 i = 5*s + 15, -9 = -i + s + 2*s. Let u(m) be the third derivative of -1/120*m**6 + i*m + 4*m**2 - 1/60*m**5 + 0*m**4 + 0 + 0*m**3. Factor u(o).
-o**2*(o + 1)
Let x(f) = 6*f**2 - 2*f**2 + 31 + f**3 - f - 35. Let q be x(-3). Determine v so that -2 + 0*v**3 + 5*v**3 - 4*v**2 - 2*v**3 - v + q*v**2 = 0.
-1, 2/3
Let v = -10670/3 + 3468. Let h = v + 90. Factor -2/3*m**5 + 0*m + 2*m**3 - h*m**2 + 0 + 0*m**4.
-2*m**2*(m - 1)**2*(m + 2)/3
Let a = -533/30 + 133/6. Factor 8/5 + a*s**2 - 24/5*s - 6/5*s**3.
-2*(s - 2)*(s - 1)*(3*s - 2)/5
Let v(s) be the first derivative of 10/3*s**3 + 8*s - 11 + 1/2*s**4 + 8*s**2. What is j in v(j) = 0?
-2, -1
Let i(w) be the second derivative of 5*w**4/12 + 5*w**3 - 40*w**2 - 4*w + 2. What is a in i(a) = 0?
-8, 2
Let h = 12 + -11. Let v be h + (20/4 - 0). Solve -w**3 - 8 + w**4 + 6*w**3 - 4*w + 0*w**4 + v*w**2 = 0.
-2, 1
Let t = -872 + 876. Let x(u) be the third derivative of 0*u**3 + 0 + 1/60*u**5 - 7*u**2 - 1/30*u**6 + 0*u + 0*u**t. Suppose x(h) = 0. What is h?
0, 1/4
Let p(d) be the first derivative of 5*d**4/4 - 130*d**3/3 - 275*d**2/2 - 140*d + 255. What is u in p(u) = 0?
-1, 28
Let m(g) be the third derivative of 5*g**3 + 0 - 5/24*g**4 + 0*g - 1/3*g**5 - 1/24*g**6 + 29*g**2. Factor m(f).
-5*(f - 1)*(f + 2)*(f + 3)
Suppose 0 + 3/4*z**2 + 3*z - 3/4*z**4 - 3*z**3 = 0. Calculate z.
-4, -1, 0, 1
Let y(p) be the second derivative of -p**6/80 - 27*p**5/160 - 21*p**4/32 - 19*p**3/16 - 9*p**2/8 - 2*p - 2. What is d in y(d) = 0?
-6, -1
Suppose 0 = -0*u + 2*u - 5*q - 27, 0 = 5*u - 2*q - 36. Solve -2*p**4 - u + 17*p**2 - 51*p**2 - 14*p**3 - 34*p - 6 = 0 for p.
-3, -2, -1
Let z(i) be the second derivative of i**10/41580 - i**9/9240 + i**8/18480 + 5*i**4/6 - 10*i. Let d(h) be the third derivative of z(h). Solve d(l) = 0 for l.
0, 1/4, 2
Let c = -349/2107 - -8/43. Let d(x) be the second derivative of -1/105*x**6 - c*x**7 + 0 - 2/21*x**3 + 1/14*x**5 + 1/42*x**4 + 0*x**2 - 4*x. Solve d(w) = 0.
-1, 0, 2/3, 1
Let j = -133921/3 + 44655. Determine f so that -242/3 + j*f - 2/3*f**2 = 0.
11
Let x(w) be the first derivative of 10 + 0*w + w**2 - 2/3*w**3. Let x(j) = 0. What is j?
0, 1
Let q = -9/32 - -137/480. Let a(g) be the third derivative of 0 - 1/24*g**3 - q*g**6 - 1/48*g**5 - 1/24*g**4 + 0*g + g**2. Find j such that a(j) = 0.
-1, -1/2
Let v(f) be the first derivative of f**6/21 - 22*f**5/35 + 20*f**4/7 - 32*f**3/7 + 275. Let v(o) = 0. Calculate o.
0, 3, 4
Let x(c) be the first derivative of -5*c**3/9 - 11*c**2/2 + 14*c/3 + 105. Determine a, given that x(a) = 0.
-7, 2/5
Let l = -20291/22 - -1845/2. Factor 0 - 4/11*k - 2/11*k**2 + l*k**3.
2*k*(k - 2)*(k + 1)/11
Let q(m) be the first derivative of m**4/18 - 14*m**3/27 - 8*m**2/9 + 2. Factor q(w).
2*w*(w - 8)*(w + 1)/9
Let i(h) be the second derivative of h**5/110 + 4*h**4/33 + 7*h**3/33 - 373*h. Factor i(j).
