actor a(z).
-2*(z - 1)**2*(3*z + 1)**2
Let p(b) be the third derivative of b**9/1008 + b**8/280 - b**7/280 - b**6/60 + 5*b**3/6 - 5*b**2. Let k(h) be the first derivative of p(h). Factor k(a).
3*a**2*(a - 1)*(a + 1)*(a + 2)
Suppose 18 = -0*w + 4*w + 5*v, 3*w + v - 8 = 0. Suppose -2/3*i**2 - 2*i**3 + 2/3 + w*i = 0. What is i?
-1, -1/3, 1
Let j(m) = -10*m**2 - 18*m. Let r(p) = -18*p**2 - 35*p + 1. Let v(y) = 9*j(y) - 4*r(y). Factor v(l).
-2*(l + 1)*(9*l + 2)
Let y(h) be the second derivative of 0*h**2 + 1/60*h**5 + 0 - 1/90*h**6 - h + 1/36*h**4 - 1/18*h**3. What is m in y(m) = 0?
-1, 0, 1
Let s = -48 + 52. Let c(w) be the first derivative of -1/9*w**2 + s + 1/18*w**4 + 0*w**3 + 0*w. Factor c(g).
2*g*(g - 1)*(g + 1)/9
Let s(r) be the first derivative of -r**5/30 + r**4/12 - r**2/6 + r/6 - 4. Let s(u) = 0. Calculate u.
-1, 1
Factor 0*j**2 + 0*j - 2/11*j**4 - 8/11*j**3 + 0.
-2*j**3*(j + 4)/11
Suppose r - l = 4, -3 = -2*l - 7. Factor -3 + 4 + h**4 + 0*h**4 - r*h**2.
(h - 1)**2*(h + 1)**2
Suppose 8/7 + 36/7*q**2 - 36/7*q + 4/7*q**3 - 12/7*q**4 = 0. What is q?
-2, 1/3, 1
Let r(a) = -a**3 + 5*a**2 + 6*a + 2. Let y be r(6). Solve 3*d**3 - 3*d**2 + 3*d**y - 2*d**2 + 3*d - 4*d**2 = 0 for d.
0, 1
Let z(p) be the first derivative of 4*p**5/5 - 2*p**4 - p**3/3 + 3. Let x(k) = 10*k**4 - 20*k**3 - 2*k**2. Let u(r) = 5*x(r) - 12*z(r). Factor u(y).
2*y**2*(y - 1)**2
Let v(y) = -y**3 - 14*y**2 + 31*y - 13. Let l be v(-16). Solve 0*g - 4/5*g**4 - 2/5*g**5 + 0 - 2/5*g**l + 0*g**2 = 0 for g.
-1, 0
Let t be (0 + (-21)/(-28))*(-8)/(-5). Factor 24/5*u**2 + t*u**3 - 3/5*u**5 + 21/5*u - 6/5*u**4 + 6/5.
-3*(u - 2)*(u + 1)**4/5
Let m be ((-1)/9)/((5 - 3) + -3). Let h(d) be the second derivative of 1/18*d**4 - 3*d + 0 + m*d**3 + 0*d**2. Find i such that h(i) = 0.
-1, 0
Determine y so that 4/7 + 4/7*y**2 - 10/7*y = 0.
1/2, 2
Suppose 5*d + 4 = -3*m + 3*d, -17 = 4*m + 5*d. Suppose 14 = 5*o + 4. Suppose -o*n**m + 0*n + n - 5*n = 0. Calculate n.
-2, 0
Factor -3*c**2 + 36*c - 9*c**2 + 20*c**2 - 4*c**2.
4*c*(c + 9)
Let b(m) be the third derivative of -m**9/7560 + m**8/3360 - m**4/24 - m**2. Let i(u) be the second derivative of b(u). Suppose i(p) = 0. What is p?
0, 1
Let u(s) be the first derivative of -s**4/40 + s**3/10 - 3*s**2/20 + s/10 + 3. Factor u(y).
-(y - 1)**3/10
Factor 4/15*y**2 + 2/5*y**3 + 0 + 0*y - 2/3*y**4.
-2*y**2*(y - 1)*(5*y + 2)/15
Let h = -190 + 11401/60. Let v(d) be the second derivative of 1/12*d**4 + 0 - 3*d + 1/9*d**3 + 0*d**2 + h*d**5. Factor v(g).
g*(g + 1)*(g + 2)/3
Suppose 0*v - 2*v = -2*r + 14, 0 = 2*r - v - 9. Suppose 23 + 2*f**r - 23 - 4*f = 0. What is f?
0, 2
Let k(p) be the second derivative of -p**5/5 + 5*p**4/3 - 14*p**3/3 + 6*p**2 - 31*p. Determine j so that k(j) = 0.
