, 1
Factor -2/3*s**3 + 2/3*s - 4/3 + 4/3*s**2.
-2*(s - 2)*(s - 1)*(s + 1)/3
Let 12 - 74*y**4 - y**2 - 118*y**3 + 14*y**2 + 28 + 128*y - 10*y**5 + 21*y**2 = 0. What is y?
-5, -2, -1, -2/5, 1
Let s(l) be the second derivative of -l**5/10 + l**4/21 - 27*l. Let s(n) = 0. Calculate n.
0, 2/7
Let k(q) be the third derivative of q**8/112 - q**7/70 - q**6/4 - 2*q**5/5 - 111*q**2. Factor k(j).
3*j**2*(j - 4)*(j + 1)*(j + 2)
Determine d, given that 22*d + 1/2*d**3 + 0 + 12*d**2 = 0.
-22, -2, 0
Suppose 3*u - 1 - 62 = 0. Let g = u - 17. Factor o - 2 + 0*o**2 + g*o**2 - 5*o**2 + 2*o**2.
(o - 1)*(o + 2)
Let z be 3*(-5)/(75/(-40)). Let l(j) be the third derivative of 0*j**5 + 0*j**4 - 6*j**2 + 0*j**3 + 0 + 1/1680*j**7 + 0*j + 0*j**6 + 1/2688*j**z. Factor l(k).
k**4*(k + 1)/8
Let s = -1 - -5. Let b(i) = 3*i - 4. Let n be b(s). Suppose 5*t**5 - 12*t**4 + 0*t**5 - 12*t**2 - 18*t**3 - 3*t - n*t**5 = 0. What is t?
-1, 0
Let m(y) be the third derivative of 9*y**8/112 - 19*y**7/35 + 31*y**6/20 - 12*y**5/5 + 17*y**4/8 - y**3 - y**2 - 4. Suppose m(b) = 0. What is b?
2/9, 1
Let k(d) be the second derivative of d**4/30 - 6*d**3 + 405*d**2 + 105*d. What is n in k(n) = 0?
45
Let m = -318 - -321. Let q(j) be the second derivative of 0 - 10/3*j**m - 4*j + 8*j**2 + 1/3*j**4. Factor q(y).
4*(y - 4)*(y - 1)
Let x = -58 - -60. Let p(y) = y**2 + y - 1. Let i(s) = s**3 + 8*s**2 + 11*s + 1. Let u(l) = x*i(l) - 6*p(l). What is n in u(n) = 0?
-2, -1
Let v(m) = -2*m + 1. Let b be v(-1). Let r be -6 + 8/2 - -3. What is s in -7 - r - 9*s + b*s**3 + 3 - 1 = 0?
-1, 2
Suppose 793*z - 397*z - 30 = 381*z. Suppose 24/7*v + 0 + z*v**3 - 2/7*v**4 - 32/7*v**2 = 0. Calculate v.
0, 2, 3
Let j(i) = -i**3 + 8*i**2 - 6*i - 8. Let r be j(7). Let o be 0 - (-3 + r/(-1)). Solve q**3 + 8 + 3*q**2 - 2*q**2 + 3*q**o + 12*q + 2*q**2 = 0.
-2
Find q such that 224 - 1450*q**3 + 1940*q**2 - 1088*q + 625/8*q**5 + 2375/8*q**4 = 0.
-7, 4/5
Let z(n) be the second derivative of -17*n + 6*n**2 + 0 - 1/4*n**4 + 3/2*n**3. Factor z(s).
-3*(s - 4)*(s + 1)
Suppose 116 = -8*r - 260. Let i = -43 - r. Suppose 0 - 1/5*v**2 + 0*v + 2/5*v**3 - 1/5*v**i = 0. What is v?
0, 1
Suppose -u**2 + 20477*u - 230 + 0*u**2 - 20372*u + 6*u**2 = 0. Calculate u.
-23, 2
Suppose -8*b + 8*b + 743*b**3 - 30976*b**2 - 39*b**3 - 4*b**4 = 0. What is b?
0, 88
Let b(w) be the second derivative of w**6/45 + 2*w**5/15 + w**4/6 - 4*w**3/9 - 4*w**2/3 + 7*w + 2. Solve b(t) = 0 for t.
-2, -1, 1
Solve 45 + 423/4*g**2 - 273/2*g - 27/8*g**3 = 0 for g.
2/3, 30
Suppose 2*g - 344 = 302. Let k = g + -2253/7. Let -4/7*o**2 - k*o**3 - 2/7 + 8/7*o + 6/7*o**4 = 0. Calculate o.
-1, 1/3, 1
Factor -11*o - 10*o**2 - 4*o**2 - 9*o**2 - 2*o**3 - 11*o + 40 + 7*o**2.
