
-l*(l + 1)**2*(4*l - 1)**2/2
Let z(y) be the third derivative of -y**6/280 + 3*y**5/140 + 2*y**4/7 + 6*y**3/7 + 314*y**2. Factor z(f).
-3*(f - 6)*(f + 1)*(f + 2)/7
Factor 32/3 - 5*i - 1/6*i**2.
-(i - 2)*(i + 32)/6
Let w(y) be the second derivative of y**4/18 + 14*y**3/9 - 32*y**2/3 + 75*y. Let w(u) = 0. What is u?
-16, 2
Determine k, given that 28*k**2 + 0 + 2/5*k**4 + 74/5*k**3 + 0*k = 0.
-35, -2, 0
Let k(b) be the third derivative of b**5/240 - b**4/8 - 7*b**3/6 + 4*b**2 + b. Factor k(c).
(c - 14)*(c + 2)/4
Suppose 19*f - 75 + 18 = 0. Suppose 0 = -f*c + 63 - 3. Factor 14*u**4 - 6/7*u**2 + c*u**3 - 40/7*u + 8/7.
2*(u + 1)**2*(7*u - 2)**2/7
Let -28*v**3 - 78*v**2 - 9 + 26*v + 9*v**4 + v**4 + 2*v**5 + 82*v**2 - 5 = 0. What is v?
-7, -1, 1
Let h be ((-51)/(-144) - (-9 - 275/(-30)))*20. Factor -6 + 3/2*y + 3/4*y**3 + h*y**2.
3*(y - 1)*(y + 2)*(y + 4)/4
Suppose -216/7*v**4 - 48/7*v**5 - 51/7*v**3 + 12/7 + 99/7*v + 204/7*v**2 = 0. What is v?
-4, -1, -1/4, 1
Let f = -16556 - -16558. Suppose -17/3*g**3 + 77/3*g**4 - 32/3*g - 73/3*g**f - 4/3 + 49/3*g**5 = 0. What is g?
-1, -2/7, 1
Let f be (-6)/(((-6)/10)/(28/35)). Let h be 13/(650/f)*10/4. Factor 0 + 2/5*j + h*j**2.
2*j*(j + 1)/5
Let p be (-4 + 292/72)/(161/(-14)). Let z = p + 209/414. Factor 0 - x**4 + 5/4*x**3 + 0*x + 1/4*x**5 - z*x**2.
x**2*(x - 2)*(x - 1)**2/4
Let u(n) be the first derivative of 5/36*n**4 + 2/9*n + 5 + 7/18*n**2 + 1/45*n**5 + 1/3*n**3. Factor u(y).
(y + 1)**3*(y + 2)/9
Let d(n) be the second derivative of -n**8/840 + n**7/420 + n**3/2 + 21*n. Let y(t) be the second derivative of d(t). Suppose y(f) = 0. Calculate f.
0, 1
Let c(x) = -20*x**2 - 28*x - 4. Let w(i) = -40*i**2 - 58*i - 8. Let m(r) = -5*c(r) + 2*w(r). Factor m(t).
4*(t + 1)*(5*t + 1)
Let p = 1681/3 + -560. Let y(t) be the first derivative of 0*t + 2 - p*t**2 - 1/9*t**3. Let y(c) = 0. What is c?
-2, 0
Let m(n) be the second derivative of -1/6*n**4 + 0*n**3 - 5*n + 4*n**2 + 0. Let m(k) = 0. Calculate k.
-2, 2
Let h(j) be the third derivative of -j**8/1344 - j**7/105 - 5*j**6/96 - 19*j**5/120 - 7*j**4/24 - j**3/3 + 2*j**2 - 32*j. Factor h(g).
-(g + 1)**2*(g + 2)**3/4
Find h, given that 2*h + h**5 + h**5 + 155*h**3 - 81*h**3 - 78*h**3 = 0.
-1, 0, 1
Let y(w) be the first derivative of 2/33*w**3 - 21 + 4/11*w**2 - 10/11*w. Solve y(m) = 0 for m.
-5, 1
Suppose 14 = -3*h + 10*h. Solve 4/9 - 4/3*w**3 + h*w - 20/9*w**4 - 2/3*w**5 + 16/9*w**2 = 0 for w.
-2, -1, -1/3, 1
Let u(k) be the third derivative of 1/27*k**4 + 1/270*k**5 + 0*k + 1/9*k**3 + 28*k**2 + 0. Factor u(w).
2*(w + 1)*(w + 3)/9
Factor -36/7 - 40/7*b**2 + 132/7*b.
-4*(b - 3)*(10*b - 3)/7
Let l(k) = 2*k**3 - 20*k**2 - 7*k + 7. Let u be l(10). Let c = u + 65. Factor j + 2/5 - 1/5*j**4 + 3/5*j**c - 1/5*j**3.
