d + d - 20 = u. Find f, given that 1 + 8*f**3 - 12*f**2 - 2*f**d - 2 - 1 + 8*f = 0.
1
Let a be (0 + 0)/(0 - 1). Let y(u) be the first derivative of a*u - 4/9*u**3 + 2/3*u**2 + 1/12*u**4 + 1. Solve y(o) = 0 for o.
0, 2
Factor 36/7*k - 16/7 - 8/7*k**2.
-4*(k - 4)*(2*k - 1)/7
Let w(c) = 3*c + 3. Let s(n) = n**3 + 1. Let d(h) = -s(h) + w(h). Factor d(t).
-(t - 2)*(t + 1)**2
Suppose -66*l = -5*l - 122. Factor 1/2*f - 1/3 - 1/6*f**l.
-(f - 2)*(f - 1)/6
Let o(b) be the second derivative of b + 0 - 1/24*b**4 + 0*b**3 + 1/4*b**2. Determine n, given that o(n) = 0.
-1, 1
Factor 35*k - 13*k**3 + 10*k**2 - 17*k**3 + 15 - 25*k**4 - 45*k**5 + 40*k**5.
-5*(k - 1)*(k + 1)**3*(k + 3)
Let o(n) be the second derivative of n**7/630 - n**6/180 - 2*n**4/3 + 8*n. Let z(u) be the third derivative of o(u). Factor z(x).
4*x*(x - 1)
Let i(s) = s**2 - 12*s + 12. Let g(w) = -w + 1. Let x(h) = 24*g(h) - 3*i(h). Suppose x(a) = 0. Calculate a.
2
Let x(o) be the second derivative of o**4/12 - o**3/3 + o**2/2 + 6*o. Let x(u) = 0. What is u?
1
Let l be (1 + (-12)/4)*(-3)/15. Factor 0 + 0*k**2 + l*k**4 - 2/5*k**3 + 0*k.
2*k**3*(k - 1)/5
Suppose -4*x + y = -0*x + 2, -x - 2 = -y. Solve 9/4*f + x*f**2 - 3*f**3 - 3/4 = 0.
-1, 1/2
Let l(m) be the third derivative of 0*m**4 - 1/300*m**6 + 0*m**3 - 1/150*m**5 + 0 + 0*m - 6*m**2. Suppose l(b) = 0. Calculate b.
-1, 0
Suppose 7*k - 9 = 4*k. Let b(x) be the first derivative of -4/9*x + 2/9*x**6 + 13/9*x**2 + 41/18*x**4 - 10/9*x**5 - 22/9*x**k + 1. Suppose b(s) = 0. What is s?
1/2, 2/3, 1
Factor -1/3*z**2 + 0*z + 0 + 1/3*z**4 + 0*z**3.
z**2*(z - 1)*(z + 1)/3
Let b(w) be the third derivative of -w**4/12 - 7*w**3/6 - 4*w**2. Let d be b(-5). Find o, given that 4*o**d - 3*o**3 - 2*o**3 + o**2 = 0.
0, 1
Let o(a) be the second derivative of 1/6*a**4 + 3*a + 1/3*a**3 + 0 - 2*a**2. Determine r so that o(r) = 0.
-2, 1
Suppose 4*v - 3*i - 50 = 3*v, -5*v + 3*i + 190 = 0. Let m be 1/1 + (-7)/v. Factor 2/5*u + 0 + 2/5*u**3 + m*u**2.
2*u*(u + 1)**2/5
Let j(v) = -5*v**2 - 10*v - 11. Let l(s) = 11*s**2 + 21*s + 23. Let p(y) = -13*j(y) - 6*l(y). Let n be p(5). What is r in 2*r**3 + n*r**3 + r**5 - 3*r**3 = 0?
-1, 0, 1
Let a(v) be the second derivative of -v**6/240 - v**5/40 + 5*v**3/3 - v. Let t(y) be the second derivative of a(y). Factor t(z).
-3*z*(z + 2)/2
Suppose -10 = r - 2*m, 2*r = -3*r - 4*m + 20. Factor i + r + 5/2*i**2.
i*(5*i + 2)/2
Let w = 286 - 284. Factor 2/5*q**4 + 0*q - 4/5*q**w + 2/5 + 0*q**3.
2*(q - 1)**2*(q + 1)**2/5
Factor 4*m**4 + 4/3*m + 0 - 20/3*m**3 + 4/3*m**2.
4*m*(m - 1)**2*(3*m + 1)/3
Let z(l) be the first derivative of 3 + 1/2*l**2 + 0*l + 0*l**3 - 1/4*l**4. Factor z(w).
