r -18/5 + 3/5*v**m + 3/5*v.
3*(v - 2)*(v + 3)/5
Factor 55*z**2 - 3*z**3 + 67*z**2 - 697*z - 8*z**2 + 460*z - 951*z + 1944.
-3*(z - 18)**2*(z - 2)
Suppose 0*i = 5*i - 25. Let -25 + 55*o**2 + 150 - i*o**3 - 81*o - 94*o = 0. What is o?
1, 5
Let t(y) be the first derivative of 0*y - 4/3*y**3 + 6*y**2 - 4. Factor t(l).
-4*l*(l - 3)
Let y(z) be the second derivative of z**7/315 - 8*z**6/225 + 17*z**5/150 - z**4/9 + z - 24. Solve y(o) = 0 for o.
0, 1, 2, 5
Let r(j) = j**4 - j**3 + j**2 - j + 2. Let s(p) = 20*p**4 - 42*p**3 + 24*p**2 + 14*p + 12. Let a(z) = -28*r(z) + 2*s(z). Find y, given that a(y) = 0.
-1, 2/3, 1, 4
Let v = 162 + -158. Suppose -v*y + y = 3*f - 3, y = 1. What is q in -1/5*q**5 + 0*q + 1/5*q**3 + 0*q**4 + f + 0*q**2 = 0?
-1, 0, 1
Let o(r) = r**2 - 22. Let w be o(0). Let h(s) = s + 32. Let y be h(w). Factor 2*q**4 + 76*q - 112*q + y*q**4 - 34*q**3 + 8 - 10*q**3 + 60*q**2.
4*(q - 1)**3*(3*q - 2)
Let r be (-1 + (-35)/(-32))*82/164. Let o = r + 229/576. Factor o*w - 2/9*w**2 - 2/9.
-2*(w - 1)**2/9
Let t = 59 + -49. Let x be (0 + (-15)/t)*(-4)/10. Solve 6/5 - 3*o + 12/5*o**2 - x*o**3 = 0 for o.
1, 2
Let j be (-28)/(-4) - -1 - 0. Let p = j - 6. Factor -i + 0*i**2 + i**3 + 2 - 6*i**2 + 4*i**p.
(i - 2)*(i - 1)*(i + 1)
Suppose 0 = 2*g + 5*h + 1, 0 = 2*g - 5*g - 4*h + 2. Suppose 6*c = 8*c - 6. Let 12*k + 0*k**2 - c*k**g - 10*k + k**3 = 0. Calculate k.
0, 1, 2
Factor 4*p**2 - 169 + 788 - 116*p - 219.
4*(p - 25)*(p - 4)
Suppose -32*a - a - 60847 + 60775 - 3*a**2 = 0. Calculate a.
-8, -3
Let y(b) be the third derivative of -b**7/16380 + b**6/1560 - b**5/390 - 11*b**4/24 - 2*b**2. Let x(n) be the second derivative of y(n). Factor x(u).
-2*(u - 2)*(u - 1)/13
Let w(k) = k**2 + 2*k - 8. Let a be w(2). Let s(v) be the first derivative of -2/21*v**3 + 0*v**2 + a*v + 2/35*v**5 + 0*v**4 + 7. Factor s(t).
2*t**2*(t - 1)*(t + 1)/7
Let k(l) be the second derivative of l**4/18 + 22*l**3/9 - 23*l**2/3 - 543*l. Solve k(v) = 0 for v.
-23, 1
Let w(u) be the second derivative of u**8/504 - u**7/315 - u**6/180 + u**5/90 + 4*u**2 + 7*u. Let y(r) be the first derivative of w(r). Factor y(f).
2*f**2*(f - 1)**2*(f + 1)/3
Solve 28900/9 + 340/9*z + 1/9*z**2 = 0.
-170
Let g(f) be the second derivative of 0 - 1/4*f**4 - 9*f - 2/3*f**3 - 2*f**2. Let s(a) = a**2 + a. Let p(h) = -g(h) - 4*s(h). Factor p(u).
-(u - 2)*(u + 2)
Suppose -2*l = 2*w - 14 - 56, -2*l = 5*w - 70. Find o, given that -l*o**4 + 20*o**4 + 11*o**4 + 2*o**5 = 0.
0, 2
Let h(v) = 15*v**4 + 89*v**3 + 75*v**2 - v. Let z(d) = 5*d**4 + 30*d**3 + 25*d**2. Let s(q) = -6*h(q) + 17*z(q). Factor s(a).
-a*(a + 2)*(a + 3)*(5*a - 1)
Let a = -3779/90 - -42. Let v(g) be the second derivative of -g + 1/15*g**5 + 1/9*g**3 + 0*g**2 - 5/36*g**4 + 0 - a*g**6. Factor v(n).
