 c(k) = -37*k**2 - 5*k + 37. Let h(v) = -3*c(v) - 5*n(v). Let d(b) = -4*h(b) + 22*q(b). Factor d(o).
4*(o - 1)*(o + 1)
Let k = -11 - -31. Factor -k*a + 3*a**4 + 20*a.
3*a**4
What is j in -2/13*j**2 + 0 + 2/13*j**4 + 0*j**3 + 0*j = 0?
-1, 0, 1
Let m be 5 - 1 - 0 - (-6150)/(-1599). Factor m*i + 0 + 2/13*i**2.
2*i*(i + 1)/13
Factor 0 + 0*y + 2/3*y**2 - 2/3*y**3.
-2*y**2*(y - 1)/3
Let a(x) be the first derivative of 4*x**5/35 + x**4/7 + 11. Factor a(f).
4*f**3*(f + 1)/7
Let o be 16/(-56)*(0 + -14). Let v(a) be the second derivative of -1/4*a**3 + 0 + 3*a + 1/2*a**2 + 1/40*a**5 + 0*a**o. Factor v(w).
(w - 1)**2*(w + 2)/2
Let l be 2*(2 + 9/(-6)). Let f be l/2 + (-3)/(-2). Factor 1/2*c**f + 0*c - 1/2.
(c - 1)*(c + 1)/2
Let x(t) be the first derivative of -3*t**4/4 - 3*t**3 - 3*t**2 + 8. Factor x(g).
-3*g*(g + 1)*(g + 2)
Suppose 12*s**5 - 64*s - 10*s**2 + 52*s**4 - 47*s**2 + 21*s**2 - 16 + 52*s**3 = 0. Calculate s.
-2, -1, -1/3, 1
Solve -4 + 0 + 1 - 12*i + 3*i**2 - 12 = 0 for i.
-1, 5
Let s be (-1)/(-3)*(10 + -1). Let m = 7 - s. Determine g so that -2*g**3 + g**2 + g**4 - 4 + m = 0.
0, 1
Let r be 2 - (4 + 7/(-3) - 1). Suppose 2*y**3 + r*y**4 + 1/3*y**5 + 4/3*y**2 + 0 + 1/3*y = 0. What is y?
-1, 0
Determine h so that 3 + 3/4*h**2 + 3*h = 0.
-2
Suppose 9*i = 4*i. Suppose i*b - 2*b = 0. Factor 3/5*u**3 - 1/5*u**2 + 4/5*u**4 + b + 0*u.
u**2*(u + 1)*(4*u - 1)/5
Let p(f) be the second derivative of f**8/315 - f**7/315 + f**6/1080 - f**3/2 + f. Let q(g) be the second derivative of p(g). What is r in q(r) = 0?
0, 1/4
Let g = -198 - -198. Solve g - 1/2*u**2 - 1/4*u - 1/4*u**3 = 0.
-1, 0
Let h(c) be the third derivative of 0*c**7 + 1/12*c**4 + 6*c**2 - 1/45*c**5 - 1/45*c**6 + 0 + 1/504*c**8 + 2/9*c**3 + 0*c. Determine z, given that h(z) = 0.
-1, 1, 2
Let n = -7 - -8. Let q be 6*n/(-2) + 5. Factor -q*h**4 + 12*h**2 - 3*h**5 - 3*h + 6*h**3 - 24*h**3 + 14*h**4.
-3*h*(h - 1)**4
Let n(z) be the first derivative of 0*z**2 + 1 + 1/12*z**3 - 1/4*z. Factor n(j).
(j - 1)*(j + 1)/4
Factor 8/9 + 10/9*q + 2/9*q**2.
2*(q + 1)*(q + 4)/9
Factor h**4 - 32*h**3 - h**2 - 2*h**4 + 30*h**3.
-h**2*(h + 1)**2
Let v = 16 - 12. Suppose 4*r + v = 4*a, -3*r - 3*a = r - 17. Factor -1/3*i**3 + 0*i**r + 1/3*i + 0.
-i*(i - 1)*(i + 1)/3
Suppose 3*n + 5*x - 11 = 15, -2*x = 2*n - 12. Factor y**2 + 0*y**n + 4*y**3 + 10*y - 6*y + 7*y**2.
4*y*(y + 1)**2
Let v(g) be the second derivative of 3*g**6/10 + 3*g**5/20 - 3*g**4/4 - g**3/2 - 41*g. Let v(p) = 0. Calculate p.
-1, -1/3, 0, 1
Let b be 2/24*4*(2 - 0). Let -1/3 - 1/3*l**4 + 2/3*l + 2/3*l**5 + b*l**2 - 4/3*l**3 = 0. Calculate l.
-1, 1/2, 1
Suppose -2*u = -u. Let t(p) be the third derivative of u + 1/36*p**5 + 1/18*p**3 - 1/12*p**4 + 0*p + p**2. Determine b so that t(b) = 0.
1/5, 1
Factor -19*t**3 - 6*t**2 + 7*t**3 + 10*t**3.
