
Let f = -5042293684/867 - -5815795. Let j = f - 1/289. Factor -1/3*h + j*h**2 - 1/3*h**4 - 1/3 + 2/3*h**3 - 1/3*h**5.
-(h - 1)**2*(h + 1)**3/3
Let v(l) be the second derivative of 1/315*l**6 - 1/105*l**5 + 0*l**3 + 0 + 1/126*l**4 - 13*l + 0*l**2. Solve v(m) = 0.
0, 1
Let j be (-12 + 10)*(-3)/2. Let v be -9*1*(j + -4). Factor 3*m**2 + m**3 - 7*m**3 + v*m**3.
3*m**2*(m + 1)
Let i = -10555 - -52777/5. Factor -2 - 12/5*k - i*k**2.
-2*(k + 1)*(k + 5)/5
Factor 2/5*v**3 + 4/5*v**2 + 2/5*v + 0.
2*v*(v + 1)**2/5
Let w(a) be the third derivative of -6*a**2 + 1/10*a**5 + 0*a - 1/8*a**4 + 1/40*a**6 - a**3 + 0. Factor w(o).
3*(o - 1)*(o + 1)*(o + 2)
Let r = -546 - -379. Let w = -165 - r. Solve -2/7*k + 2/7*k**w + 0 = 0 for k.
0, 1
Let r(g) be the second derivative of -g**6/360 - g**5/45 - g**4/18 - 45*g**2/2 - 16*g. Let a(w) be the first derivative of r(w). Factor a(z).
-z*(z + 2)**2/3
Let k(l) be the second derivative of l**6/45 + l**5/30 - l**4/6 - l**3/9 + 2*l**2/3 - 234*l. Factor k(m).
2*(m - 1)**2*(m + 1)*(m + 2)/3
Let b(a) be the third derivative of 1/40*a**4 + 18*a**2 - 1/200*a**6 + 1/100*a**5 - 1/10*a**3 + 0 + 0*a. Suppose b(h) = 0. Calculate h.
-1, 1
Let i(p) be the second derivative of 1/36*p**4 + 0 - 1/3*p**3 + 25*p + 5/6*p**2. Factor i(o).
(o - 5)*(o - 1)/3
Let p be (-1 + 0 + (-72)/36)/(-1). Factor -8/7*o**p + 0 - 2/7*o**4 - 4/7*o - 10/7*o**2.
-2*o*(o + 1)**2*(o + 2)/7
Let v(x) be the first derivative of -4*x**3/3 + 34*x**2 - 64*x - 43. Factor v(n).
-4*(n - 16)*(n - 1)
Find z such that -58/5*z - 3/5*z**3 - 24/5 - 41/5*z**2 + 1/5*z**5 + z**4 = 0.
-4, -2, -1, 3
Factor 0*a**2 + 0*a + 0 + 1/4*a**4 - 15/4*a**3.
a**3*(a - 15)/4
Let r(h) be the second derivative of h**5/20 - 3*h**4/4 + 11*h**3/6 - 10*h**2 - 4*h. Let z be r(8). Suppose -60 + 60 - 2*m**z - 3*m**5 = 0. What is m?
-2/3, 0
Let x(t) be the third derivative of -t**8/10080 - t**7/315 - 2*t**6/45 - t**5/6 - 13*t**2. Let j(z) be the third derivative of x(z). Factor j(m).
-2*(m + 4)**2
Suppose 8*m = 82 - 50. Let t be 23/6 + (-8)/(-12) - m. Determine d, given that t*d**2 + 0*d - 1/2 = 0.
-1, 1
Suppose 4*i - 15 = 5*j, 5*i - 3*j - 39 + 4 = 0. Let q = i + -19/2. Determine m, given that -1/2*m**2 + 1/2*m**3 - q*m + 1/2*m**4 + 0 = 0.
-1, 0, 1
Let a(b) be the first derivative of -5/12*b**3 - 15/2*b**4 - 5/4*b + 15/4*b**2 - 4*b**5 + 12. Suppose a(m) = 0. Calculate m.
-1, 1/4
Let g(q) be the second derivative of 1/4*q**4 + 0 - 5/2*q**3 + 6*q**2 + 32*q. Factor g(y).
3*(y - 4)*(y - 1)
Suppose 3*j = -15, 19 = 4*t - 4*j - 1. Factor -20/9*c**3 + t*c - 4/9*c**5 - 8/9*c**2 - 16/9*c**4 + 0.
-4*c**2*(c + 1)**2*(c + 2)/9
Let h = 1239 - 8635/7. Let o = 111/14 - h. Factor o*a + 1 - 7/2*a**2.
-(a - 1)*(7*a + 2)/2
Find c, given that -45/4*c**2 + 5/4*c**4 + 55/4*c - 5 + 5/4*c**3 = 0.