2*j*(j + 1)*(j + 7)/11
Suppose -2*o + 12 = -5*f, 5*f - 28 = 7*o - 70. Factor 3/4*l**4 + f + 0*l**3 + 0*l - 3/4*l**2.
3*l**2*(l - 1)*(l + 1)/4
Let t(i) be the second derivative of -i**5/5 - 6*i**4 + 134*i**3/3 + 168*i**2 - i - 441. Factor t(f).
-4*(f - 4)*(f + 1)*(f + 21)
Let z(c) be the third derivative of 7*c**6/15 - 139*c**5/15 + 170*c**4/3 + 50*c**3/3 - 97*c**2. Factor z(l).
4*(l - 5)**2*(14*l + 1)
Let j(z) be the third derivative of -z**5/30 - z**4 - 12*z**3 + 41*z**2. Suppose j(o) = 0. What is o?
-6
Let f = 161/80 - -6829/240. Let z = -149/5 + f. Determine m so that -4/3*m**4 - 5/3*m**3 - 1/3*m**5 - z*m**2 + 0 + 0*m = 0.
-2, -1, 0
Let q be (-13)/(-39)*((-821)/(-34) + -2). Let y = q - -2/17. Let -31*g**4 - 36*g**2 - 49*g**3 - y*g**5 - 1 - 23/2*g = 0. What is g?
-1, -2/15
Let l be 3 - (-3 + 2) - 60. Let i be ((-48)/l)/(4/14). Suppose -2*v**i + 10*v**2 - 11*v**2 + 3*v**3 = 0. What is v?
0, 1
Suppose 2*c = -0*c. Let p(b) = -b + 3. Let t be p(c). Factor -2*l + t*l**2 + 4*l**4 - 7*l**4 - 4*l + 8*l**3 - 2*l**3.
-3*l*(l - 2)*(l - 1)*(l + 1)
Let j be (-2)/(-5) - (-36)/10. Let k(y) = -y**2 + y + 1. Let z(u) = u**2 - 2. Suppose 2 = 2*l - n, -2*l + 3*n = l. Let q(c) = j*k(c) + l*z(c). Factor q(f).
-2*f*(f - 2)
Suppose -3*a + 6 = 0, 7*f - 10*f + 7 = 2*a. Let d(b) = -5*b**2 - 20*b + 29. Let i(v) = -1. Let p(g) = f*d(g) + 4*i(g). Let p(t) = 0. What is t?
-5, 1
Suppose 11*s - 25*s = -924. Let r = s + -61. Factor 3/4*o**r + 0 + 3/4*o**2 + 9/4*o**4 + 0*o + 9/4*o**3.
3*o**2*(o + 1)**3/4
Let m(c) be the second derivative of -c**7/56 + c**6/40 + 27*c**5/80 - 5*c**4/16 - 2*c**3 + 9*c**2/2 - 37*c. Determine r, given that m(r) = 0.
-2, 1, 3
Let u(a) be the second derivative of a**4/42 - 8*a**3/21 - 20*a**2/7 - 345*a. Factor u(k).
2*(k - 10)*(k + 2)/7
Solve -h**4 + 5*h**2 + 6*h**3 - 13*h**3 - 4 + 7*h**3 = 0 for h.
-2, -1, 1, 2
Suppose 5*z - 20 = -0*z. Let t(q) = -q**2 + 4*q + 3. Let p be t(z). Suppose 2*l - 2*l**p + 4 - l**4 - 2 + 0*l**4 - 1 = 0. What is l?
-1, 1
Let m(o) be the third derivative of -o**7/490 - 3*o**6/20 - 577*o**5/140 - 51*o**4 - 2312*o**3/7 + 3*o**2 - 33*o. Factor m(x).
-3*(x + 4)**2*(x + 17)**2/7
Let d(w) be the third derivative of -5*w**8/336 + 2*w**7/21 - w**6/4 + w**5/3 - 5*w**4/24 - w**2 + 201*w. Solve d(y) = 0.
0, 1
Let g(n) be the second derivative of -n**7/63 - 2*n**6/15 - 2*n**5/15 + n**4/3 + 5*n**3/9 - 60*n. Suppose g(d) = 0. Calculate d.
-5, -1, 0, 1
Let q(m) be the third derivative of m**4/6 + 13*m**3/3 - 2*m**2 + 4*m. Let x be q(-6). Factor -2/9*v + 0 + 4/9*v**x + 2/3*v**3.
2*v*(v + 1)*(3*v - 1)/9
Let k(b) be the first derivative of b**6/24 + b**5/20 - b**4/4 - b**3/3 - 59. Factor k(m).
m**2*(m - 2)*(m + 1)*(m + 2)/4
Let h = 15 - 44. Let k = 34 + h. Factor -14*r + 4*r**3 - 2 + k*r**2 - 2*r**3 + 15*r.