1, 3
Suppose -j + 6*j - 5 = 2*o, 5*o = 3*j - 3. Let t(x) be the first derivative of 0*x - 1/4*x**2 + o*x**3 + 1/8*x**4 - 3. Factor t(r).
r*(r - 1)*(r + 1)/2
Suppose 2*k = 2*l - 4, 0 = k - 3*k - l + 2. Let y(x) be the first derivative of 0*x - x**4 + k*x**2 + 6/5*x**5 - 4/9*x**6 + 2/9*x**3 - 3. Factor y(p).
-2*p**2*(p - 1)**2*(4*p - 1)/3
Factor 247*j**2 - 5*j - 244*j**2 - j.
3*j*(j - 2)
Let s(h) be the third derivative of -h**11/665280 - h**10/100800 + h**8/10080 + h**5/60 - 4*h**2. Let n(g) be the third derivative of s(g). Factor n(d).
-d**2*(d - 1)*(d + 2)**2/2
Let o be (-4)/(-4)*-3 - (-22)/6. Factor 2/3 + 4/3*l - 4/3*l**3 + 0*l**2 - o*l**4.
-2*(l - 1)*(l + 1)**3/3
Let x(c) be the second derivative of -c**6/90 - 7*c**5/60 - c**4/2 - 10*c**3/9 - 4*c**2/3 - 6*c. Determine z, given that x(z) = 0.
-2, -1
Let l(y) be the third derivative of -729*y**6/280 + 243*y**5/140 - 27*y**4/56 + y**3/14 + 7*y**2. Factor l(n).
-3*(9*n - 1)**3/7
Factor 0 + 0*l**2 + 2/23*l**5 + 0*l + 8/23*l**4 - 10/23*l**3.
2*l**3*(l - 1)*(l + 5)/23
Let f = -859/3 - -289. Let c = 46 + -42. Suppose -10/3*p**c - 2/3*p**2 + f*p**3 + 0 + 4/3*p**5 + 0*p = 0. What is p?
0, 1/2, 1
Let a(r) be the third derivative of 0*r - 7*r**2 + 1/168*r**8 + 0 + 0*r**6 + 0*r**5 + 0*r**3 + 0*r**4 + 0*r**7. Let a(h) = 0. What is h?
0
Let x(k) be the second derivative of k**5/90 - 2*k**4/9 + 16*k**3/9 + 3*k**2 + 4*k. Let q(i) be the first derivative of x(i). Solve q(p) = 0.
4
Suppose 0 = -0*b + 2*b + x - 4, -3*x + 6 = 0. Let o(c) = 3*c**2. Let s be o(b). What is v in -s*v**2 - 17*v**2 + 8*v**3 - 4*v**2 - v**4 - 16 + 32*v = 0?
2
Let c(j) = -j**2 + 2. Let v be c(0). Let l = v + 1. Factor 3*o + 2*o**l - 2 + 4*o**3 - o + 10*o**2.
2*(o + 1)**2*(3*o - 1)
Let r(f) = 10*f**4 - 155*f**3 + 55*f**2 - 45. Let b(k) = k**4 - 14*k**3 + 5*k**2 - 4. Let a(q) = -45*b(q) + 4*r(q). Suppose a(x) = 0. What is x?
0, 1
Let a = -770 + 3871/5. Factor 4/5 + 16/5*x + 9/5*x**3 + a*x**2.
(x + 1)*(3*x + 2)**2/5
Let i(y) = 3*y**2 - y - 7. Let f(x) = -3*x**2 + 9. Let p(l) = -5*f(l) - 6*i(l). Factor p(o).
-3*(o - 1)**2
Let n(z) = 13*z**2 + 3*z - 3. Let v(l) = 7*l**2 + l - 2. Let k(d) = 6*n(d) - 10*v(d). Suppose k(g) = 0. Calculate g.
-1/2
Let c be 7/12 + 2/(-8). Let g(v) be the first derivative of 2/9*v**3 + 1/2*v**4 + 0*v - 2/15*v**5 - c*v**6 - 1 + 0*v**2. Solve g(z) = 0.
-1, -1/3, 0, 1
Let o(j) be the second derivative of j**5/50 + 2*j**4/15 + j**3/5 + 15*j. Let o(p) = 0. What is p?
-3, -1, 0
Let x be 4/10 - 3/15. Solve -4/5*k - 1/5 - 4/5*k**3 - 6/5*k**2 - x*k**4 = 0.
-1
Let l(u) be the second derivative of u**6/10 - 9*u**5/20 + 3*u**4/4 - u**3/2 - 11*u. Find w such that l(w) = 0.
0, 1
Let k be 50/6 + 248/(-31). Solve -k*b + 1/3*b**2 + 1/3*b**3 - 1/3 = 0 for b.
