0. Let a(n) be the third derivative of -1/96*n**4 - 4*n**2 - 1/480*n**6 + 0*n + 1/120*n**5 + 0*n**3 + l. Factor a(r).
-r*(r - 1)**2/4
Determine c so that -7/8*c + 0*c**2 - 3/4 + 1/8*c**3 = 0.
-2, -1, 3
Let f(i) be the third derivative of -i**5/480 + 5*i**4/64 - 3*i**3/4 + 5*i**2 - 8. Factor f(o).
-(o - 12)*(o - 3)/8
Suppose -2*w + 2*b = 2*w - 14, 6*b = w - 20. Factor 1/4 - 9/8*u - 3/8*u**3 + 5/4*u**w.
-(u - 2)*(u - 1)*(3*u - 1)/8
Let a(f) be the third derivative of -f**5/60 - f**4/8 + 2*f**3/3 + 8*f**2 + 7. Factor a(w).
-(w - 1)*(w + 4)
Suppose 0 = 10*v - 12*v + 10. Suppose -2*q + 2 = c + 1, 0 = -v*q - 3*c + 1. Find w, given that -2/3*w + 0*w**q - 3*w**5 + 0 + 1/2*w**4 + 19/6*w**3 = 0.
-2/3, 0, 1/2, 1
Let s = -466 + 469. Let p(y) be the second derivative of 0*y**2 + 0*y**3 + 1/3*y**4 - 1/5*y**5 - s*y + 0. Factor p(x).
-4*x**2*(x - 1)
Find m such that 9*m**4 - 51/7*m**2 - 12/7 - 51/7*m**3 + 9*m - 12/7*m**5 = 0.
-1, 1/4, 1, 4
Let d = 82/141 - -4/47. Factor 0*w + 1/3*w**4 + 0 + d*w**3 + 1/3*w**2.
w**2*(w + 1)**2/3
Let t be (4/2)/(32/336). Factor 4*d + 0*d**3 + d**3 - t*d**2 + 12*d**2 + 13*d**2.
d*(d + 2)**2
Suppose -5*z + 4*k - 79 - 6 = 0, -4*z = 3*k + 99. Let w = z - -29. Factor r**2 + 5*r**2 + 2*r**3 - w + 0*r**2.
2*(r - 1)*(r + 2)**2
Let k(g) be the first derivative of -g**3 - 3*g**2 - 3*g - 50. Determine d so that k(d) = 0.
-1
Let x be (-53)/(-5) + (-7)/(-5) + -1. Let m be 3/(12/8*x). Factor 0 + 4/11*n**2 - m*n**3 - 2/11*n.
-2*n*(n - 1)**2/11
Let s be (-21)/(-6) - 7/14. Suppose 0 = -6*a + 7*a - s. Suppose 2*g**a - g**3 + 0 - 2 - 3*g = 0. Calculate g.
-1, 2
Factor 237*f**3 - 2*f - 8*f**2 - 480*f**3 + 237*f**3.
-2*f*(f + 1)*(3*f + 1)
Suppose 429 - 453 = -6*z. Let x(l) be the second derivative of 3/20*l**5 + 0 - 9/20*l**6 + 0*l**z + 0*l**2 + 0*l**3 + 5/14*l**7 + 2*l. Factor x(m).
3*m**3*(2*m - 1)*(5*m - 2)/2
Let t(f) be the first derivative of -2*f**5/35 + 4*f**3/21 - 2*f/7 - 335. What is v in t(v) = 0?
-1, 1
Let t(y) be the first derivative of y**6/180 - 3*y**5/10 + 27*y**4/4 + 19*y**3/3 + 28. Let f(q) be the third derivative of t(q). Factor f(d).
2*(d - 9)**2
Let a(c) be the third derivative of c**6/360 - c**5/20 + 23*c**4/72 - 5*c**3/6 + 2*c**2 - 261*c. Factor a(p).
(p - 5)*(p - 3)*(p - 1)/3
Let a(w) = 27*w**3 - 22*w**2 + 7*w - 96. Let f(l) = -7*l**3 + 6*l**2 - 2*l + 24. Let x(g) = -6*a(g) - 23*f(g). Factor x(u).
-(u - 2)*(u + 2)*(u + 6)
Suppose 43*n = -p + 39*n + 14, 2*p - 4*n = -8. Factor -16/7 - 4/7*r**3 + 4/7*r + 16/7*r**p.
-4*(r - 4)*(r - 1)*(r + 1)/7
Let q(n) = n - 13. Let c be q(5). Let h be ((-12)/14)/(c/28). Factor 3/5*o**h + 9/5*o**2 - 3/5*o**4 + 6/5 - 3*o.
-3*(o - 1)**3*(o + 2)/5
Let j(q) be the second derivative of -q**4/24 - q**3/3 + 5*q**2/4 - 17*q. Factor j(o).
