Let w = -52 + 57. Factor 2*x**2 - 2*x**w - 2*x**3 + 3*x**3 + x**3 - 2*x**4.
-2*x**2*(x - 1)*(x + 1)**2
Let c(d) be the first derivative of -15*d + 10*d**2 + 7 - 5/3*d**3. Factor c(g).
-5*(g - 3)*(g - 1)
Solve 1/6*c**4 - 26/3*c + 1/6*c**3 - 3*c**2 - 20/3 = 0 for c.
-2, 5
Let b(t) be the first derivative of -t**6/72 + t**5/24 + t**3 - 31. Let v(l) be the third derivative of b(l). Solve v(h) = 0 for h.
0, 1
Let l(w) be the second derivative of -w**5/20 + 3*w**4/4 - 4*w**3 + 8*w**2 - 138*w. What is y in l(y) = 0?
1, 4
Suppose 2*b - 12 = -4*k, -8*b - 6 = -2*k - 4*b. Let w(o) be the second derivative of 0 + 1/4*o**4 + k*o + 0*o**2 + 3/20*o**5 + 0*o**3. Solve w(j) = 0 for j.
-1, 0
Let a = 12061/4824 - 1/4824. Suppose -3/2 + 1/2*k**3 - 1/2*k**2 - a*k = 0. What is k?
-1, 3
Let k(c) be the first derivative of 14 + 1/9*c**3 - 1/3*c**2 + 0*c. Factor k(o).
o*(o - 2)/3
Let r = 70 + -67. Let -3 - 6 + v**3 + 4*v**2 + 11 - 5*v - 2*v**r = 0. Calculate v.
1, 2
Suppose 4*s - 5*x - 15 = 0, -s + 2*x + 123 = 117. Factor -9/5*a**2 + s - 1/5*a**3 + 0*a.
-a**2*(a + 9)/5
Suppose -2*z = -9*z + 14. Let -4*x - 30*x**z + 37*x**2 + 1 - 4 = 0. Calculate x.
-3/7, 1
Suppose -3*o**4 + o**4 + 1503*o**5 + 22*o - 1475*o**5 - 50*o**3 + 10*o**2 - 8 = 0. What is o?
-1, 1/2, 4/7, 1
Let s = 194 + -192. Let x be (-8)/288 + 0 + s/8. Let 2/9 - x*u**3 + 2/3*u**2 - 2/3*u = 0. Calculate u.
1
Factor 242/5*z**2 + 128/5 - 352/5*z.
2*(11*z - 8)**2/5
Let i(x) be the third derivative of x**8/112 - x**7/14 + 7*x**6/40 + x**5/20 - x**4 + 2*x**3 - 117*x**2. Let i(m) = 0. Calculate m.
-1, 1, 2
Let t(i) be the second derivative of 0 + 16/5*i**2 - 32/5*i**3 + 84/25*i**5 + 49/75*i**6 - 8*i + 44/15*i**4. Factor t(j).
2*(j + 2)**2*(7*j - 2)**2/5
Factor -l**2 + 176*l + 322 + 327 - 649.
-l*(l - 176)
Suppose 2*a = 5*a - 66. Suppose -a = -3*b - 3*n - n, -n = 3*b - 10. Factor b*g - 2*g + 2*g**2.
2*g**2
Factor -14/19*z**2 + 0*z**3 + 2/19*z**4 + 12/19*z + 0.
2*z*(z - 2)*(z - 1)*(z + 3)/19
Let s(m) be the third derivative of -m**8/2184 - 8*m**7/1365 + 2*m**6/195 + 16*m**5/65 - 12*m**4/13 + 79*m**2. Factor s(j).
-2*j*(j - 2)**2*(j + 6)**2/13
Let a = -618/5 + 4336/35. Factor 0 + 12/7*r**2 + 18/7*r + a*r**3.
2*r*(r + 3)**2/7
Let x = 4/7319 + -1427221/29276. Let k = x - -49. Suppose 0 - k*r + 1/4*r**2 = 0. Calculate r.
0, 1
Factor 20 - 15*f**2 - 86*f**3 - 96*f**3 - 20*f - 84*f**3 + 286*f**3 - 5*f**4.
-5*(f - 2)**2*(f - 1)*(f + 1)
Factor 2248/5*t + 315844/5 + 4/5*t**2.
4*(t + 281)**2/5
Let j(k) be the first derivative of -2*k**6/3 + 12*k**5/5 + 11*k**4 - 20*k**3 - 92*k**2 - 96*k + 393. Let j(m) = 0. Calculate m.
-2, -1, 3, 4
Let k(j) be the second derivative of -2/3*j**3 - 17/140*j**5 - 1/70*j**6 + 0 - 17/42*j**4 - 4/7*j**2 + 16*j. Solve k(l) = 0 for l.
