(1). Solve 0 - 2/5*n**3 + 0*n**2 + f*n - 4/5*n**4 = 0 for n.
-1/2, 0
Let p(h) be the second derivative of h**6/105 + 11*h**5/35 - h**4/14 - 64*h**3/21 + 44*h**2/7 - 806*h. Determine d, given that p(d) = 0.
-22, -2, 1
Let s = 574 + -572. Suppose 5*r = r. Factor 0*h + r*h**s + 0 + 1/4*h**3.
h**3/4
Let d be (-1 - (-21)/15)*15. Suppose 8 = t + d. Factor 3*f + f - 5*f**2 - f**2 + t*f**3.
2*f*(f - 2)*(f - 1)
Let r(z) = 5*z**5 + 20*z**4 + 5*z**3 - 20*z**2 - 20*z - 10. Let p(n) = -n**5 - n**4 + n**3 + 1. Let f(v) = 10*p(v) + r(v). Find l, given that f(l) = 0.
-1, 0, 2
Let g(j) be the first derivative of -2*j**3/3 + 51*j**2 + 212*j - 255. Suppose g(i) = 0. Calculate i.
-2, 53
Let h be (-4)/(-18) - (-22)/(-99). Suppose z + h = 2. Factor 3*g**4 - 40*g**z + 40*g**2.
3*g**4
Let d(s) = -9*s**3 - 156*s**2 - 303*s - 156. Let t(i) = -19*i**3 - 312*i**2 - 606*i - 313. Let g(l) = -13*d(l) + 6*t(l). Factor g(v).
3*(v + 1)**2*(v + 50)
Let z(d) be the third derivative of -d - 1/36*d**4 + 11*d**2 - 1/1260*d**7 + 0 - 1/144*d**6 - 1/45*d**5 + 0*d**3. Determine i, given that z(i) = 0.
-2, -1, 0
Suppose -3*k - 1 = -5*l, -l - l + 8*k - 20 = 0. Factor -1/3 - 2/3*z**3 - 2/3*z**l + 7/6*z.
-(z + 2)*(2*z - 1)**2/6
Let n(w) be the third derivative of 0*w - 4*w**2 + 0*w**4 - 1/2*w**3 + 1/20*w**5 + 0. Let n(b) = 0. What is b?
-1, 1
Suppose 3*v = -5*o + 171, v + 2*v - 3*o = 171. Suppose -4*t + 3 = -v. Factor -3*w**5 + 5*w**3 + 4*w**3 + w**4 - 3*w + 9*w - t*w**2 + 2*w**4.
-3*w*(w - 1)**3*(w + 2)
Suppose 9*c - 10 = 4*c. Suppose 3*w - 26 = -4*t, -4*w = w - 3*t - 53. Factor 10*j - 26 - 6*j**c + w + 12.
-2*(j - 1)*(3*j - 2)
Let u = -24 - -25. Let v be (u/2)/(1/4). Suppose 4 - 4 + p - p**v = 0. Calculate p.
0, 1
Suppose -2*q + 24 = -2. Let x(y) = 2*y - 2. Let w be x(2). Solve -q*f + 22*f**w + 24 - 7*f**2 - 6*f - 47*f = 0.
2/5, 4
Let o(i) = -i**2 + i + 1. Let z(q) = 4*q**2 - 141*q + 4758. Let t(u) = 3*o(u) + z(u). Factor t(p).
(p - 69)**2
Let k be 1/(-1)*((-69)/21 - -3). Let j(s) be the first derivative of -1/14*s**4 + 1 + 0*s - 2/7*s**2 - k*s**3. Factor j(c).
-2*c*(c + 1)*(c + 2)/7
Let l(r) = -r**3 + 2*r + 17. Let g be l(0). Suppose -33 = -4*q + 5*n, 2*q - 5*n + g = 46. Suppose -9*m**q + 3*m**2 + 5*m**2 + 2 + m = 0. What is m?
-1, 2
What is u in 3*u - 6 - 3/4*u**3 + 15/2*u**2 - 3/4*u**5 - 3*u**4 = 0?
-2, 1
Let f(v) be the second derivative of v**9/7560 - v**8/672 + v**7/180 - v**6/120 - 5*v**4/4 - 7*v. Let w(d) be the third derivative of f(d). Factor w(j).
2*j*(j - 3)*(j - 1)**2
Let c = -23453/18 - -1303. Let m(g) be the first derivative of 4 - 2/9*g**3 + 0*g + 5/12*g**4 - 4/15*g**5 + c*g**6 + 0*g**2. Suppose m(n) = 0. What is n?
0, 1, 2
Let k(c) = c**2. Suppose 5*i - 40 = 3*i. Let y be (-2)/(1/((28/8)/7)). Let x(j) = 15*j**2 + 30*j - 45. Let t(v) = i*k(v) + y*x(v). Factor t(s).
