ctor 16*y**2 + 24*y**3 + 4*y**5 + o*y**4 + 3 + 8*y - 4*y - 3.
4*y*(y + 1)**4
Let l = -42 - -42. Suppose -p + j = -l*p, -5*j = -2*p. Suppose -1/2*u + p + 1/2*u**2 = 0. What is u?
0, 1
Let t be (-216)/(-324)*((-14)/63 - 22/(-18)). Let 0 + t*g - 1/3*g**3 + 1/3*g**2 = 0. What is g?
-1, 0, 2
Let b be 72/(-28) + 12/(-28). Let y = 13 - b. Find s, given that -12*s + 100*s**5 - 68*s - y + 180*s**4 - 4*s**3 - 16*s - 164*s**2 = 0.
-1, -2/5, 1
Let q(k) be the third derivative of k**9/100800 + k**8/33600 - k**5/10 + 3*k**2. Let c(p) be the third derivative of q(p). Factor c(n).
3*n**2*(n + 1)/5
Let -j**2 + 0 - 1/2*j**3 - 1/2*j = 0. What is j?
-1, 0
Suppose -3*m + 6*m = 5*v - 13, -5*v - 2*m + 8 = 0. Let q = 3 + 6. Suppose -19*a**v - q - 2*a**2 + 48*a - 3 = 0. Calculate a.
2/7, 2
Let k(h) be the first derivative of 2*h**3 + 0*h**2 + 40 + 1/2*h**4 - 8*h. Factor k(m).
2*(m - 1)*(m + 2)**2
Determine q so that -3*q**4 + 2*q**5 + 66*q**3 - 80*q**2 - 17*q**4 + 0*q**4 + 32*q + 0*q**5 = 0.
0, 1, 4
Suppose 75*l + 55/2*l**4 + 5/2*l**5 - 235/2*l**2 + 25/2*l**3 + 0 = 0. Calculate l.
-10, -3, 0, 1
Let x(k) = 2*k**2 - 11*k - 20. Let l be x(10). Let w be (-2 - -1) + 3 - l/49. Suppose -10/7*h**3 + w*h**2 + 10/7*h - 4/7 = 0. What is h?
-1, 2/5, 1
Let h(c) be the third derivative of c**5/120 + 5*c**4/24 - 57*c**2. Suppose h(m) = 0. Calculate m.
-10, 0
Let m be 2/6 + 396/27. Let t be ((-2)/9*m)/(-2)*3. Find z, given that 2/11*z**3 + 4/11*z**2 - 2/11*z**t + 0*z + 0 - 4/11*z**4 = 0.
-2, -1, 0, 1
Let q(r) be the second derivative of 1/12*r**4 + 1/30*r**5 + 1/180*r**6 + 0*r**2 + 10*r + 0 + 1/6*r**3. Let a(t) be the second derivative of q(t). Factor a(d).
2*(d + 1)**2
Let j(p) be the third derivative of -p**7/105 - p**6/30 + p**2 + 47*p. Factor j(b).
-2*b**3*(b + 2)
Suppose -9*u - 88 = -5*u - 5*f, u + 43 = -4*f. Let p = u - -30. Factor 0*y**2 + 2/3*y**p - 2/3*y + 0.
2*y*(y - 1)*(y + 1)/3
Let w(c) = -5*c**5 + 20*c**4 - 31*c**3 - 10*c**2 + 25*c + 1. Let j(f) = f**5 - 4*f**4 + 6*f**3 + 2*f**2 - 5*f. Let b(z) = 22*j(z) + 4*w(z). Solve b(r) = 0.
-1, 1, 2
Suppose -2*h + 4*p = 12, -8*h - 2*p = -4*h - 6. Let b(f) = f**2 - 6*f + 11. Let d be b(4). Factor 8/11*g**2 + h + 8/11*g**4 - 2/11*g - 12/11*g**d - 2/11*g**5.
-2*g*(g - 1)**4/11
Let 0 + 6*x - 3/7*x**2 = 0. Calculate x.
0, 14
Let n = -126 + 139. Let z be (-1)/2 + n/26. Factor -1/2*h**3 + h - 1/2*h**2 + z.
-h*(h - 1)*(h + 2)/2
Let o(n) = 6*n**2 - 52*n + 342. Let s(q) = 7*q**2 - 52*q + 343. Let b(g) = -5*o(g) + 4*s(g). Solve b(x) = 0.
13
Find z such that -8/11*z**4 + 4/11*z - 2*z**2 + 26/11*z**3 + 0 = 0.
0, 1/4, 1, 2
Let q(m) = m**2 + 90*m + 871. Let s be q(-11). Solve -2/11 + 2/11*c**s + 0*c = 0 for c.
