mine t so that -1/2*t**2 + 1/4*t**3 + l*t + 0 = 0.
0, 1
Let f(m) be the second derivative of -m**5/40 - m**4/6 - 5*m**3/12 - m**2/2 + 622*m. Factor f(q).
-(q + 1)**2*(q + 2)/2
Let s = 92 + -92. Let u be 2*5/30 + s. Determine f so that -u + 1/3*f**2 - 1/3*f**3 + 1/3*f = 0.
-1, 1
Let m(p) be the second derivative of -p**6/540 - p**5/135 - p**4/108 + 15*p**2/2 - 16*p. Let r(g) be the first derivative of m(g). Find a such that r(a) = 0.
-1, 0
Let c(a) = 2*a**3 - 5*a**2 + 9*a. Let l(g) be the second derivative of -g**5/20 + g**4/12 - g**3/3 + 20*g. Let x(w) = -c(w) - 4*l(w). Factor x(j).
j*(j + 1)*(2*j - 1)
Let i(u) be the first derivative of u**4/42 - 2*u**3/21 - 10*u - 12. Let m(b) be the first derivative of i(b). Factor m(p).
2*p*(p - 2)/7
Let o be 16/36 + (70/(-21))/10. Suppose 0*n**4 - o*n**5 + 2/3*n**3 + 1/3*n - 8/9*n**2 + 0 = 0. What is n?
-3, 0, 1
Suppose -230/3*n**4 - 25/3*n**5 - 243*n - 54 - 258*n**3 - 384*n**2 = 0. What is n?
-3, -2, -3/5
Let h(l) = 7*l**2 - 266*l + 17665. Let x(n) = 8*n**2 - 266*n + 17661. Let f(p) = 7*h(p) - 6*x(p). Determine v so that f(v) = 0.
133
Let k = -17050 + 68201/4. Factor 3/4*o + 5/4*o**2 - 1/4*o**4 + 0 + k*o**3.
-o*(o - 3)*(o + 1)**2/4
Let v = -3 + 16. Suppose -7*a = -15 - v. What is z in -3/4*z**2 + 3*z**5 - 21/4*z**3 + 0*z**a + 9/4*z + 3/4 = 0?
-1, -1/2, 1
Let l = -83 + 83. Suppose -2*j - 3*j - 2*j = l. Factor 2/11*c**2 + 0*c - 2/11*c**4 + 0 + j*c**3.
-2*c**2*(c - 1)*(c + 1)/11
Let y(z) be the first derivative of 5*z**6/6 + 5*z**5 + 25*z**4/4 - 25*z**3/3 - 15*z**2 + 92. Determine o, given that y(o) = 0.
-3, -2, -1, 0, 1
Let g be (126/15)/(6/15). Factor -3*x**3 + x**3 - 3*x - g*x**2 + 6 + 5*x**3 + 15*x**2.
3*(x - 2)*(x - 1)*(x + 1)
Let w(b) = -b**2 - 1. Let d(y) = 4*y**2 + 12*y + 18. Let i(h) = -2*h - 50. Let v be i(-24). Let o(k) = v*w(k) - d(k). Factor o(g).
-2*(g + 2)*(g + 4)
Suppose -2*g + 2*n = -0*n - 4, 3*g + 5*n - 38 = 0. What is b in 4 + g*b - 2*b**2 + 8 - 2 + 2*b = 0?
-1, 5
Let g = -608/15 - -836/15. Find r such that 64/5*r**2 + 26/5*r + 4/5 + 44/5*r**4 + g*r**3 + 2*r**5 = 0.
-1, -2/5
Let h(y) be the second derivative of y**8/21 + y**7/3 - 31*y**6/72 + y**5/6 + 4*y**3/3 + 30*y. Let v(c) be the second derivative of h(c). Factor v(l).
5*l*(l + 4)*(4*l - 1)**2
Let r(k) = -k**3 - 3*k**2 - k. Let z(l) = -45*l**5 + 107*l**4 - 56*l**3 - 30*l**2 + 15*l + 4. Let f(x) = r(x) - z(x). What is o in f(o) = 0?
-2/5, -2/9, 1
Suppose 67*b - 62*b - 6 = 4. Solve -1/3*g**3 + g**b - 1/2*g**5 + 5/6*g + 1/6 - 7/6*g**4 = 0.
-1, -1/3, 1
Let q(z) be the second derivative of -2/3*z**4 + 1/15*z**5 - 3*z**2 - 7*z + 0 + 8/3*z**3. Let r(p) be the first derivative of q(p). Factor r(s).
4*(s - 2)**2
Let q(x) = 3*x**2 + 34*x + 17. Let j be q(-11). Let u be j/(-20)*(-5 - 1). Let 0*l + 0 + 3/5*l**5 - 3/5*l**2 - 9/5*l**4 + u*l**3 = 0. Calculate l.