5*(s - 3)**2
Let s be (-108)/(-28) + (-1)/(-7). Let t(y) be the first derivative of -4/3*y**3 - 1/4*y**s + 2 - 1/2*y**2 + 1/3*y**6 + 7/10*y**5 + 1/2*y. Factor t(l).
(l - 1)*(l + 1)**3*(4*l - 1)/2
Factor 3*z**3 - 63/8*z**2 + 0 + 27/4*z - 3/8*z**4.
-3*z*(z - 3)**2*(z - 2)/8
Let g(d) = 2*d**2 + 17*d - 52. Let w be g(-11). Let q(m) be the first derivative of 0*m - 1/3*m**2 + 7 - 2/9*m**w. Factor q(y).
-2*y*(y + 1)/3
Let j(y) be the third derivative of -y**6/40 - y**5/4 - y**2 + 21. Let v(z) = 3*z**3 + 14*z**2. Let n be 3*(-1*1 + 2). Let o(l) = n*v(l) + 2*j(l). Factor o(i).
3*i**2*(i + 4)
Let c be 3/(-6)*(-18 - -18). Let s be (8/33*-3)/(-2 + c). Factor 0 + 2/11*i**4 + 0*i - s*i**2 + 2/11*i**3.
2*i**2*(i - 1)*(i + 2)/11
Suppose 0 = -15*j + 16*j - 2. Let m be 1/j*((-30)/(-9))/5. Factor 1/3 + 0*s - m*s**2.
-(s - 1)*(s + 1)/3
Let t = -78 - -82. Let v(z) be the second derivative of 5*z + 2*z**2 + 2/3*z**3 + 1/12*z**t + 0. Find a, given that v(a) = 0.
-2
Let g(j) = -5*j**4 + j**3 + 2*j**2 + 2*j. Let z(u) = 46*u**4 - 15*u**3 - 12*u**2 + 10*u**3 - 12*u - 17*u**4. Let q(i) = -34*g(i) - 6*z(i). Factor q(y).
-4*y*(y - 1)*(y + 1)**2
Let y = 7/534 - -2087/3738. Factor 10/7*x**2 - 2/7*x**4 - 2/7*x**5 + 6/7*x**3 + y*x + 0.
-2*x*(x - 2)*(x + 1)**3/7
Let j(n) be the second derivative of 5*n**7/42 + 77*n**6/6 + 1121*n**5/2 + 74005*n**4/6 + 788785*n**3/6 + 651605*n**2/2 + 38*n. Factor j(i).
5*(i + 1)*(i + 19)**4
Factor 117/7*l + 150/7*l**2 - 891/7*l**4 - 522/7*l**3 - 27/7 - 363/7*l**5.
-3*(l + 1)**3*(11*l - 3)**2/7
Let w = -2312 - -11562/5. Factor -4/5*f**3 - 2/5*f**4 + 4/5*f**2 - 2/5 + 2/5*f + w*f**5.
2*(f - 1)**3*(f + 1)**2/5
Suppose 3*g + 28 = 5*u + 59, -4*u = -g + 22. Determine w, given that 1/2*w**5 + 2*w**g + 0*w - 3/2*w**4 + 0*w**3 + 0 = 0.
-1, 0, 2
Let a(k) = -k**2 - 8*k - 7. Let w be a(-7). Let h be 8/60*(w + 6 + 314). Factor -32/3*q + h*q**2 + 2/3.
2*(8*q - 1)**2/3
Suppose -28*w - 204 = -79*w. Factor -9/7*p**2 - 6/7 + 3/7*p**w + 3/7*p**3 - 15/7*p.
3*(p - 2)*(p + 1)**3/7
Let g(s) be the first derivative of s**4/38 - 2*s**3/19 + 2*s**2/19 - 121. Factor g(w).
2*w*(w - 2)*(w - 1)/19
Let u(r) be the first derivative of -r**7/70 - 4*r**6/75 - 7*r**5/100 - r**4/30 + 5*r - 8. Let x(z) be the first derivative of u(z). Factor x(v).
-v**2*(v + 1)**2*(3*v + 2)/5
Let c(l) = l**4 + l**3 + 2*l**2 + l + 1. Let r(j) = -j**5 + 18*j**4 - 12*j**3 - 12*j**2 + 17*j + 2. Let z(y) = 4*c(y) - 2*r(y). Solve z(h) = 0 for h.
-1, 0, 1, 15
Let j(d) be the first derivative of -d**6/15 + 158*d**5/5 - 5841*d**4 + 509652*d**3 - 18435681*d**2 - 192119202*d/5 - 633. Factor j(s).
-2*(s - 99)**4*(s + 1)/5
Let r(m) = -4*m - 4. Let t be r(-2). Let x be -2*t/8*-3. Factor o + 2*o**3 + 4*o**3 - x*o**5 + 3*o**4 - o.