-2, -1, -2/3
Let r(b) be the first derivative of 35*b**6/6 - 33*b**5 + 55*b**4/4 + 205*b**3/3 - 45*b**2 - 40*b - 40. What is y in r(y) = 0?
-1, -2/7, 1, 4
Let s(z) be the second derivative of -5*z**3 - 1/4*z**4 - 75/2*z**2 + 8*z + 0. Factor s(x).
-3*(x + 5)**2
Let b(f) be the first derivative of 4*f**4 + 92*f**3/3 + 28*f**2 - 20*f + 66. Factor b(u).
4*(u + 1)*(u + 5)*(4*u - 1)
Let r be (-1829)/(-2301) - (-6)/(-13). Factor 2/3*z**2 - 1/3*z**4 - r + 0*z**3 + 0*z.
-(z - 1)**2*(z + 1)**2/3
Suppose -72*g + 68*g = -92. Let y = g + -137/6. Factor -1/6*b + y*b**2 + 0.
b*(b - 1)/6
Let u(q) = q**3 + 25*q**2 + 22*q - 27. Let y be u(-24). Let z be y/216 - 6/(-48). Suppose 2/9*m**3 + 2/9 - 2/9*m**2 - z*m = 0. What is m?
-1, 1
Suppose 3*k + 2 = -12*h + 20, 0 = -k - 3*h + 6. Suppose k*y**2 + 3/2*y**4 - 2*y - 11/2*y**3 + 0 = 0. What is y?
0, 2/3, 1, 2
Let y = 23/1050 - -2/175. Let n(b) be the second derivative of 0 + 1/3*b**2 - 1/18*b**4 + 5*b + y*b**5 - 1/9*b**3. Factor n(u).
2*(u - 1)**2*(u + 1)/3
Let l = 6 - -1. Let 2 + 3*w + w**2 + 3*w + l = 0. Calculate w.
-3
Factor 5/4*g**2 + 17/4*g + 3/2.
(g + 3)*(5*g + 2)/4
Let j = -11 - -13. Suppose 15 = j*z - 9. Let z*n**3 + 6*n**3 - 4*n - 14*n**5 + 2*n**4 + 10*n**2 + 0*n - 12*n**4 = 0. What is n?
-1, 0, 2/7, 1
Let d be 2/(-1*(-3)/6). Determine v so that -24/7*v**3 + 24/7*v + 6/7*v**d - 24/7 + 18/7*v**2 = 0.
-1, 1, 2
Let g(t) = -3*t**3 + 10*t + 13*t**2 - 24 - 4*t**3 + 6*t**3 - 8*t. Let p be g(13). Find b such that -1/3*b**5 + 0*b**p + 0*b + 0 - 2/3*b**4 - 1/3*b**3 = 0.
-1, 0
Let g(c) be the third derivative of -c**5/5 - 2*c**4 + 14*c**3/3 + 9*c**2. Let d(s) = s**2 + s. Let l(h) = -16*d(h) - g(h). Factor l(q).
-4*(q - 7)*(q - 1)
Suppose 5*o - 8 = 32. Suppose -3*a + o*a = 10. Let 0*f + 0 - 1/6*f**4 + 1/3*f**3 + 0*f**a = 0. What is f?
0, 2
Let h(y) = 8*y. Let j be h(-1). Let w be (-462)/91 - (j - -2). Factor w - 10/13*r + 2/13*r**2.
2*(r - 3)*(r - 2)/13
Suppose -5*i = -4*f + 61 - 17, 4*f = -3*i + 12. Find w such that 8*w**3 - w**3 - 3*w**4 - 12*w + 6 + f*w**2 - 14 = 0.
-1, -2/3, 2
Let m(k) be the second derivative of -3/13*k**2 + 0 - 1/78*k**4 + 4/39*k**3 + 9*k. Factor m(y).
-2*(y - 3)*(y - 1)/13
Let f(v) be the third derivative of 2*v**7/245 - 2*v**6/105 - 2*v**5/105 + 2*v**4/21 - 2*v**3/21 + 318*v**2. Let f(u) = 0. What is u?
-1, 1/3, 1
Suppose 16*v = 12*v + 12. Let c(u) be the third derivative of 1/120*u**4 + 1/600*u**5 + 1/60*u**v - 9*u**2 + 0*u + 0. Factor c(z).
(z + 1)**2/10
Let m(q) be the third derivative of 3/8*q**6 - 2*q**2 + 0*q + 1/21*q**7 + 0 + 5/3*q**3 + 15/8*q**4 + 7/6*q**5. Factor m(u).
5*(u + 1)**2*(u + 2)*(2*u + 1)
Suppose 66*z - 2090 = -1958. Factor 345/2*n**3 - 114*n - 36 - 126*n**4 + 29*n**z + 49/2*n**5.