-(o - 1)*(o + 5)/2
Determine c, given that -22/7*c**3 - 2/7*c**4 - 8/7*c**2 + 0 + 120/7*c = 0.
-10, -3, 0, 2
Let q(a) be the third derivative of -a**7/840 + a**6/180 - a**5/120 + 11*a**3/3 - 21*a**2. Let v(h) be the first derivative of q(h). Factor v(l).
-l*(l - 1)**2
Let a = 936 - 934. Let -2/15 - 4/15*j - 2/15*j**a = 0. Calculate j.
-1
Let r(c) be the second derivative of 8*c**3 - 4*c**2 + 5/2*c**5 - 15/2*c**4 + 10*c + 0. Factor r(q).
2*(q - 1)*(5*q - 2)**2
Determine l so that -3/5*l**4 - 18/5*l**2 - 3*l**3 + 24/5 + 12/5*l = 0.
-2, 1
Let w(j) = j**4 - 9*j**3 + 2*j**2 - 6. Let d(q) = q**3 + 1. Let u(b) = b + 15. Let h be u(-9). Let a(p) = h*d(p) + w(p). Factor a(n).
n**2*(n - 2)*(n - 1)
Factor -2/11*q**3 - 960/11*q + 1600/11 + 84/11*q**2.
-2*(q - 20)**2*(q - 2)/11
Suppose 7*j + 5*j - 36 = 0. Solve 31*l**5 - 10 + 10*l**4 + 35*l - 40*l**2 + 3*l**3 + 7*l**j - 36*l**5 = 0 for l.
-2, 1
Let g be 2/(-18)*-6*(3 - -3). Let h be g*(6/(-9) + 1). Let 1/3*d**2 - 4/3 - h*d + 1/3*d**3 = 0. Calculate d.
-2, -1, 2
Factor 8/21*x**2 + 0 + 8/21*x + 2/21*x**3.
2*x*(x + 2)**2/21
Let 2/7*m**2 + 2 - 16/7*m = 0. Calculate m.
1, 7
Let d be 5*9/72*1. Let z(b) be the third derivative of 1/5*b**5 + 0 + 0*b + 1/40*b**6 + b**3 - b**2 + d*b**4. Factor z(o).
3*(o + 1)**2*(o + 2)
Let a(c) be the second derivative of -c**5/330 + c**3/33 + 27*c**2/2 - 10*c. Let b(i) be the first derivative of a(i). Let b(w) = 0. What is w?
-1, 1
Let c be 4 + -1 + (-2 - -1). Let u(j) = j + 3*j - 10*j**2 + c + 4. Let y(n) = -9*n**2 + 4*n + 5. Let f(q) = -5*u(q) + 6*y(q). Let f(o) = 0. Calculate o.
0, 1
Let b be (-6)/18 + 57/9 - (7 + -1). Factor -12/11*m**2 + 6/11*m + b + 6/11*m**3.
6*m*(m - 1)**2/11
Let k(d) be the first derivative of d**4 + 8*d**3 + 18*d**2 + 16*d + 42. Solve k(y) = 0.
-4, -1
Suppose -4*a + 24 = -3*a. Let -17*z**4 + a*z**3 - 10*z**5 + 18*z**2 - 15*z - 6 + 5*z**4 + z**5 = 0. What is z?
-2, -1, -1/3, 1
Let x = 1087/5 + -8681/40. Factor -x*t**2 - 3/4 - 9/8*t.
-3*(t + 1)*(t + 2)/8
Solve -1/2*p**4 - 39/2*p**2 + 41/2*p**3 - 41/2*p + 20 = 0.
-1, 1, 40
Let r(m) = 11*m**4 - 4*m**3 - 34*m**2. Let d(n) = -10*n**4 + 5*n**3 + 35*n**2. Let c(o) = -6*d(o) - 5*r(o). Factor c(s).
5*s**2*(s - 4)*(s + 2)
Let d(z) = -z - 2. Let p be d(-4). Find s, given that -16*s**p - 5 + 36*s**3 + 0*s**2 + 16*s**4 + 8*s**2 - 3 - 36*s = 0.
-2, -1, -1/4, 1
Let t = 6836/5 - 1367. Suppose -9/5*q**2 - t*q**4 - 7/5*q - 2/5 - q**3 = 0. What is q?
-2, -1
Let c(t) be the second derivative of t**6/27 + 11*t**5/30 + 41*t**4/54 + t**3/9 - 10*t**2/9 - 278*t. Suppose c(z) = 0. Calculate z.
-5, -1, 2/5
Let z(l) be the first derivative of -2*l**6/45 - 11*l**5/30 + l**4/2 + 22*l**3/3 + 24. Let r(f) be the third derivative of z(f). Factor r(a).