-2*t**2*(t + 3)
Let i(r) be the first derivative of 6/25*r**5 + 7/10*r**4 + 0*r + 0*r**2 - 1 + 4/15*r**3. Suppose i(u) = 0. Calculate u.
-2, -1/3, 0
Let r(o) be the third derivative of o**6/40 + o**5/10 - o**4/8 - o**3 + 30*o**2. Factor r(j).
3*(j - 1)*(j + 1)*(j + 2)
Suppose 2*g = 3*g. Find o such that g*o + 0*o**2 + 0*o**4 - 2/9*o**5 + 2/9*o**3 + 0 = 0.
-1, 0, 1
Let d = -18 - -32. Let f be (-8)/(-28) + (-4)/d. Solve f + 1/4*h**2 + 0*h + 1/4*h**3 = 0.
-1, 0
Determine u, given that 2*u**2 + 2/3*u + 1/6*u**5 + u**4 + 13/6*u**3 + 0 = 0.
-2, -1, 0
Suppose 3/7*l**2 + 12/7 - 15/7*l = 0. What is l?
1, 4
Let f(w) be the second derivative of -w**6/10 + 3*w**5/4 - 2*w**4 + 2*w**3 + 12*w. Suppose f(r) = 0. Calculate r.
0, 1, 2
Suppose 4*t + l = 4*l + 39, -5*l = -3*t + 43. Suppose -t = -3*n + n. Factor 0*q**2 - 6*q**3 - 2*q**4 + n*q**2 + 2*q**3 - 5*q**2.
-2*q**2*(q + 1)**2
Factor -1/4*x + 0 + 0*x**2 + 1/4*x**3.
x*(x - 1)*(x + 1)/4
Let l = 59/2 + -29. Let i(m) be the first derivative of -1 - 2*m**3 - 2*m - 3*m**2 - l*m**4. Factor i(b).
-2*(b + 1)**3
Factor 5*v + 5/3*v**2 + 10/3.
5*(v + 1)*(v + 2)/3
Let w(l) = l**3 - 41*l**2 + 59*l. Let q(f) = -f**3 + 20*f**2 - 29*f. Let g(m) = -5*q(m) - 2*w(m). Solve g(j) = 0 for j.
0, 3
Find f such that 59*f**3 - 3*f**4 - 65*f**3 + 2*f**2 - 5*f**2 = 0.
-1, 0
Let z(g) be the third derivative of 0 + 1/225*g**5 + 0*g**3 - 1/900*g**6 + 9*g**2 - 1/1575*g**7 + 0*g**4 + 0*g. Solve z(q) = 0.
-2, 0, 1
Let i(o) be the third derivative of -1/70*o**7 + 0 - 4*o**2 + 0*o**4 + 0*o + 0*o**3 - 1/40*o**6 + 0*o**5. Let i(u) = 0. Calculate u.
-1, 0
Let l be (-16)/6 - (-124)/31. Factor l - 1/3*p**3 + 0*p - p**2.
-(p - 1)*(p + 2)**2/3
Let 2/3*k**2 - 2*k + 4/3 = 0. What is k?
1, 2
Let v = 14 + -12. Let m(g) be the second derivative of -1/14*g**4 + 5/21*g**3 - 2/7*g**v + g + 0. Solve m(i) = 0 for i.
2/3, 1
Suppose 4*d - 8*d + 12 = 0. Factor -7*f**2 + d + 9*f**2 - 5*f**2.
-3*(f - 1)*(f + 1)
Suppose 0 - v + v**2 + 1/4*v**5 + 3/4*v**3 - v**4 = 0. Calculate v.
-1, 0, 1, 2
Suppose -3*j = -0*j. Let f(t) be the second derivative of 0 + t + 1/42*t**4 + 0*t**3 + 1/70*t**5 - 1/147*t**7 - 1/105*t**6 + j*t**2. Let f(n) = 0. What is n?
-1, 0, 1
Let m(c) = 8*c**4 - 9*c**3 + 35*c**2 + 17. Let i(a) = -3*a**4 + 3*a**3 - 12*a**2 - 6. Let p(b) = 17*i(b) + 6*m(b). Factor p(f).
-3*f**2*(f - 1)*(f + 2)
Suppose 0 = 2*f - 5*r + 6, 4*f + 3*r + 0 - 14 = 0. Suppose 9/5*l**f - 3/5*l - 9/5 + 3/5*l**3 = 0. What is l?
-3, -1, 1
Let x(s) be the third derivative of 1/112*s**8 + s**2 + 0 - 1/20*s**5 + 0*s + 0*s**4 + 1/70*s**7 + 0*s**3 - 1/40*s**6. Solve x(n) = 0 for n.
-1, 0, 1
Suppose -10*u - 14*u = 0. Determine c, given that u*c + 2/3*c**3 + 0 + 1/3*c**4 + 1/3*c**2 = 0.
-1, 0
Solve -1/7*m**3 + 0*m**2 + 3/7*m - 2/7 = 0.