-1, 1
Let b(v) be the second derivative of -v**7/6300 - v**6/900 - v**5/300 + 13*v**4/12 - 13*v. Let c(i) be the third derivative of b(i). Factor c(x).
-2*(x + 1)**2/5
Let y(f) be the first derivative of f**6/1980 - f**5/66 + 25*f**4/132 + 20*f**3/3 - 10. Let s(k) be the third derivative of y(k). Let s(d) = 0. What is d?
5
Let k(f) = 9*f**5 + 5*f**4 - 28*f**3 - 16*f**2 + 4. Let a(h) = -125*h**5 - 70*h**4 + 390*h**3 + 225*h**2 - 55. Let w(t) = -4*a(t) - 55*k(t). Factor w(u).
5*u**2*(u - 2)*(u + 1)*(u + 2)
Let u(t) be the second derivative of t**8/16800 + t**7/3150 - 5*t**4/12 + 11*t. Let y(w) be the third derivative of u(w). Find q such that y(q) = 0.
-2, 0
Suppose 5*x - 30 = 2*x. Suppose -x = -5*j + 25. Factor -7 + j*v**3 + 6*v**4 + 10*v + 3 - 2*v**2 - 17*v**3.
2*(v - 1)**2*(v + 1)*(3*v - 2)
Suppose 27*z + 75 = 30*z. Factor 5*a**3 - 608 + z*a - 25*a**2 + 588 + 15*a.
5*(a - 2)**2*(a - 1)
Let l(y) be the third derivative of -16*y**5/45 + 28*y**4/9 - 98*y**3/9 + 119*y**2. Factor l(z).
-4*(4*z - 7)**2/3
Find t, given that 1/3 + 0*t**3 + 0*t - 2/3*t**2 + 1/3*t**4 = 0.
-1, 1
Let z(r) = 152*r - 454. Let c be z(3). Determine j, given that -j**3 - 1/4 + 1/4*j**c + j = 0.
-1, 1/4, 1
Let j be (-6)/14*(-14)/8. Find n, given that 1/4 + 3/4*n**2 + j*n + 1/4*n**3 = 0.
-1
Let h be (-148)/111*(-6)/16. Let d(b) be the first derivative of 2*b - h*b**3 + b**2 - 1. Find n such that d(n) = 0.
-2/3, 2
Find v, given that 10*v**3 - 79*v**2 - 2*v**4 - 68*v**2 + 159*v**2 = 0.
-1, 0, 6
Let s be -3 - 5/(20/(-32)). Suppose -l + 3 + 2 = -d, -3*l - s*d - 17 = 0. Determine c so that 3 + 8 - 3*c**2 + l = 0.
-2, 2
Let j(i) = -8 + 8*i**2 + 27 - 7*i**3 - i**3 + 17*i + 28*i. Let x(o) = 4*o**3 - 4*o**2 - 22*o - 10. Let d(y) = 2*j(y) + 5*x(y). Suppose d(s) = 0. Calculate s.
-1, 3
Let h = -137 + 140. Let s(f) be the second derivative of -8/15*f**3 - 1/50*f**5 - 4/5*f**2 + 0 + h*f - 1/6*f**4. Let s(j) = 0. Calculate j.
-2, -1
Let k(w) = -w**3 - 8*w**2 - 8*w - 3. Suppose 0*g - g = -3*c + 16, 0 = -4*g - 5*c - 13. Let i be k(g). Factor -1/4*v**i + 0*v + 1/4*v**3 + 0*v**2 + 0.
-v**3*(v - 1)/4
Let z(b) be the first derivative of -3*b**4/2 + 34*b**3/3 - 21*b**2 - 18*b - 137. Factor z(j).
-2*(j - 3)**2*(3*j + 1)
Let v(x) be the second derivative of -x**6/15 + x**5/2 - x**4/2 - 5*x**3/3 + 4*x**2 - 7*x. Factor v(w).
-2*(w - 4)*(w - 1)**2*(w + 1)
Let u(d) be the third derivative of d**8/112 + d**7/70 - 7*d**6/20 - 7*d**5/5 + d**4 + 16*d**3 + 122*d**2. Factor u(k).
3*(k - 4)*(k - 1)*(k + 2)**3
Let z(h) be the first derivative of -h**6/27 + 2*h**5/9 + 5*h**4/18 - 50*h**3/27 - 40*h**2/9 - 32*h/9 - 18. Factor z(y).
-2*(y - 4)**2*(y + 1)**3/9
Let g = 5873/5 - 1174. Factor -6/5*z + 0 + g*z**4 + 6/5*z**3 - 3/5*z**2.
3*z*(z - 1)*(z + 1)*(z + 2)/5
Let s be 1/((-20)/(-48)) - (-2)/(-5). Suppose 0 = s*p - l - 12, 4 = -4*p - 0*l - 5*l. Find o, given that -o**3 - 9/4 - 1/4*o**p + 3*o + 1/2*o**2 = 0.
