(m - 3)**3/3
Let u be 12/8*140/3. Factor 48*d**3 + 8*d**2 + d - 2*d + u*d**4 + d.
2*d**2*(5*d + 2)*(7*d + 2)
Let x be 6 + -2 - (4 + -2). Suppose 4*l - 12 = 0, 5*z + 0*l + x*l = 21. Factor -1/4 - 1/4*g**5 + 1/2*g**z - 1/4*g + 1/2*g**2 - 1/4*g**4.
-(g - 1)**2*(g + 1)**3/4
Let u be (-36)/(-5) - (-4)/(-20). Let p(w) = w - 5. Let y be p(u). Factor -3*l**3 + 0*l + 20*l**y + 49*l**5 + 4*l - 3*l**4 - 67*l**4.
l*(l - 1)**2*(7*l + 2)**2
Suppose -2/9 - 2*k**2 - 4/3*k = 0. Calculate k.
-1/3
Let h(q) be the second derivative of -q**9/37800 + q**8/8400 - q**7/6300 + q**4/6 - q. Let p(x) be the third derivative of h(x). Suppose p(n) = 0. Calculate n.
0, 1
Let c(b) = 3*b**3 - 2*b**2 + 1. Let h = -22 + 23. Let l be c(h). Factor 0 + 0*v + 1/3*v**l - 1/3*v**3.
-v**2*(v - 1)/3
Suppose -9*y + 14*y - 45 = 0. Factor -6*k - 7*k + y*k - 14*k**2.
-2*k*(7*k + 2)
Let c be 10/(-15)*(-9)/12. Let g(f) be the second derivative of -f**2 - 1/12*f**4 - f - c*f**3 + 0. Factor g(t).
-(t + 1)*(t + 2)
Let p(x) = -x**3 + 7*x**2 + 9*x - 8. Let z = 25 + -17. Let v be p(z). Factor -2/7*t**2 + v*t + 2/7.
-2*(t - 1)*(t + 1)/7
Let r(l) be the second derivative of -l**8/6720 + l**6/720 - l**4/12 - 2*l. Let x(w) be the third derivative of r(w). Find s such that x(s) = 0.
-1, 0, 1
Let b(z) = z**2 - 2*z - 3. Let n be b(3). Determine r so that 0*r**4 + 0*r**5 - r**3 + n*r**4 + r**5 = 0.
-1, 0, 1
Suppose 0*c + c - 5 = -g, -2*c + 7 = g. Factor -k**2 - c*k + 7*k**2 + 8*k**3 + 0*k.
2*k*(k + 1)*(4*k - 1)
Find z, given that 5*z + 3*z**5 - 3*z + 6*z**4 - 6*z**2 - 5*z = 0.
-1, 0, 1
Let -2/7*s**3 - 2*s**2 - 12/7 + 2/7*s**4 + 26/7*s = 0. Calculate s.
-3, 1, 2
Let l(w) = w**3 - 4*w**2 - 1. Let d be l(3). Let t be 6/15 + 4/d. Suppose 8/3*s**2 + 2/3*s**5 + 8/3*s**4 + t + 4*s**3 + 2/3*s = 0. What is s?
-1, 0
Let n(t) be the third derivative of t**11/1164240 - t**10/529200 - t**5/30 - t**2. Let f(h) be the third derivative of n(h). Factor f(s).
2*s**4*(s - 1)/7
Let g(c) be the second derivative of 0*c**2 + 0*c**3 - 1/48*c**4 - 3*c + 0. Suppose g(r) = 0. Calculate r.
0
Factor 2*k + 4*k**2 - 3*k + 4*k - k**2.
3*k*(k + 1)
Let v(h) = 4*h - 11. Let b be v(5). Let y be -15*((-6)/2)/b. Factor 0*u**4 + 0*u**2 + 0*u + 0 - 2/3*u**3 + 2/3*u**y.
2*u**3*(u - 1)*(u + 1)/3
Let x(c) = -10*c**2 - 45*c - 35. Let v(a) = -5*a**2 - 23*a - 18. Let j(n) = 5*v(n) - 2*x(n). Find q such that j(q) = 0.
-4, -1
Let h(j) = 6*j**4 - 8*j**3 - 2*j**2. Let k(w) = 13*w**4 - 16*w**3 - 5*w**2. Let v(l) = 5*h(l) - 2*k(l). Let v(c) = 0. What is c?
0, 2
Let m = 83 + -81. Let a(l) be the second derivative of 0 - 1/4*l**m + 1/8*l**3 + 0*l**4 - 1/80*l**5 + l. Factor a(v).
-(v - 1)**2*(v + 2)/4
Let n(w) be the second derivative of 3*w**5/20 + 3*w**4/2 + 14*w. Factor n(b).