-2, 1
Let q = 9 + -5. Factor 2*d**3 + q*d - 3*d - 3*d.
2*d*(d - 1)*(d + 1)
Let q(c) = -7*c**2 - 8*c - 10. Let s(m) = 2*m**2 + 1. Let p(l) = q(l) + 3*s(l). Factor p(u).
-(u + 1)*(u + 7)
Suppose -4*y - 3*y = 0. Factor -2*h + 81*h**4 + y*h - 95*h**3 + 23*h**3 + 8*h**2 + 13*h**2.
h*(3*h - 1)**2*(9*h - 2)
Let f = 58 - 55. Solve -4/11*i + 0 + 2/11*i**2 - 6/11*i**4 + 8/11*i**f = 0.
-2/3, 0, 1
Let g be 2 + -31 + 0 + 0. Let w = g - -89/3. Solve -2/3*o + 0 + w*o**2 = 0 for o.
0, 1
Let v be -1 + 36/14 + (7 - 8). Factor v*o + 2/7*o**2 + 0.
2*o*(o + 2)/7
Let s(m) be the second derivative of -m**4/12 - 5*m**3/6 + 2*m. Let f be s(-5). Factor -g - g**2 + 0*g**2 + f*g.
-g*(g + 1)
Let v = -1 + 18. Let s be 6/(-8) - v/(-12). Let 4/3*o + 0 + s*o**2 = 0. Calculate o.
-2, 0
Let j(y) be the second derivative of -7/24*y**3 + 1/4*y**2 + 7/80*y**5 - 4*y + 0 - 1/24*y**4. Factor j(t).
(t - 1)*(t + 1)*(7*t - 2)/4
Let z(o) be the third derivative of -3*o**6/40 - o**5/20 + 3*o**4/8 + o**3/2 - 5*o**2. Solve z(i) = 0.
-1, -1/3, 1
Let o(t) be the third derivative of -t**5/60 + 5*t**4/12 - 25*t**3/6 + 3*t**2 - 12*t. Suppose o(n) = 0. What is n?
5
Let d(y) = -y**5 - 24*y**4 + 43*y**3 - 24*y**2 - y. Let k(l) = -l**5 - 12*l**4 + 22*l**3 - 12*l**2 - l. Let t(s) = 4*d(s) - 7*k(s). Factor t(h).
3*h*(h - 1)**4
Factor -24 + 3*h**2 - 2*h**2 - 4*h**2 + 27*h.
-3*(h - 8)*(h - 1)
Let c be (10/105)/(-1 - (-10)/7). Factor -2/9*k**4 + 4/9*k**2 + 0*k**3 + 0*k - c.
-2*(k - 1)**2*(k + 1)**2/9
Suppose -2*w + 21 = 9. Solve -5*z**2 - 3*z - 3*z**4 - z**3 + 4*z**3 + 2*z**2 + w*z**4 = 0.
-1, 0, 1
Let z(t) = t + 5. Let y be z(-3). Suppose 3*v - 1 = -y*m, m + 0 = -3*v + 2. Factor -w**2 + 0*w**2 - v + 2*w**2.
(w - 1)*(w + 1)
Let r(l) be the second derivative of 7*l**5/100 + l**4/5 + l**3/10 - l**2/5 + 19*l. Let r(b) = 0. Calculate b.
-1, 2/7
Let w = 1 - 13. Let t be ((-2)/30)/(2/w). Factor -2/5*r - 4/5*r**2 + t + 4/5*r**3 + 2/5*r**4 - 2/5*r**5.
-2*(r - 1)**3*(r + 1)**2/5
Let c(k) be the second derivative of -5/14*k**7 + 0 - 3*k**2 + 3/2*k**3 - 33/10*k**5 + 9/5*k**6 + 2*k**4 - 4*k. Factor c(r).
-3*(r - 1)**4*(5*r + 2)
Suppose h + 6*h - 14 = 0. Factor 1/3*b**h - 1/3*b**3 + 0 + 0*b.
-b**2*(b - 1)/3
Factor 3/2*y**2 + 0 - 3/2*y.
3*y*(y - 1)/2
Factor -23*s**5 + 649 + 928*s**2 - 137 - 344*s**3 - 1152*s - 17*s**4 + 77*s**4 + 19*s**5.
-4*(s - 4)**3*(s - 2)*(s - 1)
Let j(y) be the second derivative of 2*y**7/21 + 8*y**6/15 + 3*y**5/5 - 4*y. Factor j(t).
4*t**3*(t + 1)*(t + 3)
Suppose -4 = z, 2*m + 3*z = -3*m - 2. Let a be 1/1 + m/(-6). Factor 0*i - 4/3*i**3 - a*i**2 - 2/3*i**4 + 0.
-2*i**2*(i + 1)**2/3
Suppose 0 = -2*b + 6*b - 2*z, -5*z = -20. Factor 1 + 4/3*q**3 + 11/3*q**b + 10/3*q.
(q + 1)**2*(4*q + 3)/3
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