-n*(n - 2)*(n - 1)**2/3
Let k(m) = 77*m**3 + 1109*m**2 + 1381*m + 463. Let n(r) = 38*r**3 + 554*r**2 + 690*r + 230. Let d(i) = -2*k(i) + 5*n(i). Determine f, given that d(f) = 0.
-14, -2/3
Let r(n) be the second derivative of -n**5/8 - 25*n**4/4 - 105*n**3 - 490*n**2 - 3*n - 30. Factor r(a).
-5*(a + 2)*(a + 14)**2/2
Suppose -4*b - 5*d + 41 = 0, 4*b + 3*d = 5*d + 34. Suppose 0 = -4*v + b + 3. Factor 0 + 0*w - 3/4*w**2 - 3/4*w**v.
-3*w**2*(w + 1)/4
Let n(o) = o**4 + o**2 + o + 2. Let w(h) = 36*h**5 + 38*h**4 + 17*h**3 - 4*h**2 - 6*h - 12. Let q(c) = 6*n(c) + w(c). Factor q(t).
t**2*(2*t + 1)**2*(9*t + 2)
Factor 32*u + 56*u + 3*u**3 - 132*u**2 + 2*u + 39*u.
3*u*(u - 43)*(u - 1)
Factor -33/2*o + 0 + 1/2*o**2.
o*(o - 33)/2
Let q be (-2)/6*-9*(-3)/9. Let y be q/(-2)*0/2 - 0. Suppose y - h**2 + 3/4*h**3 - h = 0. Calculate h.
-2/3, 0, 2
Let k(i) be the first derivative of 0*i - 10 - 4/9*i**3 - 1/3*i**2 - 1/6*i**4. Let k(q) = 0. What is q?
-1, 0
Let w = 1 - -4. Let k(y) = -3*y**2 + 5*y - 5. Let m(d) = 2*d**2 - 3*d + 3. Let p(s) = w*m(s) + 3*k(s). Factor p(i).
i**2
Let 17*g + 31*g - 39 - 4*g**2 + 8*g**2 - 13*g**2 + 0*g**2 = 0. Calculate g.
1, 13/3
Let f = -127/6 - -53/2. Let u(l) be the first derivative of 1 - 1/6*l**4 - 4*l**2 - f*l - 4/3*l**3. Suppose u(v) = 0. What is v?
-2
Let f(n) = 29*n**2 + 10*n + 48. Let j(c) = 82*c**2 + 28*c + 144. Let p(k) = -17*f(k) + 6*j(k). Factor p(r).
-(r - 6)*(r + 8)
Let h(n) = 2*n. Let y be h(4). Suppose g - y = -3*j, 2*g - 5*g = 5*j - 16. Find f, given that -1/2 - f - 1/2*f**g = 0.
-1
Let q(g) be the first derivative of g**6/360 - g**5/40 + g**4/12 + 4*g**3 - 2. Let i(t) be the third derivative of q(t). Factor i(s).
(s - 2)*(s - 1)
Let f(h) be the second derivative of -h**6/55 + 21*h**5/110 - 13*h**4/22 - 3*h**3/11 + 54*h**2/11 - 15*h - 10. Solve f(g) = 0 for g.
-1, 2, 3
Let y = -71 + 74. Solve -14*m - 4*m**3 - m**5 + 19*m**4 + 4 + 16*m**2 + y*m**5 - 23*m**4 = 0.
-2, 1
What is r in -16/3*r**4 - 1/3*r**5 - 30*r**2 - 27*r**3 + 108*r + 216 = 0?
-6, -3, 2
Suppose 289*b + 158*b - 765 - 129 = 0. Suppose 0 + 0*m - 1/2*m**b - 3/4*m**3 - 1/4*m**4 = 0. What is m?
-2, -1, 0
Let h(r) be the second derivative of 4*r - 1/7*r**7 - 3/4*r**4 + 0 + 3/20*r**5 + 1/2*r**3 + 3/10*r**6 + 0*r**2. Suppose h(p) = 0. What is p?
-1, 0, 1/2, 1
Let k = -19429/58 - -335. Let d = k + 113/174. Factor -8/3*j**2 - 7/3*j + d*j**4 + 1/3*j**5 - 2/3 - 2/3*j**3.
(j - 2)*(j + 1)**4/3
Let y(m) be the second derivative of -1/10*m**6 + 1/4*m**4 + 0 + 3/70*m**5 + 0*m**2 - 14*m - 1/7*m**3. Solve y(v) = 0.
-1, 0, 2/7, 1
Let x(k) = 4*k - 32. Suppose 0 = -3*c + 28 - 4. Let l be x(c). What is h in l - 4/7*h**2 + 2/7*h + 2/7*h**3 = 0?