-(j - 2)*(j + 1)**3/5
Let k(g) be the first derivative of 2/7*g**3 - 12/7*g**2 + 0*g + 23. Determine f so that k(f) = 0.
0, 4
Determine z, given that 30*z + 26 + 2*z**3 + 44*z - 116*z + 40*z - 26*z**2 = 0.
-1, 1, 13
Let u(r) = -2*r**3 - 2*r**2 - 121*r + 520. Let d be u(0). Factor -575/2*m**3 - 1205/2*m**2 - 160 - 5/2*m**5 - d*m - 95/2*m**4.
-5*(m + 1)**3*(m + 8)**2/2
Let d(r) = -4*r + 75. Let y be d(18). Suppose 2*o + 2*g + g = 0, -y*o - 5*g = 0. Factor 1/4*h - 1/4*h**2 + 1/4*h**4 - 1/4*h**3 + o.
h*(h - 1)**2*(h + 1)/4
Suppose 2*l + 1 + 7 = -2*s, 2*l = -8. Let z(m) be the second derivative of -3/10*m**3 + s + 3/5*m**2 + 3/100*m**5 + 6*m + 0*m**4. Factor z(q).
3*(q - 1)**2*(q + 2)/5
Let m = 27 - 25. Determine o, given that -m*o**3 + 4*o**3 - 15*o**2 + 8*o**2 + 10*o - 4 - o**2 = 0.
1, 2
Let x be (-5 + 246/48)/(7/(224/24)). Let -1/6*a**2 + 0*a + x = 0. Calculate a.
-1, 1
Let p(y) be the first derivative of -1/5*y**5 + 0*y**2 + 1/6*y**6 + 0*y**3 + 0*y - 9 + 0*y**4. Factor p(c).
c**4*(c - 1)
Let s(w) be the first derivative of -1/4*w**5 + 0*w - 5/16*w**4 - 24 + 0*w**2 + 5/12*w**6 + 0*w**3. Solve s(u) = 0.
-1/2, 0, 1
Factor -14/3 + 1/3*h**2 - 5/3*h.
(h - 7)*(h + 2)/3
Let g(o) = -4*o**4 - 2*o**3 + o**2 + o. Let b(k) = -22*k**4 - 12*k**3 + 49*k**2 - 83*k + 48. Let j(h) = -2*b(h) + 10*g(h). Factor j(p).
4*(p - 2)**2*(p - 1)*(p + 6)
Suppose -1562*r - 78 = -1588*r. Factor 8/5*z**4 + 8/5*z**2 + 2/5*z**5 + 0 + 12/5*z**r + 2/5*z.
2*z*(z + 1)**4/5
Let r(i) be the first derivative of -4*i**3/3 + 2*i**2 + 21. Suppose -l - 5 = 1. Let p(b) = -4*b**2 + 4*b. Let m(y) = l*r(y) + 5*p(y). Factor m(g).
4*g*(g - 1)
Let d(c) be the second derivative of -c**7/168 + c**6/30 - c**5/20 - c**4/24 + 5*c**3/24 - c**2/4 - c - 61. Determine l so that d(l) = 0.
-1, 1, 2
Find k such that 20/9 + 2*k - 2/9*k**2 = 0.
-1, 10
Suppose -h + 3*q + 4 = -11, 15 = 5*h - 3*q. Let z(g) be the third derivative of 0*g**3 - 1/150*g**6 + 6*g**2 - 1/75*g**5 + 0*g + h*g**4 + 0. Factor z(s).
-4*s**2*(s + 1)/5
Let d(i) = -10*i**4 - 110*i**3 - 65*i**2 + 40*i. Let w(z) = -9*z**4 - 109*z**3 - 65*z**2 + 41*z. Let n(x) = 6*d(x) - 5*w(x). Factor n(v).
-5*v*(v + 1)*(v + 7)*(3*v - 1)
Let a(d) = -8*d**2 + 16*d + 12. Let q(c) = 7*c**2 - 14*c - 12. Let z(s) = 3*a(s) + 4*q(s). Factor z(t).
4*(t - 3)*(t + 1)
Let j be (1/4)/((-2430)/(-1080)). Factor 1/3*p**3 + 0*p + 0 - j*p**2 - 2/9*p**4.
-p**2*(p - 1)*(2*p - 1)/9
Let s be (16/36)/2 + (-50)/(-18). Factor 9*p**4 - 2*p**4 + 3*p**3 - s*p**4 - 6*p**2 - p**4.
3*p**2*(p - 1)*(p + 2)
Let h(c) be the first derivative of c**7/840 - c**6/180 - c**5/40 + 49*c**3/3 - 50. Let s(v) be the third derivative of h(v). Factor s(m).
m*(m - 3)*(m + 1)
Let r(k) = -k**5 + 18*k**4 - 7*k**3 - 9*k**2 - 10*k - 18. Let l(f) = 2*f**4 - f**3 - f**2 - f - 2. Let q(z) = 45*l(z) - 5*r(z). Factor q(c).