-4*(a + 3)*(4*a - 1)
Let a be 7/(-14) - (2 + (-9)/(-2)). Let v = a + 25/3. Factor 5/3*q**2 - v*q**3 + 1/3*q**4 + 0 - 2/3*q.
q*(q - 2)*(q - 1)**2/3
Let 11*n - 12 - 37*n + 0*n**3 + n**2 + 2*n**3 + 2*n**4 - 12*n**2 - 3*n**2 = 0. What is n?
-2, -1, 3
Let -3/2*o**2 + 0*o + 0 = 0. What is o?
0
Suppose 25/2 + 11*u**3 + 37*u - 1/2*u**4 + 36*u**2 = 0. What is u?
-1, 25
Let s = -13001/3 - -4347. Suppose -12*v**2 - s*v - 14/3*v**3 - 2/3*v**4 - 16/3 = 0. Calculate v.
-2, -1
Suppose 4*v + d - 163 = 0, -3*v - 5*d + 127 = 26. Suppose -4*c + v = 14. Factor c*i + 2*i**2 + 3*i - 8*i.
2*i*(i + 1)
Suppose 3*y - 2*f = -413 + 409, -3*f = 4*y - 23. Factor 1/5*c**y + 49/5 + 14/5*c.
(c + 7)**2/5
Let g be -1 - 1 - (-6)/2*1. Let x be 0/(g - (-3 + 2)). Find a such that -1/3*a**2 + 1/3*a + x = 0.
0, 1
Let p(s) = -17*s**2 - 5*s**3 + 60*s - 64*s - s**4 + 13*s**2. Let j(k) = k**3 + k**2 + k. Let g(y) = -4*j(y) - p(y). Let g(f) = 0. What is f?
-1, 0
Factor -11*u - 6*u + 33*u - 200 + 49*u - 5*u**2.
-5*(u - 8)*(u - 5)
Let k(c) be the second derivative of 10*c - 8/5*c**2 + 0 - 1/3*c**4 + 8/5*c**3. Factor k(d).
-4*(d - 2)*(5*d - 2)/5
Let a = -87 + 42. Let t be -2*1/8*120/a. Factor t + 2/9*z**2 - 2/9*z**3 + 10/9*z.
-2*(z - 3)*(z + 1)**2/9
Factor -9*s**2 + 8*s**3 + 32*s - 10*s**2 + 5*s**2 - 6*s**3 - 24.
2*(s - 3)*(s - 2)**2
What is w in 30/7 + 2/7*w**2 - 32/7*w = 0?
1, 15
Let o(c) = -31*c**2 - 14*c + 8. Let z(a) = 8*a**2 + 3*a - 2. Let k(m) = 2*o(m) + 9*z(m). Determine l, given that k(l) = 0.
-2/5, 1/2
Let o(m) = -138*m + 969. Let j be o(7). Let v(z) be the first derivative of -2/15*z**j - 6 - 6/5*z + 4/5*z**2. What is w in v(w) = 0?
1, 3
Suppose 0 = -4*p + 8 + 8. Factor 5*a**2 + 11*a**p - 2*a**4 - 16*a**2 + 2 + 7*a**3 - 7*a.
(a - 1)*(a + 1)**2*(9*a - 2)
Let w(a) be the second derivative of -a**4/3 - 26*a**3/3 + 64*a + 4. Suppose w(k) = 0. What is k?
-13, 0
Let w(m) be the third derivative of -m**7/1260 - m**6/120 + m**5/6 + 43*m**4/24 + 7*m**2 - 1. Let q(k) be the second derivative of w(k). Factor q(f).
-2*(f - 2)*(f + 5)
Let l(b) be the second derivative of -b**6/90 + b**5/6 - 2*b**4/3 - 2*b**3 - 11*b. Let w(p) be the second derivative of l(p). Factor w(i).
-4*(i - 4)*(i - 1)
Let j(l) be the second derivative of l**4/12 + 19*l**3/3 + 37*l**2/2 - 179*l. Factor j(f).
(f + 1)*(f + 37)
Suppose -18 = -2*d + 4*p, -2*d = -d + 6*p + 15. Suppose -8*y + 15 = -1. Factor 1/2*h + 0 + 1/4*h**y - 1/4*h**d.
-h*(h - 2)*(h + 1)/4
Let n = -31 + 41. Find d, given that -9*d**4 + 4*d - 2*d + n*d**4 - 2*d**2 - d**2 = 0.
-2, 0, 1
Let q(x) be the third derivative of 2/3*x**4 + 0 - 7/30*x**6 - 2/35*x**7 - 36*x**2 + 0*x + 0*x**3 + 0*x**5. Solve q(u) = 0.
-2, -1, 0, 2/3
Let x be 165/(-22)*4/(-10). Suppose -x*u - 2*i + 38 = 0, 2*u + 6*i - 2*i = 36. Suppose 2*y**2 - 3*y**4 + u*y