0, 1
Let z(l) be the third derivative of 25*l**2 + 0 - 1/3*l**4 + 0*l**3 + 0*l + 1/30*l**5. Factor z(x).
2*x*(x - 4)
Let r(p) = 3*p**5 - 3*p**4 + p**3 - p**2 - 4*p - 10. Let n(o) = o**5 - o**4 - o - 3. Let c(t) = -7*n(t) + 2*r(t). Determine s so that c(s) = 0.
-1, 1
Let l(o) be the first derivative of o**6/900 + 43*o**3/3 - 27. Let q(n) be the third derivative of l(n). Factor q(a).
2*a**2/5
Let u(b) be the third derivative of -b**6/24 - b**5/4 + 10*b**3/3 + 315*b**2. Factor u(h).
-5*(h - 1)*(h + 2)**2
Find t, given that -38*t**5 - 52*t - 70*t**5 + 46*t**2 - 311*t**2 - 1440*t**3 + 106*t**2 - 313*t**2 - 1512*t**4 = 0.
-13, -1/3, 0
Find x, given that 4/7*x**5 + 0 - 100/7*x + 96/7*x**3 + 40/7*x**4 - 40/7*x**2 = 0.
-5, -1, 0, 1
Let t(m) be the first derivative of 0*m - 2/5*m**3 + 9/10*m**2 + 1/20*m**4 + 9. Factor t(n).
n*(n - 3)**2/5
Let r(p) be the first derivative of 3*p**6 + 22*p**5/5 - 61*p**4/2 - 46*p**3/3 + 52*p**2 + 24*p - 156. Suppose r(c) = 0. Calculate c.
-3, -1, -2/9, 1, 2
Let b(g) be the first derivative of -3/2*g**4 + 0*g - g**3 + 27 + 0*g**2 - 3/5*g**5. Solve b(t) = 0.
-1, 0
Solve -4 + 70/3*z - 8/3*z**4 - 100/3*z**2 + 50/3*z**3 = 0 for z.
1/4, 1, 2, 3
Let 24/7*r - 36/7 - 4/7*r**2 = 0. Calculate r.
3
Let c(x) be the third derivative of -x**7/42 + x**6/6 - x**2 - 234*x. Solve c(v) = 0.
0, 4
Let m(c) = 25*c**3 - 578*c**2 + 436*c - 72. Let s(n) = n**2 + n - 2. Let g(j) = 5*m(j) + 40*s(j). Solve g(u) = 0.
2/5, 22
Let 306/11*x**2 + 403/11*x - 7/11*x**3 + 90/11 = 0. Calculate x.
-1, -2/7, 45
Solve -2/9*g**2 - 32/9 - 16/9*g = 0.
-4
Let j(t) = -t - 2. Let y be j(-5). Suppose -3*s + 4*n = -2*s - 22, -3*s + 2*n = -16. Factor -q**s + 2*q - q - y*q + 3*q**3.
q*(q - 1)*(3*q + 2)
Let z(b) be the third derivative of -10/3*b**3 - 1/42*b**7 + 14*b**2 - 5/4*b**5 + 7/24*b**6 + 65/24*b**4 + 0 + 0*b. Factor z(w).
-5*(w - 4)*(w - 1)**3
Let l = -2264/7 + 324. Solve -12/7*y + 36/7 - l*y**3 - 20/7*y**2 = 0.
-3, 1
Let w = -15 + 27. Solve 11*u**3 - w + 13*u + 14*u**2 + 7*u**2 - 25*u + u**3 - 9*u**4 = 0.
-1, -2/3, 1, 2
Let n(v) = 4*v**2 + 98*v + 182. Let i(k) = k**2 + 2*k - 2. Let z(h) = -i(h) - n(h). Let z(x) = 0. What is x?
-18, -2
Let j(a) = a + 9. Let q be j(-9). Suppose q*l + l = 50. Find o, given that 47*o**3 - 3*o**4 + 0*o + 3*o + 3*o**2 - l*o**3 = 0.
-1, 0, 1
Let z(h) be the second derivative of 1/35*h**5 + 0*h**2 + 1/28*h**4 - 1/42*h**3 - 3*h + 0. Let z(p) = 0. Calculate p.
-1, 0, 1/4
Let c(r) be the first derivative of -14*r**6/3 - 52*r**5 - 109*r**4 + 148*r**3/3 + 232*r**2 + 112*r + 125. Find p, given that c(p) = 0.
-7, -2, -1, -2/7, 1
Let g(v) be the third derivative of v**6/30 + v**5/15 - 2*v**4/3 - 8*v**3/3 - 2*v**2 - 111. Let g(u) = 0. Calculate u.
-2, -1, 2
Let l = 209 - 411/2. Let b = l - 17/6. Suppose 8/3*t**2 + 0 - b*t**3 - 8/3*t = 0. Calculate t.
0, 2