-w*(w - 1)*(w + 1)
Let d(z) be the second derivative of 5/8*z**3 - 1/40*z**6 + 0 - 9/40*z**5 + 9/8*z**2 - 1/8*z**4 + 1/56*z**7 + 2*z. Suppose d(g) = 0. What is g?
-1, 1, 3
Let w(r) be the first derivative of 2*r**3/3 + r**2 - 12*r + 5. Factor w(y).
2*(y - 2)*(y + 3)
Factor -1/2*v**3 + 0 + 0*v**2 + 1/2*v.
-v*(v - 1)*(v + 1)/2
Let u = -17/38 - -18/19. Determine a so that u*a**3 + 0*a - 1/2*a**5 - 1/2*a**4 + 1/2*a**2 + 0 = 0.
-1, 0, 1
Find m such that -4/19*m**2 + 0*m + 2/19*m**4 + 0 + 2/19*m**3 = 0.
-2, 0, 1
Suppose 0*w = 5*w - 35. Let k be 12/7 - (-2)/w. Factor -3*p + p - p**4 + 0*p**3 + 1 + k*p**3.
-(p - 1)**3*(p + 1)
Solve -57*g**4 - 6*g + 5*g**2 + 4*g + 2*g**3 + 52*g**4 = 0 for g.
-1, 0, 2/5, 1
Let a(d) be the third derivative of 0*d**4 + 0*d - 1/21*d**3 + 1/210*d**5 + 0 + 6*d**2. Let a(x) = 0. What is x?
-1, 1
Let n(a) be the third derivative of a**8/1008 + a**7/315 - a**6/72 - a**5/30 + 11*a**2. Find g such that n(g) = 0.
-3, -1, 0, 2
Let w = -42 + 49. Let i(y) be the second derivative of -1/2*y**5 + 1/6*y**6 + 5/6*y**4 - 1/42*y**w - 5/6*y**3 + 1/2*y**2 + 2*y + 0. Solve i(k) = 0.
1
Let r be (-4)/10 - (-245)/300. Let o(b) be the second derivative of -1/4*b**2 - 1/6*b**4 - 2*b + 0 + r*b**3. Factor o(d).
-(d - 1)*(4*d - 1)/2
Let z = 446 + -444. Let -2*n**3 + 1/4*n**4 + 9/2*n**z + 0*n - 27/4 = 0. What is n?
-1, 3
Determine o, given that -14 - 2*o + 4*o**3 - 2*o**4 - o**5 + 4*o**2 + 12 - o**5 = 0.
-1, 1
Let w(j) be the second derivative of -j**4/4 + j**3/2 + 3*j**2 + 11*j. Factor w(p).
-3*(p - 2)*(p + 1)
Let u be (162/(-945))/(3/(-5)). Suppose 2/7 + u*m - 2/7*m**2 - 2/7*m**3 = 0. What is m?
-1, 1
Determine p so that 2/3 + p**2 - 14/3*p**3 + 3*p = 0.
-1/2, -2/7, 1
Let n = -3/86 - -23/43. Factor 5*i**2 - 5*i**3 + 1/2 + 5/2*i**4 - 5/2*i - n*i**5.
-(i - 1)**5/2
Let p(f) be the third derivative of 2*f**7/735 - f**5/35 + f**4/21 - 16*f**2. Factor p(s).
4*s*(s - 1)**2*(s + 2)/7
Let z = -868 - -870. Factor 2/7*v - 4/7*v**z + 4/7*v**4 + 0*v**3 + 0 - 2/7*v**5.
-2*v*(v - 1)**3*(v + 1)/7
Let w(s) = -9*s**4 - 8*s**3 - 9*s**2 + 5. Let n(m) = -m**4 - m**2 + 1. Let r(u) = 5*n(u) - w(u). Determine l, given that r(l) = 0.
-1, 0
Suppose 0*l - 2*l - 26 = -4*q, 4*l = q - 24. Factor -q - 9*i**3 + 4 + 11*i**3 + 2*i**4.
2*i**3*(i + 1)
Let n(j) = j**3 + j**2 + 3. Let z be n(0). Factor 2*q**3 + q**2 + 2*q - z*q**3 - 1 - q.
-(q - 1)**2*(q + 1)
Let d(x) be the third derivative of x**10/15120 + x**9/7560 - x**8/3360 - x**7/1260 + x**4/8 - 4*x**2. Let m(n) be the second derivative of d(n). Factor m(c).
2*c**2*(c - 1)*(c + 1)**2
Let q = -429 - -429. Factor q + 3/5*m - 1/5*m**2.
-m*(m - 3)/5
Let i(k) be the first derivative of -k**5/10 - 5*k**4/8 - 2*k**3/3 + 29. Suppose i(q) = 0. Calculate q.
-4, -1, 0
Let y(g) be the third derivative of 5*g**8/336 - g**7/70 - 7*g**6/120 + g**5/20 + g**4/12 - 2*g**2. Solve y(n) = 0.