(r + 1)*(r + 2)*(2*r - 1)
Let z(l) be the second derivative of -4/3*l**3 + 1/3*l**4 - 10*l + 0*l**2 + 0. Factor z(f).
4*f*(f - 2)
Find m such that 22*m**2 + 27*m**2 + 8*m**4 - 2*m**5 - 66*m**2 + 25*m**2 - 15*m**3 + 3*m**3 - 2*m = 0.
0, 1
Let r(p) = p**2 - 40*p + 47. Let q be r(35). Let v = -255/2 - q. Suppose 0 + v*d + 3/2*d**3 - 1/2*d**4 - 3/2*d**2 = 0. What is d?
0, 1
Let s(v) be the first derivative of v**4/26 - 20*v**3/39 - 24*v**2/13 - 233. Solve s(i) = 0.
-2, 0, 12
Suppose 138/13 + 2/13*g**3 - 138/13*g**2 - 2/13*g = 0. Calculate g.
-1, 1, 69
Let q(f) be the first derivative of -12*f - 8 + 8/3*f**3 - 10*f**2. Let q(k) = 0. What is k?
-1/2, 3
Suppose -o + 1 = -6. Suppose 3*c = 2*r - o*r + 17, 3*r + 5 = 2*c. Determine g so that 2*g**3 - g**5 + c*g**4 + g**5 - 14*g**4 + 8*g**5 = 0.
0, 1/4, 1
Let w(v) be the third derivative of 0*v**3 - 15*v**2 + 0*v + 0*v**4 - 1/1890*v**7 + 0*v**5 + 0 + 0*v**6. Factor w(h).
-h**4/9
Factor -20*d**3 - 24*d**4 + 16*d**3 - 5*d**5 + 96*d**2 + d**5 - 64*d.
-4*d*(d - 1)**2*(d + 4)**2
Let f(y) be the third derivative of -2*y**2 + 0*y + 0*y**3 + 1/108*y**4 + 0 + 1/270*y**5. Factor f(q).
2*q*(q + 1)/9
Let i(p) be the second derivative of -p**7/84 - 13*p**6/60 - 8*p**5/5 - 37*p**4/6 - 40*p**3/3 - 16*p**2 + 76*p. Suppose i(o) = 0. Calculate o.
-4, -2, -1
Let h(s) be the first derivative of -2*s**4/15 + s**3/15 - 31*s + 9. Let q(x) be the first derivative of h(x). Suppose q(l) = 0. Calculate l.
0, 1/4
Let a(k) be the second derivative of -k**5/10 - 5*k**4/6 + 8*k**3/3 + 48*k**2 - 173*k. Factor a(b).
-2*(b - 3)*(b + 4)**2
Suppose -g - 11 = -4*n, -6*g + 9*g + 3 = -3*n. Factor -63*l + 37*l**2 - 305 + 101 - 3*l**3 - l**n - 90.
-3*(l - 7)**2*(l + 2)
Let x(l) be the first derivative of l**6/12 - 3*l**5/2 + 37*l**4/4 - 82*l**3/3 + 42*l**2 - 32*l - 72. Factor x(s).
(s - 8)*(s - 2)**3*(s - 1)/2
Find o such that -22*o - 32/3 - 12*o**2 - 2/3*o**3 = 0.
-16, -1
Determine p so that -6/5*p**3 - 4/5*p**2 + 2/5*p**4 + 24/5*p - 16/5 = 0.
-2, 1, 2
Let w = 2/1699 - -3380/15291. Let a = 2690/99 - 294/11. Suppose -2/9*x**2 - 2/3*x**3 + a - w*x**4 + 2/3*x = 0. What is x?
-2, -1, 1
Suppose 0 = 4*y + 5*f - 23, -3*y + 252*f + 9 = 253*f. Factor 1/8*l**y + 0 - 3/8*l.
l*(l - 3)/8
Let n(o) be the third derivative of o**4/6 + o**3/3 - 5*o**2. Let s be n(0). Find x, given that 3/5*x - x**s + 1/5*x**3 + 9/5 = 0.
-1, 3
Let u(w) be the second derivative of -w**5/110 + 7*w**4/66 + 5*w**3/33 - 75*w**2/11 + 21*w - 2. Suppose u(g) = 0. Calculate g.
-3, 5
Let c be (-48)/(-32) - (-58)/4. Let i be (-2)/(-4)*c/2. Factor 36*z - 64*z**2 + i*z**5 - 1 - 24*z**4 - 15*z**3 - 7 + 71*z**3.
4*(z - 2)