-3, 1
Factor 310*b**2 - 41*b**3 - 52*b**3 - 145*b**3 + 73*b**3 + 5*b**4.
5*b**2*(b - 31)*(b - 2)
Let b(w) be the first derivative of 28*w**5/5 + 37*w**4 + 236*w**3/3 + 70*w**2 + 24*w - 84. Factor b(h).
4*(h + 1)**2*(h + 3)*(7*h + 2)
Let c(q) be the first derivative of -q**4/2 + q**3/3 + 71. Let c(v) = 0. What is v?
0, 1/2
Let r be 5/4*(-1776)/(-555). Let q(t) be the first derivative of 1/4*t**r + 4 + 0*t + 0*t**2 - 2/3*t**3. Factor q(o).
o**2*(o - 2)
Let v(u) = -u**3 - 2*u. Let x(l) = 10*l**3 + 15*l**2 - 35*l + 25. Let f(r) = 5*v(r) + x(r). Factor f(s).
5*(s - 1)**2*(s + 5)
Determine n so that 9*n**3 - 1/4*n**5 - 19/2*n**2 + 13/4*n + 0 - 5/2*n**4 = 0.
-13, 0, 1
What is f in 5/6*f - 1/6*f**2 + 0 = 0?
0, 5
Let q(n) = 17*n**2 - 1. Let r be q(-1). Let s = 19 - r. Suppose -z**2 + 0 + 1/2*z**s + 1/2*z = 0. What is z?
0, 1
Let b(n) = -135*n**2 - 785*n - 1875. Let l(r) = 23*r**2 + 131*r + 312. Let w(d) = -6*b(d) - 35*l(d). Factor w(i).
5*(i + 3)*(i + 22)
Let o(b) = 4*b**2 + 5. Let y(g) be the first derivative of -7*g**3/3 + g**2/2 - 9*g + 7. Let k(w) = 5*o(w) + 3*y(w). Find a, given that k(a) = 0.
1, 2
Let n(h) be the third derivative of -h**8/168 - h**7/105 + h**6/30 - 20*h**2. Factor n(u).
-2*u**3*(u - 1)*(u + 2)
Let k be -3*(-6)/(-54)*(-5 - -5). Let i(r) be the first derivative of 4/5*r**5 - 5 + k*r**4 - r**2 + 0*r - 4/3*r**3 + 1/3*r**6. Suppose i(c) = 0. What is c?
-1, 0, 1
Let l = 73/9 + -70/9. Let y(s) be the third derivative of -1/6*s**6 - 1/21*s**7 - 5/12*s**4 + 3*s**2 - 1/168*s**8 + 0 - 1/3*s**3 + 0*s - l*s**5. Factor y(n).
-2*(n + 1)**5
Let h(s) = -s. Let n be -2 + -1 + 0 - -2. Let b(l) = l**2 - l. Let j(y) = -7*y**2 + 12*y. Let z(f) = 5*b(f) + j(f). Let v(m) = n*z(m) - 5*h(m). Factor v(o).
2*o*(o - 1)
Let y = 143 + -139. Let d(m) be the third derivative of 7*m**2 + 5/27*m**y - 5/189*m**7 + 0*m + 4/27*m**3 + 0 - 1/27*m**6 + 7/90*m**5. Let d(b) = 0. What is b?
-1, -2/5, 1
Factor -10 - 45/4*g - 5/4*g**2.
-5*(g + 1)*(g + 8)/4
Let w = -7/1773 + 10729/23049. Suppose 6/13*n + 2/13*n**3 - w*n**2 - 2/13 = 0. Calculate n.
1
Let i(b) = b**4 - 2*b**2 - b - 1. Let s(p) = 2*p**4 - p**3 - 6*p**2 - 3*p - 3. Let n(q) = -3*i(q) + s(q). Find m, given that n(m) = 0.
-1, 0
Let p(k) be the first derivative of 2/55*k**5 - 1/11*k**4 + 0*k**3 + 2/11*k**2 - 9 - 2/11*k. Factor p(v).
2*(v - 1)**3*(v + 1)/11
Solve -2/5*b**4 - 38/5 - 24*b**2 + 116/5*b + 44/5*b**3 = 0.
1, 19
Let d(n) = -n**4 + n**3 + n**2. Let p(t) = 5*t**4 - 4*t**3 - 6*t**2 - 2*t + 1. Let z(k) = 6*d(k) + p(k). Find q such that z(q) = 0.
-1, 1
Let j = 318 + -196. Let v = j - 78. Factor 45*n**3 - v*n**3 + 3*n**4 + 0*n**4.
n**3*(3*n + 1)
Factor 16/3*s**2 + 0*s + 50/9*