-4, 1
Let q(x) = -2*x**3 - 10*x**2 - 7*x + 7. Let g be q(-4). Let y(u) be the first derivative of -1/9*u**g + 1/3*u - 1/6*u**2 - 2 + 1/12*u**4. Factor y(c).
(c - 1)**2*(c + 1)/3
Let g(u) = -23 - 9 + 3*u + 19. Let m be g(9). Determine a so that m + a**2 - 14 + 2*a = 0.
-2, 0
Let l = 36946/5 - 7389. Factor 1/5 - 1/5*j**2 - 1/5*j + l*j**3.
(j - 1)**2*(j + 1)/5
Let a(d) be the third derivative of -2*d**5/15 - 23*d**4/6 + 8*d**3 + 48*d**2 - 4. Factor a(p).
-4*(p + 12)*(2*p - 1)
Suppose 3*k + 3*l = -9, 0*k + 3*l + 9 = k. Let o be (2/(-15)*(-10 - -1))/3. Suppose 0*c + o*c**2 + k = 0. Calculate c.
0
Let t be (-10)/25 + (-4)/(-10). Factor 1/10*w**3 + t + 0*w + 0*w**2.
w**3/10
Let 10*b**3 + 35*b + 36 + 0 - 26 + 35*b**2 = 0. Calculate b.
-2, -1, -1/2
Let u(y) be the first derivative of -3*y**2 + 3*y + 12. Let m be u(0). Factor 8/13*i**2 + 10/13*i + 2/13*i**m + 4/13.
2*(i + 1)**2*(i + 2)/13
Find j, given that 850*j - 8*j**4 - 49*j**4 - 972*j**2 + 3*j**5 - 202*j + 378*j**3 = 0.
0, 1, 6
Let w(v) = v**2 - 1. Let f(h) = -h**3 - 6*h**2 + h + 6. Let i be (30/2)/((2 + -8)/(-6)). Let q(l) = i*w(l) + 3*f(l). What is y in q(y) = 0?
-1, 1
Suppose -9*c + 34 = -2. Let a(t) be the third derivative of 1/330*t**5 + 0*t + 0 + 0*t**4 - 1/660*t**6 + 0*t**3 + c*t**2. Suppose a(b) = 0. What is b?
0, 1
Let p be (22/4 + 3)*38. Let c = -321 + p. Determine l, given that -2/7*l**c + 0 - 4/7*l + 2/7*l**3 = 0.
-1, 0, 2
Let k(i) = 5*i + 2. Let l be k(0). Factor -47*r - 4*r**2 - r**2 + 32*r + l*r**2.
-3*r*(r + 5)
Let n(s) = -4*s**4 - 24*s**3 - 12*s**2 + 28*s. Let m(t) = 4*t**4 + 23*t**3 + 11*t**2 - 29*t. Let w(q) = -4*m(q) - 3*n(q). Factor w(f).
-4*f*(f - 1)*(f + 2)*(f + 4)
Factor -1589 + 35*m - 7*m - m**2 + 72*m - m**2 + 339.
-2*(m - 25)**2
Let m(v) be the third derivative of -v**5/180 - 19*v**4/72 + 10*v**3/9 - 218*v**2. What is w in m(w) = 0?
-20, 1
Factor -180*t**2 + 336*t - 225 + 33 + 39*t**3 + t**4 - 4*t**4.
-3*(t - 4)**3*(t - 1)
Factor 3/4*z**3 - 27/4*z**2 + 21/2*z + 0.
3*z*(z - 7)*(z - 2)/4
Let h be ((-50)/3)/(22/(-33)) - 4. Let t be (-48)/168*h/(-4). Determine y, given that -3/2*y**2 - t*y**3 + 3/2*y**4 + 0 + 3/2*y**5 + 0*y = 0.
-1, 0, 1
Suppose -2*y - 3*j = 11, 11 = 3*y + 9*j - 10*j. Factor 8/5*q - 16/5 - 2/5*q**3 + 4/5*q**y.
-2*(q - 2)**2*(q + 2)/5
Let a be -4 + 2996/665 + (-24)/60. Suppose 18/19*t**4 - 12/19*t**3 - 8/19*t**5 + a*t**2 + 0*t + 0 = 0. Calculate t.
0, 1/4, 1
Let t = 7 - 6. Let p be (-2)/t*(-8 + 6). Suppose x**4 - 6*x**4 + 4*x**p = 0. Calculate x.
0
Let h be (9/(-3) - 44) + 1. Let n = -44 - h. Solve -4/3*r**n + 0 - 1/3*r - 1/3*r**5 - 2*r**3 - 4/3*r**4 = 0.
-1, 0
Let b(a) be the third derivative of a**6/300 - 31*a**4/60 + 2*a**3 - 34*a**2. Determine l so that b(l) = 0.
