(-10)). Factor 0*s + 0 - 2/11*s**2 + 2/11*s**4 - d*s**3 + 2/11*s**5.
2*s**2*(s - 1)*(s + 1)**2/11
Let y be ((-2)/15)/(8/(-10)). Let m(l) be the third derivative of -3*l**2 - 1/60*l**6 + 0*l**3 + 0 + 0*l - 1/30*l**5 + y*l**4. Find q such that m(q) = 0.
-2, 0, 1
Let s be (-1*6)/((36/(-6))/3). Let j(u) be the third derivative of 0*u + 0 - 1/30*u**6 - 1/6*u**s + 0*u**5 + 1/8*u**4 - u**2. Factor j(o).
-(o + 1)*(2*o - 1)**2
Let x be 6/((6/(-4))/(-1)). Factor -z**2 - 3*z + 3*z**2 - x*z + 6*z - z**3.
-z*(z - 1)**2
Let b = -4/11 + 23/33. Let l(y) be the first derivative of -b*y + 2 - 1/9*y**3 + 1/3*y**2. Factor l(w).
-(w - 1)**2/3
Let i(v) be the second derivative of -v**5/15 - v**4/3 + 8*v**2/3 + 5*v. Factor i(k).
-4*(k - 1)*(k + 2)**2/3
Let o be 37/(-222)*(-3)/2. Factor 1/4 + o*j - 1/4*j**2 - 1/4*j**3.
-(j - 1)*(j + 1)**2/4
Let g(v) = v**2 - 2*v + 2. Let p be g(2). Let s be (1 + 1 + -2)/2. Factor -1/3*q**3 + 2/3*q**p + s + 0*q.
-q**2*(q - 2)/3
Let o(k) be the first derivative of 2*k**5/35 + 3*k**4/7 + 26*k**3/21 + 12*k**2/7 + 8*k/7 - 24. What is q in o(q) = 0?
-2, -1
Let k(o) be the first derivative of -2 - 1/5*o**2 - 2/15*o**3 + 4/5*o. What is t in k(t) = 0?
-2, 1
Let -25*w**2 + 4*w**3 - 37*w**2 + 46*w**2 = 0. What is w?
0, 4
Let j = -3493 + 10367/3. Let r = j - -38. Determine d, given that 2/3*d**4 - r*d + 2*d**2 - 2*d**3 + 0 = 0.
0, 1
Let m = 8/9 + -23/36. Factor -m*b**2 - 3/4*b - 1/2.
-(b + 1)*(b + 2)/4
Suppose 0*s**3 - 4/3*s**5 + 4/3*s + 0 - 8/3*s**2 + 8/3*s**4 = 0. Calculate s.
-1, 0, 1
Suppose -6 = -4*w + j - 0, -2 = 3*w - 4*j. Let d(t) be the first derivative of -2 + 2/3*t**3 + 2*t**2 + w*t. What is x in d(x) = 0?
-1
Let w(f) be the third derivative of f**6/840 + f**5/140 + 5*f**2. Factor w(r).
r**2*(r + 3)/7
Find c such that -3 + 3 + 4 + 10*c**4 + 7*c**3 - 14*c**2 - c**3 - 6*c = 0.
-1, 2/5, 1
Let y = -105 - -112. Let n(b) be the third derivative of 0*b + 0 + 1/30*b**5 - 1/12*b**4 + 1/60*b**6 + b**2 + 0*b**3 - 1/105*b**y. Factor n(x).
-2*x*(x - 1)**2*(x + 1)
Let n(r) be the first derivative of 9*r**5/10 - 3*r**4 - 17*r**3/6 + 5*r**2 + 6*r + 20. Factor n(g).
(g - 3)*(g - 1)*(3*g + 2)**2/2
Let m be (0 - (-3389)/29)/6. Let l = m + 69/58. Determine q, given that 0 + 0*q - 40/3*q**3 - 10*q**5 + l*q**4 + 8/3*q**2 = 0.
0, 2/5, 2/3, 1
Let a be (-1 + 14/20)/(18/(-48)). Factor -2*w**2 + a*w + 0.
-2*w*(5*w - 2)/5
Let b(s) be the second derivative of -s**4/6 - s**3/3 - 44*s. What is w in b(w) = 0?
-1, 0
Let j(k) be the first derivative of 3/2*k + 3/16*k**4 - 1 + 15/8*k**2 + k**3. Factor j(l).
3*(l + 1)**2*(l + 2)/4
Let h = 4 + 0. Suppose l - 15 = -h*l. Suppose -2*s - 2*s**2 + s**4 - s**4 + 2*s**l + 2*s**4 = 0. What is s?
-1, 0, 1
Let g = -12 - -12. Suppose x - 8 + 6 = 0. Factor g - 1/3*u**x - 2/3*u.
