3.
-2*(t - 1)**2*(t + 1)**2/7
Suppose 3*f + 3 = -3*t, -f + 4*f + 9 = 0. Find m such that -m + m**2 + m**t + 7*m - 4*m = 0.
-1, 0
Let v(i) be the first derivative of i**3 - 3*i**2 + 9. Factor v(d).
3*d*(d - 2)
Let u be -1 - 6/18 - (-32)/15. Factor 0 + u*y + 2/5*y**2.
2*y*(y + 2)/5
Let z be ((-12)/9)/(-4) - -5. Let f = z - 61/12. Solve 1/2*x**2 - f*x**5 + 1/4 - 3/4*x**4 - 1/2*x**3 + 3/4*x = 0 for x.
-1, 1
Let z(n) be the first derivative of -5*n**4/4 - 5*n**3 + 10*n**2 + 29. Determine y, given that z(y) = 0.
-4, 0, 1
Suppose -2/3*f**3 - 4/3 + 2/3*f**4 - 2*f**2 + 10/3*f = 0. Calculate f.
-2, 1
Let q(v) be the second derivative of -v**6/135 + v**5/270 + v**4/27 - v**3/27 - 5*v**2/2 - 2*v. Let p(f) be the first derivative of q(f). Factor p(i).
-2*(i - 1)*(i + 1)*(4*i - 1)/9
Solve 3/4*d**4 - 1/4 - 1/2*d**3 - 1/2*d**2 + 3/4*d - 1/4*d**5 = 0.
-1, 1
Suppose -3/4*x**2 - 15/2*x + 0 = 0. Calculate x.
-10, 0
Let i be -2 + 5/((-10)/(-8)). Suppose 5*b - 20 = -4*q, 10 + 2 = 3*b + i*q. Suppose 0*v - 2/9*v**2 + 2/9*v**b - 2/9*v**5 + 0 + 2/9*v**3 = 0. Calculate v.
-1, 0, 1
Suppose 12*d - 21 = 5*d. Let x(g) be the second derivative of -1/4*g**2 - 1/60*g**6 - 1/12*g**3 - d*g + 1/20*g**5 + 1/12*g**4 + 0 - 1/84*g**7. Factor x(a).
-(a - 1)**2*(a + 1)**3/2
Let n(k) be the first derivative of k**3 - 3*k - 52. Find z such that n(z) = 0.
-1, 1
Let m(r) = 4*r - 2. Suppose -3*q + 1 = 2*v - 1, -3*v - 6 = 0. Let p be m(q). Suppose 1 - p + 2 + 2 - 16*l**2 - 8*l = 0. Calculate l.
-1/4
Let w(t) be the first derivative of 0*t + 0*t**2 + 1/5*t**5 - 1 - 1/3*t**3 + 0*t**4. Determine y so that w(y) = 0.
-1, 0, 1
Suppose 9 = 3*f - 18. Let a = f - 7. Factor -2/5*s**a + 0 - 2/5*s.
-2*s*(s + 1)/5
Let y(o) = -2*o**5 - 5*o**4 - 21*o**3 - 8*o**2 - 5*o - 5. Let g(c) = -3*c**5 - 7*c**4 - 32*c**3 - 12*c**2 - 8*c - 8. Let m(f) = -5*g(f) + 8*y(f). Factor m(x).
-x**2*(x + 1)*(x + 2)**2
Let n be (-2)/6 + (-2)/(-3). Factor -2/3*h**4 + 2/3*h**2 + n*h + 0*h**3 - 1/3*h**5 + 0.
-h*(h - 1)*(h + 1)**3/3
Suppose -1/3*s**4 + 0*s + 0 + 1/3*s**5 + 1/3*s**2 - 1/3*s**3 = 0. What is s?
-1, 0, 1
Let x(c) = 2*c**2 + 3. Let r(b) = -5*b**2 - b - 7. Let y(p) = -3*r(p) - 7*x(p). Let w(q) = 2*q**2 + 4*q. Let m(j) = -2*w(j) + 3*y(j). Factor m(a).
-a*(a - 1)
Let g(x) = 13*x**2 - 1. Let a be g(1). Suppose 0 = -y + 5*y - a. Factor 9*s**2 + 0 - 81/4*s**y - s.
-s*(9*s - 2)**2/4
Let c(q) be the second derivative of 0*q**3 - 2*q + 0*q**2 + 1/60*q**5 + 0 + 0*q**4. Let c(u) = 0. Calculate u.
0
Let o = 295 + -293. Factor -5/7*q**o - 2/7 + 11/7*q.
-(q - 2)*(5*q - 1)/7
Let v(a) = -1. Let w(u) = -5 + 0 + 9*u**3 + 3*u**3 + 2*u + 12*u**2 + u. Let f(c) = 5*v(c) - w(c). Factor f(y).