-6, 1, 5
Let u = 17849 + -17848. Find d such that 3/4*d**2 + d - d**3 - u + 1/4*d**4 = 0.
-1, 1, 2
Let d(n) be the first derivative of 7 - 1/22*n**4 + 6/11*n + 5/11*n**2 + 2/33*n**3. Factor d(r).
-2*(r - 3)*(r + 1)**2/11
Let g(f) be the second derivative of f**7/21 - 2*f**6/15 - 7*f**5/5 - 4*f**4/3 + 13*f**3/3 + 10*f**2 + 68*f + 1. Determine n, given that g(n) = 0.
-2, -1, 1, 5
Let n = 1314 + -59129/45. Let u(g) be the second derivative of 0 - 7*g - n*g**4 - 1/15*g**3 - 1/15*g**2. Factor u(w).
-2*(w + 1)*(2*w + 1)/15
Let p be 6*(-3 + 70/12). Let m = 26 - p. Factor -m*r + 6*r - 2*r**2 - 2 + r**2.
-(r + 1)*(r + 2)
Let p(z) be the second derivative of z**6/450 + z**5/75 - 13*z**3/3 + 11*z. Let l(o) be the second derivative of p(o). Factor l(m).
4*m*(m + 2)/5
Suppose -4*h - 5*q - 95 = 0, -2*q + 0*q = 4*h + 86. Let y be (-46)/(-24) + (-1)/((-16)/h). Factor 4/3*k**2 - 8/3*k - 16/3 + y*k**3.
2*(k - 2)*(k + 2)**2/3
Let t be (-20)/24*(-28)/10. Suppose -13*f - 518 = -570. Solve 5/6*r - 1/6 - 1/3*r**2 + 1/2*r**f - t*r**3 + 3/2*r**5 = 0.
-1, 1/3, 1
Let o(t) be the third derivative of -t**8/11760 - t**7/4410 - t**5/6 + 16*t**2. Let g(r) be the third derivative of o(r). Let g(s) = 0. Calculate s.
-2/3, 0
Let v be ((-11 - -11) + 1)/5. Let 3/5*b**2 - 3/5*b - v*b**3 + 1/5 = 0. Calculate b.
1
Let i be 15/20*(42/(-7) - -8). Let r(d) be the first derivative of 1 - 9/2*d - i*d**2 - 1/6*d**3. Find u, given that r(u) = 0.
-3
Suppose -709 + 163 = -6*b. Let q = -545/6 + b. Factor 8/3*k**3 - q - 4*k**2 + 3/2*k.
(k - 1)*(4*k - 1)**2/6
Let v = 143 + -141. Let f(y) be the third derivative of 1/72*y**4 + 0*y + 0*y**3 + 1/180*y**5 - 2*y**v + 0. Factor f(i).
i*(i + 1)/3
Suppose -5*d - 2*f + 13 = 0, 13*f + 2 = 11*f. Solve 0 - 2/9*j**d - 8/9*j**2 - 8/9*j = 0 for j.
-2, 0
Let f(y) = 9*y**3 + 17*y**2 - 4*y. Let z(b) = -36*b**3 - 69*b**2 + 15*b. Let v(d) = -9*f(d) - 2*z(d). Find a, given that v(a) = 0.
-2, 0, 1/3
Let h(n) be the first derivative of 18*n**5/25 - 33*n**4/10 - 44*n**3/3 - 92*n**2/5 - 48*n/5 + 891. What is v in h(v) = 0?
-1, -2/3, 6
Let s = -4739/3 + 1581. Factor 1/3*y**3 - s + y**2 + 0*y.
(y - 1)*(y + 2)**2/3
Solve 0 + 9/8*p + 9*p**4 - 6*p**2 - 27/8*p**5 + 21/4*p**3 = 0 for p.
-1, 0, 1/3, 3
Factor -6/7*p + 2/7*p**4 - 10/7*p**2 - 2/7*p**3 + 0.
2*p*(p - 3)*(p + 1)**2/7
Let w(o) be the third derivative of -1/18*o**4 - 2*o**2 + 0 + 1/105*o**7 - 2/45*o**5 + 1/9*o**3 + 0*o + 1/90*o**6. Solve w(q) = 0.
-1, 1/3, 1
Let r(m) = 5*m**2 - 22*m + 85. Let s be r(6). Let v = s - 130. Factor 2/5*w**2 + 1/5*w + 1/5*w**v + 0.
w*(w + 1)**2/5
Factor 92/5*f**2 - 4/5*f**4 + 88/5*f**3 + 0 + 0*f.
-4*f**2*(f - 23)*(f + 1)/5
Let n(v) be the second derivative of v**5/4 + 3*v**4/2 + 7*v**3/2 + 4*v**2 - 65*v. Factor n(y).
(y + 1)**2*(5*y +