0, 1
Solve -172/5*n**2 - 784/5 - 2/5*n**5 + 1288/5*n + 56/5*n**4 - 386/5*n**3 = 0.
-2, 1, 14
Let -5*j + 17/4*j**2 + 1 - j**3 = 0. Calculate j.
1/4, 2
Let b(a) be the first derivative of a**4/4 + 10*a**3/3 - 2*a**2 - 40*a - 72. Let g be b(-10). Determine x, given that 6/11*x**2 + g*x - 8/11 + 2/11*x**3 = 0.
-2, 1
Let b(l) be the third derivative of l**6/1440 - l**5/160 - 7*l**3/6 + 6*l**2. Let k(v) be the first derivative of b(v). Let k(a) = 0. Calculate a.
0, 3
Let t(q) be the first derivative of -3*q**5/20 + 21*q**4/16 - 11*q**3/4 - 21*q**2/8 + 9*q + 907. Let t(k) = 0. Calculate k.
-1, 1, 3, 4
Let r = 668 + -391. Factor -r*b + 2*b**2 + 17 - 45 + 251*b.
2*(b - 14)*(b + 1)
Let o(c) = 11*c**2 + 33*c + 58. Let s(a) = -8*a**2 - 32*a - 56. Let q(m) = -2*o(m) - 3*s(m). Let q(i) = 0. Calculate i.
-13, -2
Suppose -3*d - 2*d = -5. Let w be (d + -1)/(2 + (-12)/4). Factor w - 2/3*t + 2/3*t**2.
2*t*(t - 1)/3
Let y(z) = 7*z - 44. Let p = -100 - -107. Let a be y(p). Let 3/5*t + 0*t**3 + 0 + 6/5*t**4 - 3/5*t**a - 6/5*t**2 = 0. What is t?
-1, 0, 1
Let s = 2113/4 + -2111/4. Solve 0*y**4 - s*y + 0*y**2 - 1/2*y**5 + y**3 + 0 = 0.
-1, 0, 1
Let o(u) be the second derivative of -5*u**3/2 + 63*u**2/2 - 5*u. Let v be o(4). Factor 2/9*a**4 + 2/9*a**2 - 2/3*a**v - 4/9 + 2/3*a.
2*(a - 2)*(a - 1)**2*(a + 1)/9
Let y(h) be the first derivative of 2*h**3/9 - 7*h**2/3 + 20*h/3 - 49. Solve y(g) = 0 for g.
2, 5
Let t(r) be the second derivative of -r**5/14 + r**4/42 + 25*r + 2. Factor t(o).
-2*o**2*(5*o - 1)/7
Suppose 0 = 2*h - 5*x, 6 = -2*x + 5*x. Let q(g) be the third derivative of 6*g**2 + 1/5*g**h - 1/12*g**4 + 0*g + 0 - 1/12*g**6 + 0*g**3. Factor q(r).
-2*r*(r - 1)*(5*r - 1)
Let c = 605/138 + 8/69. Let n = c + -19/6. Factor -n - 1/3*z**3 + 0*z + z**2.
-(z - 2)**2*(z + 1)/3
Suppose -2*d - d - f + 17 = 0, -2*f - 14 = -2*d. Let k = d + 1. Suppose 9 + 4*w**4 - 6*w + k*w**2 - 19*w**3 + 32*w + 13*w = 0. What is w?
-1, -1/4, 3
Factor 0*d**4 - 2/19*d**5 - 40/19*d**2 + 20/19*d**3 - 8/19 + 30/19*d.
-2*(d - 1)**4*(d + 4)/19
Let g(s) be the first derivative of s**7/126 - 2*s**6/45 + s**5/30 + s**4/9 - s**3/6 + 2*s + 8. Let n(m) be the first derivative of g(m). Factor n(w).
w*(w - 3)*(w - 1)**2*(w + 1)/3
Let r(s) be the third derivative of s**6/240 + 3*s**5/40 + 7*s**4/24 - 113*s**2. Find k, given that r(k) = 0.
-7, -2, 0
Suppose 3*a - 46 = 38. Factor -36 - 66*z + z**3 - a*z**2 - 12*z**2 - z**3 - 8*z**3.
-2*(z + 2)*(2*z + 3)**2
Let f(t) be the third derivative of 0*t - 7/10*t**3 + 13/40*t**4 - 1/20*t**5 + 0 - 1/200*t**6 + 19*t**2. Factor f(x).
-3*(x - 1)**2*(x + 7)/5
Let c be -1 - 18 - (-2 - -1). Let w be 4/c - (-38)/9. Find a such that -12/5*a**2 - 6/5*a**5 + 4/5 + 8/5*a**w - 2/5*a + 8/5*a**3 = 0.