3*b**2*(b + 6)
Let w(q) be the third derivative of q**6/660 + 9*q**5/110 + 81*q**4/44 + 243*q**3/11 + 29*q**2. What is d in w(d) = 0?
-9
Let k(r) = 5*r**4 + 13*r**3 + 21*r**2 + 27*r + 10. Let w(f) = -14*f**4 - 38*f**3 - 64*f**2 - 81*f - 30. Let n(h) = -11*k(h) - 4*w(h). Solve n(o) = 0 for o.
-5, -2, -1
Factor -4/3*x**2 + 0 + 0*x + 2/3*x**4 - 2/3*x**3.
2*x**2*(x - 2)*(x + 1)/3
Suppose 0*x - 10 = -2*x. Solve t**3 + 4*t**4 - 9*t**x - 4*t**2 - 5*t**5 + 13*t**3 = 0.
-1, 0, 2/7, 1
Let a(p) be the first derivative of -2*p**3/9 + 20*p**2/3 - 38*p/3 - 50. Factor a(z).
-2*(z - 19)*(z - 1)/3
Let c = 7 + -4. Determine k so that -6*k + 24*k**2 - 9*k**3 - k**5 + 13*k**5 + c*k**3 - 3 - 21*k**4 = 0.
-1, -1/4, 1
Factor -w - 6*w - 7*w + 2*w - 3*w**2.
-3*w*(w + 4)
Let v(x) be the second derivative of -2*x**7/105 + 4*x**5/25 + 2*x**4/15 - 2*x**3/5 - 4*x**2/5 + 14*x. Solve v(f) = 0 for f.
-1, 1, 2
Let i(x) be the second derivative of -2*x - 1/18*x**4 - 1/3*x**2 + 2/9*x**3 + 0. Factor i(t).
-2*(t - 1)**2/3
Determine y so that 45/4*y**3 + 0 + 5/4*y**2 + 35/4*y**5 + 75/4*y**4 + 0*y = 0.
-1, -1/7, 0
Let c be ((-6)/(-21))/((-9)/(-21)). Factor 0 + 4/3*a**3 - c*a - 2/3*a**2.
2*a*(a - 1)*(2*a + 1)/3
Let q(k) = -12*k**3 + 23*k**2 + 3*k - 6. Let b(m) = -36*m**3 + 69*m**2 + 9*m - 17. Let r(u) = 4*b(u) - 11*q(u). Solve r(i) = 0.
-1/3, 1/4, 2
Let k(y) be the third derivative of -3*y**2 + 1/840*y**7 + 0*y**4 + 0*y + 1/240*y**6 + 0*y**3 + 0 + 1/240*y**5. Factor k(n).
n**2*(n + 1)**2/4
Let h(p) be the second derivative of -p**4/6 + 10*p**3/3 - 9*p**2 - 26*p. Factor h(g).
-2*(g - 9)*(g - 1)
Let t = -17963/40 + 449. Let y = t - -107/360. Find k, given that -y*k - 2/9*k**2 + 0 = 0.
-1, 0
Let w(x) = 11. Let m(s) = 3. Let t(o) = 12*m(o) - 3*w(o). Let r(j) = j**2 - j - 4. Let i(a) = 3*r(a) + 2*t(a). Factor i(h).
3*(h - 2)*(h + 1)
Suppose n + 0*l = 2*l + 6, -n + 5*l = -21. Let i(d) = d**2 + 4*d + 2. Let h be i(n). Factor w**4 - 2/3*w**3 + w - 2/3*w**h - 1/3*w**5 - 1/3.
-(w - 1)**4*(w + 1)/3
Let y(x) be the third derivative of 1/48*x**4 + x**2 + 1/60*x**5 + 0*x + 1/240*x**6 + 0 + 0*x**3. Factor y(v).
v*(v + 1)**2/2
Solve -2/9*o**2 + 0 - 2/9*o = 0.
-1, 0
Let g(q) be the third derivative of -2*q**7/105 - q**6/30 + q**5/15 + q**4/6 + 9*q**2. Factor g(t).
-4*t*(t - 1)*(t + 1)**2
Let j(b) be the second derivative of 2*b + b**3 + 0 + 1/12*b**4 + 9/2*b**2. Factor j(v).
(v + 3)**2
Let n(k) = -k**3 - k**2 + k. Let c(d) = -4*d**3 - 10*d**2 + 13*d - 4. Let r(b) = -c(b) + 5*n(b). Factor r(z).
-(z - 2)**2*(z - 1)
Let y(b) be the second derivative of 1/24*b**4 - 2/3*b**3 + 4*b**2 - 3*b + 0. Factor y(k).
(k - 4)**2/2
Let j be (-2)/5 - (-78)/(-120)*-1. Factor j*q**2 - 1/2 - 1/4*q.