-1, 1
Let j(p) be the third derivative of -p**6/480 + p**5/10 - 2*p**4 + 64*p**3/3 + 8*p**2. Suppose j(n) = 0. What is n?
8
Let l = 4 - 3. Let z = 1 - l. Suppose -u + 0*u**2 + z*u + u**2 = 0. Calculate u.
0, 1
Let i(r) = 25*r**2 - 27*r - 1. Let x be (0 + 2/3)*-3. Let f(g) = -6*g**2 + 7*g. Let z(a) = x*i(a) - 9*f(a). Determine q, given that z(q) = 0.
1/4, 2
Let i be -6 + 5 - 37/(-52). Let n = i - -7/13. Factor 1/4*z**4 + 1/2*z**3 + 0*z + 0 + n*z**2.
z**2*(z + 1)**2/4
Let y(v) = 3*v**2 - v. Suppose 4*p = 8*p - 4. Let z be y(p). Solve -4*u**4 - 2 + 1 - z*u**5 + 1 - 2*u**3 = 0 for u.
-1, 0
Let y(i) be the second derivative of 0 + 0*i**2 - 1/40*i**6 - 1/80*i**5 + 0*i**3 + i + 0*i**4. Let y(n) = 0. What is n?
-1/3, 0
Let j = -69 - -71. Let g(y) be the first derivative of 3 - 13/4*y**4 + y**5 - 2*y + 3*y**3 + 1/2*y**j. Solve g(c) = 0.
-2/5, 1
Factor 55*f**3 - 3*f**3 - 17*f**3 + 40*f**3 - 135*f**2 + 72*f - 12.
3*(f - 1)*(5*f - 2)**2
Let i(w) be the second derivative of w**7/252 + w**6/18 - 18*w. Determine g, given that i(g) = 0.
-10, 0
Let 5*r - 4*r**5 - 6 - 6*r**2 + r**5 + 10*r + 12*r**4 - 12*r**3 = 0. What is r?
-1, 1, 2
Suppose -1 = 21*f - 43. Factor 0*j + 0*j**f + 0 + 2/9*j**3 + 4/9*j**4 + 2/9*j**5.
2*j**3*(j + 1)**2/9
Let r(o) be the first derivative of 2/5*o**2 + 2/5*o + 2/15*o**3 + 4. Solve r(s) = 0 for s.
-1
Factor 1/9*q**2 + 2/3 - 5/9*q.
(q - 3)*(q - 2)/9
Let v(q) be the third derivative of -1/20*q**6 + 0*q + 0 - 1/12*q**4 + 1/105*q**7 - q**2 + 1/10*q**5 + 0*q**3. Factor v(t).
2*t*(t - 1)**3
Let i = -256/45 + 29/5. Let d(m) be the second derivative of -i*m**3 + 1/6*m**2 + 0 + m + 1/36*m**4. Factor d(c).
(c - 1)**2/3
Let i(f) be the first derivative of f**5/5 + f**4/2 + f**3/3 + 21. Solve i(c) = 0 for c.
-1, 0
Suppose -4*v + 8 = 4. Let x be -2 + 0 + 3 + v. Factor 0 - b - 1/2*b**x.
-b*(b + 2)/2
Let w(n) = 3*n**4 - 6*n**3 - 3*n**2 + 6*n + 6. Let s(o) = -3*o**4 + 7*o**3 + 3*o**2 - 7*o - 7. Let k(x) = -6*s(x) - 7*w(x). Factor k(d).
-3*d**2*(d - 1)*(d + 1)
Let i = -17 + 18. Let g(j) be the first derivative of 1/12*j**3 - 1/4*j**2 - i + 1/4*j. Factor g(q).
(q - 1)**2/4
Let x(b) be the second derivative of -b**8/11200 + b**6/1200 + 11*b**4/12 - 2*b. Let d(o) be the third derivative of x(o). Suppose d(z) = 0. What is z?
-1, 0, 1
Factor -10*n + 15 - 38*n**2 + 33*n**2 + 0*n.
-5*(n - 1)*(n + 3)
Let b(g) be the third derivative of 2*g**2 + 0*g**5 + 0*g**3 + 1/525*g**7 + 0*g**4 + 0 + 0*g - 1/300*g**6. Let b(r) = 0. What is r?
0, 1
Let b(s) be the first derivative of s**4/34 - 8*s**3/17 + 36*s**2/17 + 8. Suppose b(q) = 0. What is q?
0, 6
Factor -3*i**2 - i + 4 - 5 + 2*i**2 + 2 + i**3.
(i - 1)**2*(i + 1)
Let c(f) = 4*f**4 - 4*f**3 + f**2 - f - 5. Let a(y) = 5*y**4 - 5*y**3 + y**2 - y - 6. Let g(x) = -5*a(x) + 6*c(x). Solve g(s)