-u*(u + 2)/3
Let x(a) be the first derivative of 0*a**5 + 0*a + 4 + 0*a**2 + 1/4*a**6 - 3/8*a**4 + 0*a**3. Factor x(n).
3*n**3*(n - 1)*(n + 1)/2
Let x(s) be the second derivative of -s**9/60480 + s**8/26880 + s**7/10080 - s**6/2880 - s**4/4 - 3*s. Let p(o) be the third derivative of x(o). Factor p(h).
-h*(h - 1)**2*(h + 1)/4
Let r(i) = 16*i**5 + 17*i**4 + i**3 + i**2 + 8*i + 7. Suppose -3 = -k - 1. Let b(l) = -l**4 + l**2 + l + 1. Let j(g) = k*r(g) - 14*b(g). Factor j(z).
2*z*(z + 1)**2*(4*z - 1)**2
Let m = -393 - -393. Factor -3/5*g**4 + 0*g + m*g**2 + 0 - 6/5*g**3.
-3*g**3*(g + 2)/5
Let s(c) be the third derivative of c**6/1080 + c**5/180 + c**4/72 - 2*c**3/3 + 2*c**2. Let f(x) be the first derivative of s(x). Factor f(q).
(q + 1)**2/3
Let w(n) be the third derivative of n**7/315 + n**6/180 - n**5/30 - n**4/36 + 2*n**3/9 - 7*n**2. Factor w(l).
2*(l - 1)**2*(l + 1)*(l + 2)/3
Let g(w) be the third derivative of -w**6/12 + 7*w**5/12 - 35*w**4/24 + 5*w**3/3 - 62*w**2. Let g(l) = 0. Calculate l.
1/2, 1, 2
Suppose c = -3*l - 11, -3*l - 13 = 4*c - 5. Let b be 6*(-3)/24 + c. Factor b*i + 0 + 1/4*i**2.
i*(i + 1)/4
Let v = 165 + -1979/12. Let o(a) be the third derivative of -1/3*a**4 + 2/3*a**3 + v*a**5 + 0*a - 1/120*a**6 + 0 - a**2. Determine g, given that o(g) = 0.
1, 2
Suppose -86*c = -77*c - 1620. Factor -300*g**2 - 36 + 500/3*g**3 + c*g.
4*(5*g - 3)**3/3
Factor 6*x**2 - 13*x + 6*x**3 - 7*x**4 + 5*x + 2*x**5 - x**4 + 2*x**2.
2*x*(x - 2)**2*(x - 1)*(x + 1)
Let s = -62 - -64. Factor -4/5 - 2/5*t**s + 6/5*t.
-2*(t - 2)*(t - 1)/5
Suppose 0 = -5*k + 4*v - 9*v + 10, -k - 10 = -3*v. Let s be (-2 + (3 - k))/1. Factor -2*b + 1/2 - 1/2*b**s + 2*b**3.
(b - 1)*(b + 1)*(4*b - 1)/2
Suppose -5*o + 3 = -2*o, 29 = 3*x + 5*o. Suppose 2*d + 2*d - x = 0. Factor -3*n**4 - 2*n**3 - n**d - 4*n**5 + 3*n**2 + 3*n**5 + 3*n + 1.
-(n - 1)*(n + 1)**4
Let w(t) be the third derivative of t**8/5040 + t**7/2520 - t**6/1080 - t**5/360 + t**3/6 + 2*t**2. Let g(i) be the first derivative of w(i). Factor g(s).
s*(s - 1)*(s + 1)**2/3
Let q(n) be the first derivative of -4*n**6/33 - 6*n**5/55 + 29*n**4/22 - 2*n**3/11 - 25*n**2/11 + 12*n/11 - 53. Suppose q(y) = 0. What is y?
-3, -1, 1/4, 1, 2
Let f(d) be the third derivative of 2*d**7/105 - 3*d**6/40 + d**5/10 - d**4/24 - 2*d**2. Suppose f(z) = 0. What is z?
0, 1/4, 1
Suppose 6/5*s**2 + 0*s + 3*s**3 + 0 = 0. What is s?
-2/5, 0
Find f, given that -34*f**2 - f**3 + 142*f - 128 + 3*f**3 + 18*f = 0.
1, 8
Suppose -12 = -6*b + 3*b. Let u = 227 - 227. Factor -1/4*z**2 - 1/4*z**b + 1/2*z**3 + u*z + 0.
-z**2*(z - 1)**2/4
Suppose 2*u**2 + u**2 + 9*u - 25 + 25 = 0. What is u?
-3, 0
Let n be -65 - -66 - (1 + 1 - 1). Factor -2/9*b**4 + 4/9*b**2 + n*b + 2/9*b**3 + 0.