(q - 2)*(q + 1)/4
Let b = -16 - -11. Let j = b - -8. Factor -9*n + 1 + 28*n**2 - 9*n**j - 4*n**2 - 7.
-3*(n - 2)*(n - 1)*(3*n + 1)
Let c(h) be the third derivative of 0*h**4 + 2*h**2 + 0*h**3 - 1/30*h**5 + 0 + 0*h. Factor c(i).
-2*i**2
Let b = 53 - 49. Let t(i) be the third derivative of 0 - 1/6*i**3 + 1/120*i**6 + 1/60*i**5 + 0*i - 1/24*i**b - 3*i**2. Factor t(c).
(c - 1)*(c + 1)**2
Let f(c) be the second derivative of c**5/10 - 5*c**4/6 + 7*c**3/3 - 3*c**2 - 5*c. Factor f(g).
2*(g - 3)*(g - 1)**2
Let l(i) be the third derivative of -2*i**7/315 + i**6/60 - i**4/36 + 35*i**2. Factor l(y).
-2*y*(y - 1)**2*(2*y + 1)/3
What is u in -6*u**4 - 11*u**4 - 4*u**4 + 27*u**2 - 25*u**3 - 6 + 15*u + 10*u**3 = 0?
-1, 2/7, 1
Let f = 11/12 + -2/3. Factor f*x + 0 - 1/4*x**2.
-x*(x - 1)/4
Let v(j) be the third derivative of j**8/504 + 2*j**7/315 - 7*j**6/180 + 2*j**5/45 - 53*j**2. What is t in v(t) = 0?
-4, 0, 1
Let l(f) be the third derivative of -f**10/30240 - f**9/7560 + f**7/1260 + f**6/720 + f**4/8 + f**2. Let b(g) be the second derivative of l(g). Factor b(j).
-j*(j - 1)*(j + 1)**3
Let r(j) = -2*j + 6. Let n be r(0). Let i(c) be the third derivative of 1/40*c**n + 0*c**3 - 1/60*c**5 + 0*c**4 + 0*c + 2/105*c**7 + 0 - c**2. Factor i(s).
s**2*(s + 1)*(4*s - 1)
Let j(n) = -n. Let d(y) = -2*y - 1. Let g(i) = 2*d(i) - 3*j(i). Let t be g(-6). Find p such that p**2 - 5*p**3 - p**t + p**5 + 3*p**3 + p**3 = 0.
-1, 0, 1
Let x(k) = -60*k**2 - 1200*k - 5975. Let q(n) = 5*n**2 + 100*n + 498. Let v(w) = 25*q(w) + 2*x(w). Determine f so that v(f) = 0.
-10
Let a = -23 - -32. Factor -a + 9 + 9*s**2 + 6*s.
3*s*(3*s + 2)
Let z(k) be the second derivative of 3*k**5/140 + k**4/14 - k**3/14 - 3*k**2/7 + 25*k. Suppose z(n) = 0. Calculate n.
-2, -1, 1
Let b(u) be the second derivative of -u**4/60 + u**3/5 - 9*u**2/10 + 2*u. Factor b(m).
-(m - 3)**2/5
Suppose -3 = n, -5*n - 44 - 7 = 2*q. Let b = q - -42. What is x in 15/2*x**4 - 6 + 75/2*x**5 - 3/2*x**2 + b*x - 123/2*x**3 = 0?
-1, 2/5, 1
Factor -8/5*d**5 + 0 + 0*d**3 + 0*d + 0*d**2 + 2/5*d**4.
-2*d**4*(4*d - 1)/5
Let n = -154 - -158. Factor 0 + 5/3*j**3 - 4/3*j**n + 0*j - 1/3*j**2.
-j**2*(j - 1)*(4*j - 1)/3
Suppose -1 + 1 = -13*h. Let s(n) be the second derivative of n + h*n**3 + 0*n**4 + 1/30*n**6 + 0*n**2 - 1/20*n**5 + 0. Factor s(q).
q**3*(q - 1)
Let k(q) be the third derivative of 8*q**3 + 0 + 0*q - 1/5*q**6 - 5*q**2 + 1/70*q**7 + 6/5*q**5 - 4*q**4. Factor k(s).
3*(s - 2)**4
Let p be (-13)/(-4) + 2/(-8). Factor p*j - 2*j - 4*j**2 + j + 2*j**3.
2*j*(j - 1)**2
Let n(w) be the first derivative of -w**3 + 3*w**2 - 3*w - 7. Solve n(r) = 0 for r.
1
Let j(q) be the third derivative of -q**5/20 + q**4/4 - q**3/2 - 4*q**2. Factor j(a).
-3*(a - 1)**2
Suppose -24*t + 19*t = 0. Suppose t*y = -2*y. Factor -2/5*i**2 + y - 2/5*i.
-2*i*(i + 1)/5
Suppose 3*q + 