-2*(o - 1)*(o + 4)*(o + 5)
Let o = 2138746/63 - 33951. Let q = o - -29/9. Find g, given that -10/7*g**3 - 4/7 + 10/7*g + q*g**2 = 0.
-1, 2/5, 1
Let r(v) = -24*v + 4*v**2 + 13*v - 3 + 5*v. Let y(w) be the third derivative of w**5/20 - 5*w**4/24 - w**3/3 + w**2. Let t(d) = -4*r(d) + 5*y(d). Factor t(g).
-(g - 1)*(g + 2)
Let w(d) be the first derivative of 14*d**5/25 - 11*d**4/5 + 16*d**3/5 - 2*d**2 + 2*d/5 - 29. Factor w(p).
2*(p - 1)**3*(7*p - 1)/5
Let s(g) be the third derivative of g**6/120 + 23*g**5/60 - g**4/24 - 23*g**3/6 + 172*g**2. Factor s(q).
(q - 1)*(q + 1)*(q + 23)
Let c = -1169/5 + 234. Let b(v) be the third derivative of 9/70*v**7 + 5/224*v**8 + 0 + 0*v**4 - 4*v**2 + 0*v**3 - c*v**5 + 3/20*v**6 + 0*v. Factor b(r).
3*r**2*(r + 2)**2*(5*r - 2)/2
Solve 2*a**4 - 6*a**5 - 6 + 25 - 19 = 0 for a.
0, 1/3
Suppose 5*p - 22 = -l - 2*l, 2*p = 3*l - 8. Factor 4*x**2 + 2*x**3 + 1740 - 1740 - p*x**4.
-2*x**2*(x - 2)*(x + 1)
Factor -5/4*u**2 + 7/2 - 17/8*u - 1/8*u**3.
-(u - 1)*(u + 4)*(u + 7)/8
Let f = 59 - 57. Let v(q) be the first derivative of -3/8*q**4 + 0*q**f + 0*q - 5 - q**3. What is j in v(j) = 0?
-2, 0
Let f(z) be the first derivative of z**5/10 - z**4/2 + z**3 - z**2 + 14*z + 18. Let g(t) be the first derivative of f(t). Solve g(s) = 0.
1
Let r = -925/3 - -309. Factor 2 + 10/3*g + r*g**2 - 2/3*g**3.
-2*(g - 3)*(g + 1)**2/3
Let y(f) be the first derivative of f**6/450 + 2*f**5/75 - f**4/6 - 19*f**3/3 - 10. Let x(a) be the third derivative of y(a). Factor x(d).
4*(d - 1)*(d + 5)/5
Let v be (52/(-221))/2 + (-63)/(-102). Solve -6*j - 18 - v*j**2 = 0.
-6
Factor -3*d**2 + 0*d**2 + 19 + 37 - 69*d + 178.
-3*(d - 3)*(d + 26)
Let c(o) = 58*o**2 - 1009*o - 194. Let b(y) = 11*y**2 - 202*y - 39. Let a(s) = -22*b(s) + 4*c(s). What is n in a(n) = 0?
-1/5, 41
Let f(w) be the first derivative of -2*w**3/15 + 32*w**2/5 - 512*w/5 - 165. Factor f(j).
-2*(j - 16)**2/5
Suppose 0 = 4*j - 12, -4*z - 11 = j - 2. Let h be (z - -1) + 12 - -4. Factor -2*a**2 - 2*a**3 + h*a**2 + 6*a**3.
4*a**2*(a + 3)
Suppose 4*m + 8*x = 3*x + 672, 336 = 2*m - 3*x. Let l = m - 168. Factor l*g**3 + 4/11*g**2 + 0 + 2/11*g**5 - 2/11*g - 4/11*g**4.
2*g*(g - 1)**3*(g + 1)/11
Let u = 130 - 126. Find o, given that 27*o**4 - 24*o**u - 6*o**3 + 3*o**5 - 3*o**2 + 3*o**3 = 0.
-1, 0, 1
Let n(q) be the third derivative of -q**8/4032 - q**7/336 - q**5/12 + 19*q**2. Let d(h) be the third derivative of n(h). What is t in d(t) = 0?
-3, 0
Let m(c) be the first derivative of 1/3*c**2 - 1/6*c**4 + 4/9*c**3 - 4/3*c - 11. Factor m(w).
-2*(w - 2)*(w - 1)*(w + 1)/3
Factor -35 - 198*k**4 + 3*k**5 - 1044*k**2 - 14*k**3 - 837*k - 808*k**3 - 204*k**2 - 175.
3*(k - 70)*(k + 1)**4
Let q(v) be the second derivative of 5*v**4/6 + 10*v**3/3 + v. Suppose 745*b = 746*b - 4. Let t(k) = -2*k**2 - 4*k. Let r(p) = b*q(p) + 22*t(p). Factor r(y).