(n - 2)**3*(7*n + 3)**2/2
Let r(h) be the third derivative of h**8/1680 - h**7/350 + h**6/200 - h**5/300 + h**2 + 39*h. Factor r(d).
d**2*(d - 1)**3/5
Suppose 4*g = -3*o - 116, -3*o + 2*g = g + 121. Let s = -24 - o. Factor 2*x - 2*x + 2*x**5 - 2*x**2 - s*x**4 - 2*x**3 + 18*x**4.
2*x**2*(x - 1)*(x + 1)**2
Let r be (-1 - (-21)/9)*3. Let f be 0/4*(-13)/(-26). Let 0*b + 0*b**2 + 3/5*b**r + 0 - 3/5*b**5 + f*b**3 = 0. What is b?
0, 1
Let g(t) = t - 6. Let h = -4 + 13. Let p be g(h). Suppose -6*z**2 + 3*z**2 - 2*z**p + 3*z**2 + 7*z**5 - 5*z**4 = 0. Calculate z.
-2/7, 0, 1
Factor 0 + 3/7*j**4 + 3/7*j**2 + 0*j - 6/7*j**3.
3*j**2*(j - 1)**2/7
Let u = -122/19 + 2188/323. Let i = -52/357 - -8/21. Factor 2/17*r**2 - u - i*r.
2*(r - 3)*(r + 1)/17
Suppose 0 = 4*m - 4*s - 20, m = -3*s - s - 5. Suppose -p**4 - 7 + 44*p + m*p**3 + 7 - 48*p = 0. What is p?
-1, 0, 2
Let -2628*m**2 + 702768 + 264*m**3 + 3*m**4 + 8948*m + 5579*m**2 + 5761*m**2 + 118828*m = 0. What is m?
-22
Let u(k) = -k**3 + 4*k**2 + 7*k - 7. Let p be u(5). Factor v**p - 4 - 3*v - v + 4*v**2 + v**3 + 2*v**3.
4*(v - 1)*(v + 1)**2
Factor 4/5*n**2 - 2/5*n**3 + 2*n - 12/5.
-2*(n - 3)*(n - 1)*(n + 2)/5
Suppose 4*n - 4*j = 156, 3*n - 3*j - 101 = -8*j. Find f such that 5*f**2 + 75 - n*f + 8*f**2 - 10*f**2 + 7*f = 0.
5
Suppose 5*a - 25 - 45 = 0. Let y be (-24)/(-13) + a/91. Solve -1/6*m**y - 1/3*m**3 - 1/6*m**4 + 0 + 0*m = 0.
-1, 0
Suppose 4195*z - 6*z**2 - 4163*z + 8*z**4 - 26*z**2 - 2*z**5 = 0. What is z?
-2, 0, 2
Let y = 2372 - 16598/7. Suppose 0 - 36/7*u**3 - y*u + 27/7*u**2 + 12/7*u**4 = 0. Calculate u.
0, 1/2, 2
Suppose -19*z + 59 = -36. Let j(t) be the first derivative of -2/5*t**z - 16/3*t**3 + 3 + 0*t - 5/2*t**4 - 4*t**2. Factor j(p).
-2*p*(p + 1)*(p + 2)**2
Let u(n) = -n**2 + 5*n - 7. Let s be u(3). Let g be -20*(5/(-4) - s). Factor l**5 - 4*l**3 - 2*l**g + 2*l**4 + 3*l**3.
-l**3*(l - 1)**2
Let b = 179 - 179. Let q(h) be the first derivative of 0*h**4 + 1/30*h**5 + 0*h**2 + 0*h + 2 + b*h**3. Factor q(j).
j**4/6
Suppose 24*o = 23*o. Suppose -10 = -p - p - 2*u, o = 3*p + 4*u - 15. Suppose -17*k + 21*k + p*k**2 - k**2 - 2*k**2 = 0. Calculate k.
-2, 0
Let a = 507 + -180. Factor 16*u**3 - 329 + 3*u**4 + 12*u**2 + 3*u**4 + a.
2*(u + 1)**3*(3*u - 1)
Let c(f) be the third derivative of -f**7/35 - 31*f**6/60 - 7*f**5/30 + 31*f**4/12 + 10*f**3/3 - 160*f**2. Suppose c(r) = 0. What is r?
-10, -1, -1/3, 1
Let w(u) be the second derivative of -u**4/48 + 13*u**3/8 - 19*u**2/4 - 61*u - 2. Solve w(s) = 0.
1, 38
Let d(p) be the first derivative of -p**6/3 + 2*p**5/5 + p**4 - 4*p**3/3 - p**2 + 2*p - 26. Factor d(r).
-2*(r - 1)**3*(r + 1)**2
Let u(o) be the first derivative of -2*o**3/21 + 5*o**2/7 - 79. Factor u(l).
-2*l*(l - 5)/7
Let y be 2/(-2)*-4 + -2. Factor -2 + i**y - 6 + 3 - 5*i - 1.