-3*y*(2*y + 1)**2
Let y(a) be the third derivative of a**5/540 + 9*a**2. Factor y(t).
t**2/9
Let f(d) be the third derivative of d**7/2100 + d**6/300 + d**5/100 + d**4/60 - d**3/2 - 3*d**2. Let a(u) be the first derivative of f(u). Solve a(t) = 0 for t.
-1
Let d(u) = 2*u**3 + 3*u**2. Suppose 0 = -4*f + 3 + 21. Let k(i) = -3*i**3 - 3*i**2. Let b(q) = f*d(q) + 5*k(q). Solve b(g) = 0 for g.
0, 1
Suppose -3*k - 3 = -12. Factor 0 - 2/5*i**k + 0*i + 4/5*i**2.
-2*i**2*(i - 2)/5
Let x = -6 - 1. Let w = 10 + x. Solve r**3 - r**3 + 2*r**4 + 2*r**w = 0 for r.
-1, 0
Let m = -10 - -11. Find o such that -8*o**4 - 2*o**2 + 11*o**4 - o**5 + 0 + 3*o - 2*o**3 - m = 0.
-1, 1
Let i(j) be the second derivative of -2*j**6/45 - j**5/15 + j**4/9 + 2*j**3/9 - 4*j. Solve i(g) = 0.
-1, 0, 1
Let j = 11/54 - -1/54. Let v(h) = 3*h**2 - 2*h + 1. Let r be v(1). Factor -j - 8/9*c**r + 8/9*c.
-2*(2*c - 1)**2/9
Suppose -84*f + 80*f = -8. What is p in -8/5*p**f - 2/5*p - 2/5*p**5 + 4/5*p**3 + 4/5*p**4 + 4/5 = 0?
-1, 1, 2
Suppose 5*k = -p - 12, -8 = 4*k + 4. Suppose 0*j + 0*j**2 + 1/3*j**p + 0 + j**5 + 4/3*j**4 = 0. What is j?
-1, -1/3, 0
Let x(g) be the second derivative of g**6/15 - g**5/5 + 4*g. Factor x(o).
2*o**3*(o - 2)
Suppose l = 2*l - 2. Let f(o) = o**3 + 3*o**2 + 2*o + 3. Let y be f(-2). Let -4*p - 1 - 1 + p**2 - y*p**l = 0. Calculate p.
-1
Suppose -3*j - 4*l = 120, 0*l = -2*j - 3*l - 80. Let b be (-3)/(-4)*j/(-75). Factor b*z**2 - 12/5*z + 18/5.
2*(z - 3)**2/5
Let y(v) = 9*v**3 - 9*v**2 - 9*v + 6. Let t(a) = -9*a**3 + 10*a**2 + 9*a - 6. Let u(q) = 3*t(q) + 4*y(q). Find o, given that u(o) = 0.
-1, 2/3, 1
Let a be (-3)/(-9) - (-23)/3. Suppose 10 = 2*y - 4*t, 5*t + a = -2*y - 0. Determine o so that -1 - o**2 + y - 5*o + 4*o = 0.
-1, 0
Suppose 8*x + 2 = 9*x. Factor 4 - 8*w - 2*w**x - 8 - 2*w**2.
-4*(w + 1)**2
Let l(a) be the first derivative of a**6/15 - a**5/5 + a**4/6 - 3*a + 2. Let k(x) be the first derivative of l(x). Factor k(m).
2*m**2*(m - 1)**2
Suppose -3*b = -0*b - 9. Suppose -5*m = -4*m - b. What is y in -4*y**m - 1 + 3 + 7*y - 2*y**4 - 3*y = 0?
-1, 1
Let d(l) be the second derivative of l**6/480 - l**5/80 + l**4/32 - l**3/24 - 3*l**2/2 - 3*l. Let s(k) be the first derivative of d(k). Let s(a) = 0. What is a?
1
Let f(h) = h**2 + 7*h. Let q be f(-6). Let g be (-78)/30 - q/2. Solve 2/5*t**2 - g*t**4 + 0*t**3 + 0 + 0*t = 0.
-1, 0, 1
Let z(i) = -7*i**2 - 27*i - 26. Let x(u) = -36*u**2 - 136*u - 128. Let b(a) = 2*x(a) - 11*z(a). Factor b(c).
5*(c + 2)*(c + 3)
Let o(p) be the first derivative of -9*p**5/5 - 4*p**4 + 4*p**3/3 + 21. Factor o(k).