-4*y*(y + 2)
Let l(a) be the third derivative of 0 + 7/24*a**5 + 1/12*a**3 + 0*a + 9*a**2 - 49/240*a**6 + 13/48*a**4. Factor l(s).
-(s - 1)*(7*s + 1)**2/2
Let z(i) be the first derivative of -i**3/12 - 129*i**2/2 - 16641*i + 838. Factor z(r).
-(r + 258)**2/4
Let a(z) be the second derivative of 2*z**7/21 - 448*z**6/45 + 5296*z**5/15 - 3536*z**4 - 383968*z**3/9 + 281216*z**2/3 + 105*z. Find f such that a(f) = 0.
-4, 2/3, 26
Let 5/3*n**5 + 0*n + 16/3*n**3 + 0 + 4/3*n**2 + 17/3*n**4 = 0. Calculate n.
-2, -1, -2/5, 0
Determine c, given that 39/2*c - 3/2*c**3 + 45/2 - 9/2*c**2 = 0.
-5, -1, 3
Suppose 2*f = -4*p + 1 + 5, 0 = -6*p + 3*f + 15. Factor 21/4*b**3 - 3/4*b**p + 9/4*b**5 + 0 - 25/4*b**4 - 1/2*b.
b*(b - 1)**3*(9*b + 2)/4
Let w(t) be the second derivative of 8/3*t**3 + 51*t + 0 + 1/6*t**4 + 16*t**2. Factor w(y).
2*(y + 4)**2
Let s(c) = c**2 - 5*c - 55. Let f be s(-5). Let t be (f - 135/(-25))*10. What is n in 8/9*n**2 + 1/9*n - 2/9 - 2/3*n**t - 1/9*n**3 = 0?
-1, -2/3, 1/2, 1
Find w such that -9 + 3/2*w**3 + 6*w**2 + 3/2*w = 0.
-3, -2, 1
Let u(q) be the third derivative of -7*q**6/40 + 13*q**5/10 + 43*q**4/8 + 5*q**3 - 149*q**2 + 2*q. Factor u(k).
-3*(k - 5)*(k + 1)*(7*k + 2)
What is h in -2/3*h**2 + 2/3*h**5 + 0 - 2*h**4 + 2*h**3 + 0*h = 0?
0, 1
Let v = 16963 + -16963. Factor 8*x - 12*x**2 + 9/2*x**3 - 1/2*x**4 + v.
-x*(x - 4)**2*(x - 1)/2
Let z = -10711/105 - -715/7. Factor -2/15*r**2 - 4/15*r - z.
-2*(r + 1)**2/15
Let s(x) be the first derivative of -4/3*x**3 - 1/2*x**4 + 1/6*x**6 + 2/5*x**5 + 8 + 2*x + 1/2*x**2. Determine c, given that s(c) = 0.
-2, -1, 1
Let c(i) be the first derivative of -i**6/72 + i**5/12 - 7*i**4/48 + i**3/12 - 56. Factor c(q).
-q**2*(q - 3)*(q - 1)**2/12
Let t(i) be the third derivative of -i**6/220 - 13*i**5/330 - i**4/33 + 261*i**2. Factor t(d).
-2*d*(d + 4)*(3*d + 1)/11
Factor 7/6*w**2 + 11/6*w + 1/6*w**3 + 5/6.
(w + 1)**2*(w + 5)/6
Find q such that 175*q**2 - 4165*q**4 - 12*q**3 - 108*q - 9*q**3 - 27*q**5 + 104*q**2 + 4042*q**4 = 0.
-3, 0, 4/9, 1
Let y(j) be the third derivative of j**7/630 + j**6/180 - j**5/45 - j**4/36 + j**3/6 + 2*j**2 + 10. Factor y(t).
(t - 1)**2*(t + 1)*(t + 3)/3
Solve 18 - 30*x + 12*x + 9*x - 3*x**2 - 6 = 0 for x.
-4, 1
Let b(q) be the third derivative of -q**8/84 - 2*q**7/35 + q**6/5 + 28*q**5/15 + 4*q**4 + 536*q**2. Suppose b(p) = 0. Calculate p.
-2, 0, 3
Let s = 124 - 122. Factor 32*l**2 - 21*l + 9*l**3 + 51*l + 7*l**s + 18*l + 12.
3*(l + 2)**2*(3*l + 1)
Let m(l) be the first derivative of 2*l**3/9 - 17*l**2/3 - 76*l/3 - 70. Factor m(z).
2*(z - 19)*(z + 2)/3
Let n(d) be the second derivative of 0*d**3 - 1/24*d**4 + 0 - 1/60*d**6 + 0*d**2 - 10*d + 1/20*d**5. Let n(o) = 0. Calculate o.
0, 1