-2*b**2*(b - 2)*(b + 1)/9
Let w be ((-24)/140)/(2/(-14) - 0). What is m in 2/5*m + 2/5*m**4 + 6/5*m**3 + 0 + w*m**2 = 0?
-1, 0
Let a(g) = -2 + 14*g + 4 - 4*g - 12*g**2. Let p be -5*(-12)/(-10)*(-8)/16. Let l(o) = o**2 - o. Let b(m) = p*a(m) + 15*l(m). Suppose b(u) = 0. Calculate u.
-2/7, 1
Let i(a) = -a**3 + 4*a**2 + 22*a - 5. Let y be i(7). Factor -1/6*z**y + 0 - 1/6*z.
-z*(z + 1)/6
Suppose -2*g = 5*g - 21. Let r(o) be the second derivative of -1/8*o**g + 0 + 3*o + 1/16*o**4 - 1/80*o**5 + 1/8*o**2. Factor r(t).
-(t - 1)**3/4
Let o(n) be the third derivative of -1/4*n**4 + 0 - 5*n**2 - 3/40*n**5 - 1/4*n**3 + 0*n. Factor o(y).
-3*(y + 1)*(3*y + 1)/2
Let k(q) be the first derivative of -q**5/15 + q**4/24 + 3*q**2/2 + 3. Let j(b) be the second derivative of k(b). Determine u so that j(u) = 0.
0, 1/4
Let n(h) be the second derivative of -h**5/90 + h**4/54 + h**3/27 - h**2/9 - 6*h. Suppose n(i) = 0. What is i?
-1, 1
Let p = -48 - -48. Let s(d) be the first derivative of 0*d**3 + 1/10*d**4 + p*d - 1 - 1/5*d**2. Let s(m) = 0. Calculate m.
-1, 0, 1
Let i(b) be the first derivative of 32/25*b**5 - 7/15*b**6 - 11/10*b**4 - 3 + 4/15*b**3 + 0*b + 0*b**2. Determine g so that i(g) = 0.
0, 2/7, 1
Let -6/5*m**4 + 4/5*m + 6/5*m**2 + 0 - 2/5*m**3 - 2/5*m**5 = 0. What is m?
-2, -1, 0, 1
What is z in -63*z**2 - 324*z - 318*z**2 - 1400*z**2 - 2187*z**3 + 323*z**2 - 24 = 0?
-2/9
Suppose 2*p = -3*p. Let i(m) = -m**3 + 5*m**2 + 5. Let a be i(5). Let 0*z - 2*z + p*z - 4*z**2 + a*z**2 + 1 = 0. What is z?
1
Let g = 204 - 200. Solve 0*v + 1/2*v**g + 0*v**2 + 0 + 1/2*v**3 = 0 for v.
-1, 0
Factor r**2 - 1/4*r**4 - 1/8*r**5 + 1/4 + 1/4*r**3 + 7/8*r.
-(r - 2)*(r + 1)**4/8
Solve -3*a**2 + 16*a - 334 + 5*a**2 + 334 = 0.
-8, 0
Factor 0*h - 1/2*h**3 + 0 + h**2 - 1/2*h**4.
-h**2*(h - 1)*(h + 2)/2
Let l(p) be the third derivative of -p**8/168 - p**7/35 - p**6/60 + p**5/10 + p**4/6 + 5*p**2. Let l(d) = 0. What is d?
-2, -1, 0, 1
Let f(v) be the second derivative of -1/60*v**4 - 2*v - 1/100*v**5 + 1/10*v**2 + 0 + 1/30*v**3. Factor f(d).
-(d - 1)*(d + 1)**2/5
Let y(z) be the second derivative of -3/8*z**4 - 1/3*z**3 + 0 - 1/5*z**5 - 2*z - 1/30*z**6 - z**2. Let n(p) be the first derivative of y(p). Factor n(c).
-(c + 2)*(2*c + 1)**2
Suppose 9*x**3 - 9*x**2 + 3*x + 52 - 2*x**4 - 52 - x**4 = 0. What is x?
0, 1
Let n(l) be the third derivative of l**5/210 - l**4/84 - 6*l**2. Let n(j) = 0. What is j?
0, 1
Let u(m) be the third derivative of m**8/336 + m**7/105 + m**6/120 - 6*m**2. Suppose u(g) = 0. What is g?
-1, 0
Let w(u) = u**5 + 13*u**4 + 14*u**3 + 9*u**2 + 16*u + 9. Let x(i) = i**5 + 12*i**4 + 14*i**3 + 10*i**2 + 15*i + 8. Let n(j) = 6*w(j) - 7*x(j). Factor n(r).
-(r + 1)**4*(r + 2)
What is u in 4/5*u**4 + 48/5*u - 12/5*u**3 - 32/5 - 8/5*