-1, -2/3, 1
Let r = 7106/23 - 309. Let t = 51/115 + r. Let -6/5*y + 2/5 + 4/5*y**3 + t*y**5 - 6/5*y**4 + 4/5*y**2 = 0. Calculate y.
-1, 1
Let d(r) be the second derivative of 1/21*r**4 + 0 + 8/21*r**3 + 6*r + 6/7*r**2. Find c such that d(c) = 0.
-3, -1
Let s(x) be the second derivative of 0 - 1/12*x**3 + 0*x**2 - 4*x - 1/24*x**4. Solve s(k) = 0.
-1, 0
Let k(b) = -b**2 - b + 31. Let w be k(0). Let f = w - 29. Factor 5*h**2 - 2*h - 4*h + 0*h**2 + 34*h**f.
3*h*(13*h - 2)
Let y = -171 - -182. Suppose 0 = -0*b - b - y*b. Determine x so that -1/3*x**3 - 8/3*x**4 + 0 + 2/3*x**2 + b*x - 5/3*x**5 = 0.
-1, 0, 2/5
Solve -2/9*s**4 + 0 + 0*s - 8/9*s**3 + 8/3*s**2 = 0.
-6, 0, 2
Let s(k) be the first derivative of -5*k**6/3 - 8*k**5/5 + 5*k**4 + 16*k**3/3 - 5*k**2 - 8*k - 70. Let s(g) = 0. Calculate g.
-1, -4/5, 1
Let g = 989/18 + -109/2. Determine a, given that -4/9*a**3 + g*a - 2/9*a**2 + 2/9*a**4 + 0 = 0.
-1, 0, 1, 2
Let i(g) = -g**3 + 65*g**2 + 55*g + 726. Let k be i(66). Factor k - 4/7*v**2 - 8/7*v**3 + 4/7*v**4 + 8/7*v.
4*v*(v - 2)*(v - 1)*(v + 1)/7
Factor 1074/5*g**2 - 24*g**3 + 1323/5 + 3/5*g**4 + 504*g.
3*(g - 21)**2*(g + 1)**2/5
Suppose 0 = -2*g - 2, 2*f - 4*g = 7 + 5. Let y(w) be the second derivative of -1/16*w**f + 0 - 4*w - 1/8*w**2 + 1/8*w**3 + 1/80*w**5. Factor y(b).
(b - 1)**3/4
Let u(h) = -3*h**4 - 4*h**3 + 13*h**2 + 8*h - 3. Let m(p) = 5*p**4 + 8*p**3 - 27*p**2 - 16*p + 7. Let s(l) = -3*m(l) - 7*u(l). Factor s(a).
2*a*(a + 1)**2*(3*a - 4)
Let l(w) be the third derivative of w**6/720 + 11*w**5/90 + 175*w**4/48 + 49*w**3/2 + 121*w**2. Factor l(g).
(g + 2)*(g + 21)**2/6
Let v(k) = -5*k**5 + 5*k**4 + 3*k**3 - 2*k**2 - 7*k + 3. Let j(m) = 2 + 1 + m + m**3 - m**4 - 2 - 2 + m**5. Let f(r) = -6*j(r) - 2*v(r). Factor f(c).
4*c*(c - 2)*(c - 1)*(c + 1)**2
Let i be 40/(-25)*(-10)/4. Let h be (-20)/(-60)*-9*i/(-30). Determine g, given that 2/5*g**2 + h*g + 0 = 0.
-1, 0
Let c(p) be the first derivative of -3*p**5/5 - 3*p**4/4 + 4*p**3 + 6*p**2 + 79. Factor c(y).
-3*y*(y - 2)*(y + 1)*(y + 2)
Suppose 19*b + 3*b = -21*b + 86. Solve -8/3*v - 2 - 2/3*v**b = 0 for v.
-3, -1
Let f(n) be the third derivative of -2*n**7/105 + 3*n**6/5 + 13*n**5/5 + 10*n**4/3 - 3*n**2 + 7*n. Solve f(w) = 0 for w.
-1, 0, 20
Let u be (-1064)/(-760) - 2/(-10)*3. Factor 1/8*g**3 + 0 + 1/4*g + 3/8*g**u.
g*(g + 1)*(g + 2)/8
Let i = 76 - 67. Let -359*q + i*q**2 + 6*q**2 - 3*q**3 + 347*q = 0. Calculate q.
0, 1, 4
Suppose -4*n - l + 13 = 0, -2*l + 36 = 5*n + 19. Suppose 16/13 + 122/13*d**n - 50/13*d**5 + 44/13*d**2 - 72/13*d - 60/13*d**4 = 0. What is d?
-2, -1, 2/5, 1
Let t = -4 - -7. Factor 25*v**t - 16*v**3 - 14*v**3.
-5*v**3
Let m(n) = 8*n**3 - 18*n**2 - 2*n + 6. Let p(j) = 8