-1, -2/5, 0, 1
Suppose 43*q + 6 = 92. Determine n so that 2/5*n**3 + 2/15*n + 2/15*n**4 + 0 + 2/5*n**q = 0.
-1, 0
Suppose -33*c = -37*c + 12. Determine p, given that 1/3*p**2 + 0*p + 4/3*p**c + 0 + p**4 = 0.
-1, -1/3, 0
Let k = 4 - 4. Let f be (-1 - 1)/(-8)*2. What is a in -1/2*a**4 + 0 + 1/2*a**2 + k*a + 1/2*a**3 - f*a**5 = 0?
-1, 0, 1
Suppose -41*t = -36*t - 20. What is b in 10/3*b**3 - 10/3*b**2 + 1/3*b**5 - 1/3 + 5/3*b - 5/3*b**t = 0?
1
Let k(q) be the first derivative of 2*q**3 + 3/2*q**2 - 3*q - 2. Factor k(g).
3*(g + 1)*(2*g - 1)
Factor 10/7*w**4 - 8/7*w**2 + 0 + 2/7*w**5 + 12/7*w**3 - 16/7*w.
2*w*(w - 1)*(w + 2)**3/7
Factor -14 + 4*d**2 - 28*d - 8 - 17 + 7.
4*(d - 8)*(d + 1)
Let p(r) be the third derivative of r**5/24 + 5*r**4/16 + 5*r**3/6 + 5*r**2. Find k, given that p(k) = 0.
-2, -1
Let v(l) be the first derivative of l**6/18 - l**5/15 - l**4/12 + l**3/9 - 29. Factor v(h).
h**2*(h - 1)**2*(h + 1)/3
Let o(l) be the second derivative of 0 - 5/6*l**3 - 7*l + 9/20*l**5 + 1/2*l**2 + 1/4*l**4. Factor o(j).
(j + 1)*(3*j - 1)**2
Let q = 54 + -52. Let s(n) be the second derivative of 1/15*n**4 - 1/50*n**5 + 0 + q*n + 0*n**2 - 1/15*n**3. Solve s(z) = 0 for z.
0, 1
Let t be 3/(-2)*8/(-3). Solve -32*q**2 + 12*q**3 + 3*q + 7*q + t + 6*q**3 = 0.
-2/9, 1
Let a(l) be the first derivative of -l**5/5 - l**4/4 + l**3/3 + l**2/2 + 2. What is v in a(v) = 0?
-1, 0, 1
Let s(y) be the first derivative of y**6/900 + y**5/120 + y**4/60 + y**3/3 + 4. Let c(r) be the third derivative of s(r). Suppose c(u) = 0. Calculate u.
-2, -1/2
Suppose -5*b + 0*i = -5*i, i = 5*b - 12. Let y be (3 - -3) + 0 - b. Suppose -v**2 + 5*v**4 - 4*v**4 - 4*v**3 - 2*v**4 + 6*v**y = 0. What is v?
0, 1
Let j(a) = -8*a**3 - 3*a**2 + 3*a + 8. Let l be (-26)/(-22) + 14/(-77). Let u(c) = -4*c - l - 8 + 9*c**3 + c + 3*c**2. Let t(i) = -6*j(i) - 5*u(i). Factor t(g).
3*(g - 1)*(g + 1)**2
Let d(p) be the second derivative of p**5/220 + p**4/12 + 19*p**3/66 + 9*p**2/22 + 5*p - 1. Factor d(l).
(l + 1)**2*(l + 9)/11
Let h(o) be the first derivative of 2*o**4/3 - o**3/3 - 2*o + 4. Let c(p) be the first derivative of h(p). Find r such that c(r) = 0.
0, 1/4
Suppose -m - 2*m = -9. Factor y**3 + 6*y - 3*y**m - 4*y.
-2*y*(y - 1)*(y + 1)
Let x(g) be the first derivative of -g**6/40 + g**4/8 - g**2/2 + 3. Let r(i) be the second derivative of x(i). Factor r(k).
-3*k*(k - 1)*(k + 1)
Suppose 0 = 2*s + 42 - 46. Let x be (-5)/4*(-2)/5. Factor -3/2*n**s - x*n**3 - 3/2*n - 1/2.
-(n + 1)**3/2
Let f(b) be the second derivative of -11*b**4/6 + b**3/3 + 17*b**2 + 7*b. Let u(c) = -7*c**2 + c + 11. Let m(x) = -3*f(x) + 10*u(x). Factor m(w).
-4*(w - 2)*(w + 1)
Suppose -t + 2*g = 8, 3*t - t = -5*g + 20. Suppose -5*s + 4*s = t. Suppose -2*w - 2*w**3 + s*w*