5*c*(c - 1)**2*(c + 1)**2
Let d = 281 + -282. Let r be (-1 - d) + 19 + -17. Find j such that 12/7*j**3 - 12/7 - 20/7*j**r - 44/7*j = 0.
-1, -1/3, 3
Let w(v) = -v**4 + 2*v**3 + v**2 + 1. Let q(u) = -6*u**4 - 4*u**3 - 14*u**2 + 4. Let y(t) = q(t) - 4*w(t). Factor y(a).
-2*a**2*(a + 3)**2
Suppose 2*z - 14 = -5*z. Solve 74 + 4*v**2 - 74 - 2*v**2 + z*v = 0.
-1, 0
Let r(w) = -136*w**3 + 5*w + 131*w**3 + 4 + 1. Let g(v) = v**4 - 5*v**3 + 6*v + 6. Let y(l) = 5*g(l) - 6*r(l). Solve y(z) = 0.
-1, 0
Let k(b) be the first derivative of b**7/168 + b**6/36 - b**5/24 - 5*b**4/12 - 20*b**3/3 - 27. Let m(n) be the third derivative of k(n). Factor m(j).
5*(j - 1)*(j + 1)*(j + 2)
Let g(i) be the second derivative of i**5/30 + 11*i**4/2 + 833*i**3/3 + 2401*i**2/3 + 552*i. Solve g(h) = 0 for h.
-49, -1
Suppose -1/4*f**5 - 5 - 7/4*f**3 + 2*f + 31/4*f**2 - 11/4*f**4 = 0. What is f?
-10, -2, -1, 1
Let z(f) = -f**3 - 3*f**2 + 9*f + 29. Let d be z(-3). Find q, given that 4*q + 2/5*q**d + 10 = 0.
-5
Let u be -11 - ((-10)/((-630)/(-639)) + -1). Factor -1/7*l**2 + u*l + 2/7.
-(l - 2)*(l + 1)/7
Let a(s) be the first derivative of -1/18*s**3 + 2/3*s**2 + 5 - 8/3*s. Factor a(d).
-(d - 4)**2/6
Let p be (-18)/(-4)*(-420)/(-9). Factor -210 + p + 6*g**2 - 3*g - 3*g**3.
-3*g*(g - 1)**2
Suppose -m = 2*h, -117*h = -112*h + 5. Solve 0 + 8/13*t**3 + 0*t - 2/13*t**5 + 8/13*t**m - 2/13*t**4 = 0 for t.
-2, -1, 0, 2
Let j(r) = 3*r**4 - 6*r**3 - r**2 + 4*r. Suppose -n - 1 = -0*n. Let m(z) = z**2 - z. Let o(t) = n*j(t) + 2*m(t). Find l, given that o(l) = 0.
-1, 0, 1, 2
Let p(t) be the third derivative of t**7/735 - t**6/105 + t**5/105 + t**4/21 - t**3/7 - 10*t**2. Factor p(h).
2*(h - 3)*(h - 1)**2*(h + 1)/7
Let i be 0*((-6)/(-4) - 2). Factor i*q + 0*q + 2*q**2 + 22*q - 24.
2*(q - 1)*(q + 12)
Let u(t) be the first derivative of 3*t**4/8 + 13*t**3/2 - 87*t**2/4 + 45*t/2 - 316. Factor u(a).
3*(a - 1)**2*(a + 15)/2
Suppose -17*b = -3*p - 14*b + 3, -26 = -5*p - 2*b. Solve -3/4*r**p + 7/4*r**2 - r**3 - 1 + r = 0 for r.
-2, -1, 2/3, 1
Let f(r) = 18*r**4 - 3*r**3 - 75*r**2 + 32*r + 192. Let j(x) = 10*x**4 - x**3 - 37*x**2 + 16*x + 96. Let y(i) = 3*f(i) - 5*j(i). Suppose y(k) = 0. Calculate k.
-2, 2, 3
Let k(w) = -3*w**3 + 13*w**2 - 47*w + 22. Let m(q) = q**3 - 7*q**2 + 23*q - 11. Let l(z) = -2*k(z) - 5*m(z). Suppose l(x) = 0. What is x?
-11, 1
Factor u**2 - 243 - 4*u**2 + u**2 + 51 - 44*u.
-2*(u + 6)*(u + 16)
Let b(o) be the first derivative of -25/4*o**4 + 0*o**2 + 0*o + 37 - 5*o**3 - o**5 + 5/6*o**6. Determine a, given that b(a) = 0.
-1, 0, 3
Suppose -2*b + 2*h = 0, 0*b - 5*h = b - 30. Let g(v) = v**3 - 5*v**2 + 2*v. Let r be g(b). Factor r*c**3 + c**2 - c**2 - 2*c**2 - 3