-3*o**3*(o - 2)*(o + 1)
Suppose 89*k + 145 = 501. Factor 1 + 5/2*z - k*z**3 - 3/2*z**2 + 2*z**4.
(z - 2)*(z - 1)*(2*z + 1)**2/2
Let g(x) be the third derivative of -x**8/1008 - 2*x**7/315 - x**6/60 - x**5/45 - x**4/72 + 81*x**2. Let g(q) = 0. Calculate q.
-1, 0
Suppose -u - 4*n + 19 = 0, -6*u + 16*n = 17*n - 22. Let k(w) be the first derivative of 1/3*w**u + 2*w**2 + 11 + 3*w. Factor k(o).
(o + 1)*(o + 3)
Let k be ((-339)/132 - -3) + 38/(-209). Find l, given that k*l**3 + 1/4*l**2 - 1/2*l + 0 = 0.
-2, 0, 1
Suppose -b = 5*q + 4*b + 5, 5*b = 2*q - 33. Factor -2/5*l**2 + 2/5*l**3 - 1/5*l**5 + 1/5*l**q + 1/5 - 1/5*l.
-(l - 1)**3*(l + 1)**2/5
Let v = -19500 - -1442979/74. Let g = 8/37 - v. Factor -1/2 + 1/2*t**2 + 1/2*t**3 - g*t.
(t - 1)*(t + 1)**2/2
Let l(q) = 3*q - 11. Let a be l(5). Determine t, given that 51*t - 12*t**a + 6*t**2 - 28*t - 27*t + 22*t**3 = 0.
-1/2, 0, 1/3, 2
Let g(i) = -8*i - 95. Let l be g(-12). Let y be 2/(-8) + 26/8. Solve -12*o**4 + l - 4*o**3 + 2*o**y + 11*o**4 + 2*o = 0.
-1, 1
Let i(s) = s**3 - 8*s**2 + 13*s - 2. Let l be i(6). Solve -9*j**l - 2*j**4 + 0*j**3 - 4*j**3 + 9*j**4 = 0 for j.
-2, 0
Let b be 884/39 - (4/(-3))/(-2). Let g(a) = -3*a**3 - 7*a**2 - a + 9. Let s(n) = -16*n**3 - 36*n**2 - 4*n + 45. Let m(t) = b*g(t) - 4*s(t). Factor m(o).
-2*(o - 1)*(o + 3)**2
Let j(g) be the second derivative of g**4/4 - 75*g**3 + 16875*g**2/2 + 389*g. Factor j(d).
3*(d - 75)**2
Suppose 2*a**4 + 24*a + 4 - 3*a**3 - 4 - 3*a**3 - 8*a**2 = 0. Calculate a.
-2, 0, 2, 3
Let q(o) = -o**3 - 2*o**2 + 2*o - 3. Let c be q(-3). Suppose u + u - 20 = c. Suppose 22*y - 12*y**2 - 12*y - u*y + 28*y**3 = 0. What is y?
0, 3/7
Let k(g) = -15*g**2 - 25*g - 30. Let y(x) = -x**2 + x + 3. Let r(i) = -k(i) + 10*y(i). Let r(q) = 0. What is q?
-4, -3
Let t(h) = -4*h + 6. Let p be t(1). Factor 3*l + 0*l - 12*l**3 + 10*l**p + 5*l**2 + 3*l**4 - 9*l.
3*l*(l - 2)*(l - 1)**2
Factor -8*w - 28/3 + 4/3*w**2.
4*(w - 7)*(w + 1)/3
Let i(z) = z**2 + 9*z + 18. Let v be i(-6). Let j(u) be the first derivative of -1/3*u**3 + v*u - u**2 + 1. Let j(f) = 0. Calculate f.
-2, 0
Let k be 24/64 + (-3)/8. Suppose d - 2*d + m = k, -m + 6 = 2*d. Let -7 + 2 + 0 + 2 + g**2 + d*g = 0. Calculate g.
-3, 1
Let b(f) = 2*f**2 + 12*f + 14. Let h = 67 + -71. Let x(c) = 8*c**2 + 48*c + 55. Let o(g) = h*x(g) + 18*b(g). Factor o(m).
4*(m + 2)*(m + 4)
Let p(f) = f**3 - 6*f**2 - 2*f - 1. Let h be p(5). Let x be (-87)/(-27) + 8/h. Find l, given that 2*l**5 + 3*l**4 + 2*l**3 + x*l**5 - 2*l**5 - 2*l**5 = 0.
-2, -1, 0
Let m(r) = r**2 - 1. Let l(n) = -6*n**2 - 4*n + 7. Let z(p) = -2*l(p) - 6*m(p). Let b(c) = -c**2 - c + 1. Let g(x) = 8*b(x) + z(x). Suppose g(a) = 0. What is a?
0
Let d be (-192)/288 - 6/(-8). Let w