-k**2*(k + 2)*(9*k - 2)
Let s be ((-1)/12)/(-1*(-2)/(-6)). Factor 3/4*r**3 + s*r**5 - r**2 + r**4 - r + 0.
r*(r - 1)*(r + 1)*(r + 2)**2/4
Let g(t) be the third derivative of t**9/12096 + t**8/3360 - t**6/720 - t**5/480 - t**3/2 - t**2. Let f(y) be the first derivative of g(y). Factor f(d).
d*(d - 1)*(d + 1)**3/4
Suppose -500*j + 45 = -491*j. Factor 0*g + 0 + 0*g**4 + 1/3*g**j - 2/3*g**2 - g**3.
g**2*(g - 2)*(g + 1)**2/3
Let r be (-6)/10 + (-53)/(-5). Let f(q) = -q + 13. Let l be f(r). Factor 5/2*b + 1 + 1/2*b**l + 2*b**2.
(b + 1)**2*(b + 2)/2
Let a(w) = 21*w**3 - 59*w**2 + 80*w - 14. Let x(z) = 43*z**3 - 117*z**2 + 160*z - 27. Let m(r) = -13*a(r) + 6*x(r). Factor m(k).
-5*(k - 2)**2*(3*k - 1)
Suppose -f = -3, x - 2*f = -x. Suppose 0 = 3*m - x*c - 6, -3*c = 2*m - 3*m + 2. Suppose 0 + 3/4*k**4 - m*k**3 + 7/4*k**2 - 1/2*k = 0. Calculate k.
0, 2/3, 1
Suppose 4*m + 12 = 5*j, 0*m - 3*m = 5*j + 9. Let j + 1/3*u + 2/3*u**2 = 0. Calculate u.
-1/2, 0
Let m(h) be the second derivative of h**8/5880 - h**7/2940 - h**3/2 + 3*h. Let n(g) be the second derivative of m(g). Factor n(k).
2*k**3*(k - 1)/7
Let o(a) = 4*a**5 + 3*a**4 + a**3 - 3*a**2 + a + 3. Let v(w) = -2 + 2*w**5 - w**3 + 0 - w**4 + 1 + w**2 - 3*w**5. Let m(z) = -2*o(z) - 6*v(z). Factor m(p).
-2*p*(p - 1)**2*(p + 1)**2
Let k(b) be the first derivative of -b**8/5880 + b**7/735 - b**6/315 - 2*b**3 + 1. Let g(h) be the third derivative of k(h). Factor g(c).
-2*c**2*(c - 2)**2/7
Let m(f) = 4*f**4 + 12*f**3 + 9*f**2 - 12*f - 13. Suppose 1 - 4 = 3*r. Let n(d) = -d**4 + 1. Let b(u) = r*n(u) - m(u). Factor b(l).
-3*(l - 1)*(l + 1)*(l + 2)**2
Let f(x) = -3*x**2 - 3*x - 4. Let k(g) = -3*g - 12*g - 21 - 8*g**2 - 8*g**2. Let l(c) = -11*f(c) + 2*k(c). Solve l(s) = 0.
-2, -1
Let h(u) = -90*u**4 + 132*u**3 - 52*u**2 - 12*u - 12. Let w(n) = -36*n**4 + 53*n**3 - 21*n**2 - 5*n - 5. Let l(z) = 5*h(z) - 12*w(z). Factor l(v).
-2*v**2*(3*v - 2)**2
Let m = -18493/27 - -685. Let h(c) be the second derivative of -3*c + 0 + 23/135*c**6 + 0*c**2 + 13/54*c**4 - 3/10*c**5 - 1/27*c**7 - m*c**3. Factor h(b).
-2*b*(b - 1)**3*(7*b - 2)/9
Let k(g) be the third derivative of 0*g + 1/96*g**4 + 0 + g**2 - 1/240*g**5 + 0*g**3. Factor k(a).
-a*(a - 1)/4
Let a(h) = h**4 + h**2 - h - 1. Let v(m) = -14*m**4 - 10*m**2 + 12*m + 12. Let g(i) = -12*a(i) - v(i). Factor g(u).
2*u**2*(u - 1)*(u + 1)
Let o(t) = -t. Let g(d) = -4*d**2 + 44*d - 144. Let n(a) = g(a) - 4*o(a). Determine f, given that n(f) = 0.
6
Suppose 3*f + 51 = 5*q - 6*q, 37 = -q + 4*f. Let b be (-1)/(-3) + (-39)/q. Factor -2/5*s**3 - 2/5 - b*s - 6/5*s**2.
-2*(s + 1)**3/5
Determine w, given that -10*w**2 - 1 + 6*w + w**5 + w - 5*w**4 + 10*w**3 - 2*w = 0.
1
Let b(h) be the third derivative of h**6/360 - h**5/90 - h**4/72 + h**3/9 - 2*h**2. Factor b(z).
(z - 2)*(z - 1)*(z + 1)/3
Let o(u) be the second derivative of 3/20*u**5 + 0 - 1/2*u**3 + 0*u**2 - 3*u + 1/4*u**4 - 1/10*u**6. Let o(i) = 0. What is i?
-1, 0, 1
Suppose 5*z = 4*c - 16, 0 = 4*z - 9*z. Factor 0*n**3 - c*n + 5*n +