m?
-1, 0, 2
Let n(u) = -32*u**4 + 104*u**3 - 73*u**2 - 9*u + 1. Let q(j) = j**4 - 2*j**3 - j + 1. Let t(h) = 2*n(h) + 22*q(h). Solve t(z) = 0 for z.
-3/7, 1/3, 2
Let y = 120 - 117. Factor -f**4 - 7*f**y - 3*f**3 - 2*f + 8*f**3 - 7*f**3 + 9*f**2 + 3*f**5.
f*(f - 1)**2*(f + 2)*(3*f - 1)
Let w(s) be the second derivative of -s**5/240 - s**4/48 - s**3/24 + 7*s**2/2 - 12*s. Let n(q) be the first derivative of w(q). Let n(d) = 0. Calculate d.
-1
Let p(w) = w**3 + 34*w**2 + 31*w - 70. Let i(u) = 9*u**3 + 273*u**2 + 246*u - 561. Let g(b) = 4*i(b) - 33*p(b). Factor g(l).
3*(l - 11)*(l - 1)*(l + 2)
Let 28*s + 14*s**3 - 6*s + 9*s**2 - 6*s**2 + 3 + 1 + 29*s**2 = 0. Calculate s.
-1, -2/7
Suppose -i + 7*z + 23 = 4*z, 3*i - 61 = z. Let x be (-10)/i - (-1 - 1). Suppose 0*w**2 - x*w + 0 + 3/2*w**3 = 0. Calculate w.
-1, 0, 1
Let p(d) = d**2 - 20*d - 222. Let v be p(-8). Let a be ((-6)/(-3))/(16/4). Factor -a*t - 1/4*t**v + 3/4.
-(t - 1)*(t + 3)/4
Let o(x) = 8*x - 6. Let l = 17 - 13. Let z be o(l). Factor 0*h**3 + 27*h - z*h - h**3.
-h*(h - 1)*(h + 1)
Let q = -101 - -103. Let s(l) be the third derivative of 1/20*l**5 + l**3 + 0*l + 0 - 3/8*l**4 - 4*l**q. Determine t so that s(t) = 0.
1, 2
Suppose -3 = -h - 2*d, -4*h + 5 = 5*d - 7. Suppose -7*z + 10*z = 0. Find j, given that -2/3*j**h + z + 2/3*j**2 + 0*j = 0.
0, 1
Let f = -11/199 + 221/398. Determine b, given that 0 - b - f*b**2 + 1/2*b**3 = 0.
-1, 0, 2
Suppose 9*u = 36 + 9. Let f(b) be the second derivative of 0 + 2/21*b**3 + 0*b**2 - 1/35*b**u + 1/42*b**4 - 1/105*b**6 + 4*b. Let f(g) = 0. Calculate g.
-2, -1, 0, 1
Solve 6*o**3 + 3/4*o**4 - 12 + 45/4*o**2 - 6*o = 0 for o.
-4, -1, 1
Let m(i) = -3*i**2 - 31*i - 33. Let l be m(-9). Let h be 1 + 1*(-1)/4. Factor 0*v**l + h*v**4 + 0 - 9/4*v**2 + 3/2*v.
3*v*(v - 1)**2*(v + 2)/4
Let z(x) = 20*x**2 - 156*x - 312. Let d(r) = -2*r**2 + r. Let w(s) = 8*d(s) + z(s). Determine u, given that w(u) = 0.
-2, 39
Solve 71870*l**2 - 71858*l**2 + 2 - 14*l**3 - 2 + 2*l = 0 for l.
-1/7, 0, 1
Let g = 1226 - 1226. Let y(h) be the second derivative of g + 2*h - 1/5*h**5 + 2/3*h**3 + 0*h**2 + 0*h**4. Factor y(d).
-4*d*(d - 1)*(d + 1)
Let q(o) be the second derivative of o**4/12 + 4*o**3 + 22*o**2 + 28*o. Factor q(l).
(l + 2)*(l + 22)
Let l be (-1592)/(-6)*(-7 + 4). Let d be 8/(-52)*-1 - l/234. What is r in -16/9*r + d + 2/9*r**2 = 0?
4
Let f(z) be the second derivative of 2*z**7/35 + 26*z**6/75 + 7*z**5/25 - 17*z**4/15 - 4*z**3/5 + 129*z. Suppose f(b) = 0. What is b?
-3, -2, -1/3, 0, 1
Let g = 1233 - 1233. Factor 0 + g*i - 1/3*i**3 + 1/6*i**4 + 1/6*i**2.
i**2*(i - 1)**2/6
Factor 5*m**2 + 1/3*m**4 + 13/3*m + 4/3 + 7/3*m**3.
(m + 1)**3*(m + 4)/3
Let d(w) be the third derivative of -w**5/330 + 23*w**2 - w. Factor d(c).
-2*c**2/11
Let g(p) be the second derivative of p**4/24 + 17*p**3/12 + 4*p**2 - 113*p. What is y in g(y) = 0?
-16, -1
Let z = -8915/2 + 4458. Solve 1/4*m + z - 1/2*m**2 - 1/4*m**3 = 0 for m.
-2, -1, 1
Suppose 0 + 4 = j. Factor j*s**2 + 0*s + s + 2*s + s - 3*s**3.
-s*(s - 2)*(3*s + 2)
Let v(c) be the second derivative of -c**6/15 + 9*c**5/5 - 31*c**4/2 + 80*c**3/3 + 192*c**2 + 15*c. Determine n so that v(n) = 0.
-1, 3, 8
Let b(x) be the second derivative of x**8/3360 - x**6/200 - x**5/75 - x**4/80 - 11*x**2/2 - 6*x. Let l(p) be the first derivative of b(p). Factor l(a).
a*(a - 3)*(a + 1)**3/10
Let w(p) be the third derivative of 1/12*p**6 - 1/6*p**5 - 1/42*p**7 + 1/336*p**8 + 5/24*p**4 + 0*p + 0 - 1/6*p**3 + 9*p**2. Find d, given that w(d) = 0.
1
Factor 210*m + 223*m + 4*m**2 - 458*m - 19*m**2 + 5*m**4 + 5*m**3 - 10.
5*(m - 2)*(m + 1)**3
Let u(r) be the third derivative of r**7/630 - 11*r**6/720 - r**5/40 - r**4/2 + 5*r**2. Let b(m) be the second derivative of u(m). Solve b(p) = 0 for p.
-1/4, 3
Suppose 5*k - 6 = -4*v, -75*k + 5*v + 3 = -76*k. Let -2/3*r**k + 0 - 2*r = 0. Calculate r.
-3, 0
Let g(n) be the second derivative of 0*n**4 + 0 + 0*n**3 + 1/6*n**6 + 28*n - 5/42*n**7 + 0*n**2 + 0*n**5. Factor g(u).
-5*u**4*(u - 1)
Determine v so that -22/9*v - 1/9*v**2 - 85/9 = 0.
-17, -5
Suppose 0 = -3*g + 5 + 22. Let q be (13/6 - 2)/(g/18). Factor 8/3*d + q*d**2 + 16/3.
(d + 4)**2/3
Let o be ((-38)/(-133))/(15/294). Factor o*b**2 - 17/5*b + 4/5 + 8/5*b**4 - 22/5*b**3 - 1/5*b**5.
-(b - 4)*(b - 1)**4/5
Factor -32*i**2 - 4*i**4 - 279 + 279 + 28*i**3 - 64*i.
-4*i*(i - 4)**2*(i + 1)
Let c(g) = g**2 - 20*g + 64. Let a be c(16). Let d(t) be the first derivative of -4/21*t**3 + a*t + 3 - 1/14*t**4 - 1/7*t**2. Factor d(p).
-2*p*(p + 1)**2/7
Let r(m) = -11*m**4 + 199*m**3 + 649*m**2 + 439*m - 20. Let o(h) = 6*h**4 - 99*h**3 - 324*h**2 - 219*h + 12. Let q(y) = -5*o(y) - 3*r(y). Solve q(x) = 0.
-2, -1, 0, 37
Let y be (-686 + 692)*2/38. Let -2/19*l**4 - y*l**2 + 2/19*l + 0 + 6/19*l**3 = 0. Calculate l.
0, 1
Let i(g) = g**2 + 10*g + 3. Let p be i(-10). Let z be (0 - 0)*(-6)/(-12). Let 4 + z + 8*d + 12*d**2 - 4 + 4*d**p = 0. Calculate d.
-2, -1, 0
Let q be (2/(-8))/(70/(-4)). Let c(r) be the second derivative of -1/105*r**6 + 0*r**2 + 0*r**3 - q*r**5 + 4*r + 0*r**4 + 0. Factor c(m).
-2*m**3*(m + 1)/7
Suppose 0*n - 2*f = 2*n - 2, -2*f = -4. Let j = n - -3. Factor 2*l**4 + 2*l**2 - 5*l**3 - 6*l**4 - 3*l**j.
-l**2*(l + 1)*(4*l + 1)
Suppose -5 = 4*k - v, 4*v = -4*k - k + 20. Let c be (-3)/(-9)*k - -1. Suppose u**2 + 4*u - c - 3*u**2 - 1 = 0. Calculate u.
1
Suppose -2 + 523 = -5*d + z, 2*z - 202 = 2*d. Let b = d + 527/5. Suppose 0 - b*n**4 + 6/5*n**3 + 2/5*n**2 - 4/5*n - 2/5*n**5 = 0. Calculate n.
-2, -1, 0, 1
Let v(u) = -65*u**2 - 325*u + 350. Suppose 6*f = -266 + 26. Let w(t) = -5*t**2 - 25*t + 27. Let p(r) = f*w(r) + 3*v(r). Find g, given that p(g) = 0.
-6, 1
Let f = -4 + 9. Determine j so that -544*j**2 + f - 26 - 284*j - 15 + 64*j**3 = 0.
-1/4, 9
Let w = -42082 - -42082. Factor -12/5*i**3 - 42/5*i**4 + 0 - 6*i**5 + 0*i**2 + w*i.
-6*i**3*(i + 1)*(5*i + 2)/5
Let z(n) be the third derivative of 0 + 0*n**5 - 1/224*n**8 + 1/120*n**6 + 0*n**3 + 0*n + 0*n**4 - 1/84*n**7 + 5*n**2. Factor z(a).
-a**3*(a + 2)*(3*a - 1)/2
Let z(t) be the first derivative of 3/35*t**5 + 0*t**2 - 12 + 0*t - 3/28*t**4 + 0*t**3. Suppose z(c) = 0. What is c?
0, 1
Let g(o) be the first derivative of o**7/840 - o**5/30 + 7*o**3/3 - o**2/2 + 39. Let s(h) be the third derivative of g(h). Determine c, given that s(c) = 0.
-2, 0, 2
Let w be 136/40 + 0 + (-3)/(-5). Let s be (-3)/w*48/(-18). Factor 2/9*k**s - 4/9*k - 2/3.
2*(k - 3)*(k + 1)/9
Let y(g) be the third derivative of -2*g**7/105 - g**6/30 + 4*g**5/15 + 2*g**4/3 + 18*g**2. Solve y(r) = 0 for r.
-2