
Let n be 3/(-45)*((-82539)/12)/9. Let s = n - 203/4. Factor 2/5 - 12/5*i**3 + 9/5*i + s*i**2.
-(i - 1)*(3*i + 2)*(4*i + 1)/5
Let s = -5345/3 - -1782. Let h(y) be the second derivative of s*y**6 + 0*y**2 + 0 + 5*y + 1/4*y**5 + 0*y**4 + 0*y**3. Factor h(g).
5*g**3*(2*g + 1)
Let k(i) be the third derivative of -i**8/147 + 4*i**7/245 + 9*i**6/70 - 9*i**5/14 + 27*i**4/28 - 625*i**2. Find c, given that k(c) = 0.
-3, 0, 3/2
Find d such that -6/7*d**2 - 26/7*d - 24/7 = 0.
-3, -4/3
Factor -13/5*s**2 + 24/5 - 2*s - 1/5*s**3.
-(s - 1)*(s + 2)*(s + 12)/5
Let q(r) be the third derivative of 20/3*r**3 + 5/6*r**4 + 0 + r**2 + 2/21*r**7 - 5/6*r**5 - 5/336*r**8 - 1/24*r**6 + 0*r. Let q(h) = 0. What is h?
-1, 2
Let a(z) be the second derivative of z**5/20 + 35*z**4/12 + 323*z**3/6 + 289*z**2/2 - 159*z. Determine w so that a(w) = 0.
-17, -1
Suppose -2*t - 162 = 4*f - t, 0 = 3*f - 2*t + 116. Let r be (-2 + 4)*((-36)/f)/3. Let r*c**2 + 0*c + 0 = 0. Calculate c.
0
Suppose -4*b + b + 4*t = 4, 12 = 2*b + t. Factor 7*z**2 - 22*z**3 + 20*z**3 + z**2 - b*z**2.
-2*z**2*(z - 2)
Let r(u) be the third derivative of 0*u**4 + 0*u**3 - 1/960*u**6 + 0*u + 37*u**2 + 0 + 0*u**5. Solve r(h) = 0 for h.
0
Let w be 1630/1956 - 2/4. Let 1/3*s**3 - w*s + 1/3*s**2 - 1/3 = 0. What is s?
-1, 1
Let g = -1 + 1. Suppose -r - 2*k + 16 = 0, 13 = -g*r + r + 5*k. Factor 94*p**3 + 386*p**2 + r*p**4 + 114*p**3 + 18 + 14*p**4 + 156*p.
2*(p + 3)**2*(4*p + 1)**2
Let k(b) be the third derivative of b**7/1470 + b**6/24 - 37*b**5/140 + 113*b**4/168 - 19*b**3/21 + 315*b**2 - 1. Let k(g) = 0. What is g?
-38, 1
Let x(z) be the first derivative of -8*z**6/9 + 28*z**5/5 - 29*z**4/3 - 40*z**3/9 + 24*z**2 - 32*z/3 - 470. Suppose x(h) = 0. Calculate h.
-1, 1/4, 2
Suppose 5*o = -10*b + 11*b - 2, -5*o = 4*b - 8. Factor 2/3*w**5 + 0*w**3 + 4/3*w**4 + o - 2/3*w - 4/3*w**2.
2*w*(w - 1)*(w + 1)**3/3
Let h(g) = g**2 + 7*g - 12. Let b be h(-10). Suppose b*c - 19*c = 0. What is d in -1/6*d + 1/3*d**2 + c = 0?
0, 1/2
Suppose 3*f = 5*i + 16, 14*i - 18*i = 8. Factor 32/15*v**f + 0 + 8/15*v + 14/15*v**3.
2*v*(v + 2)*(7*v + 2)/15
Let a(u) = 5*u**2 - 11*u - 102. Let f(t) = -65*t**2 + 140*t + 1325. Let h(x) = 40*a(x) + 3*f(x). Factor h(y).
5*(y - 7)*(y + 3)
Let c(t) be the second derivative of 0 + 1/6*t**3 - 1/60*t**4 - 3/10*t**2 + 8*t - 1/100*t**5. Factor c(i).
-(i - 1)**2*(i + 3)/5
Let c be 2 - (31/(-4))/(3/12). Let s = 45 - c. Solve 45/2*j**3 - 18*j - 39*j**2 + s = 0.
-2/3, 2/5, 2
Factor 27*h + 82/3 - 1/3*h**2.
-(h - 82)*(h + 1)/3
Let k(g) be the first derivative of -27 - 3/14*g**6 + 0*g**3 + 0*g - 3/28*g**4 + 0*g**2 - 12/35*g**5. Factor k(t).
-3*t**3*(t + 1)*(3*t + 1)/7
Suppose 2*m + 12 = 8*s, 4 = m - 15*s + 16*s. Solve 2/7*y**3 - 8/7 + 18/7*y - 12/7*y**m = 0 for y.
1, 4
Let o be 5/5 - 2 - (-1 + -2). Factor 61*q**2 + 7 - 66*q**2 - o.
-5*(q - 1)*(q + 1)
Solve -47*v + 103*v + v**3 - 57*v - 20*v**2 + 0*v**3 + 20 = 0.
-1, 1, 20
Suppose 5*j - 33 + 18 = 0, -2*q + 4*j - 12 = 0. Factor -3/10*v**2 - 1/10*v**3 + q*v + 0.
-v**2*(v + 3)/10
Let g(w) be the second derivative of w**4/12 - 5*w**3/6 - 5*w**2 + 5*w. Let i be g(7). Solve 19*u**3 + 3 + 1 - 7*u**4 + u**4 - i*u - 13*u**2 = 0 for u.
-1/2, 2/3, 1, 2
Let m(w) be the third derivative of -w**8/84 - 16*w**7/35 - 76*w**6/15 - 416*w**5/15 - 88*w**4 - 512*w**3/3 - 32*w**2. Find b, given that m(b) = 0.
-16, -2
Let g(k) be the second derivative of k**5/100 - 49*k**4/60 + 104*k**3/5 - 288*k**2/5 - 30*k. Find a such that g(a) = 0.
1, 24
Let u(l) be the second derivative of l**4/16 - 3*l**3 - 254*l. Suppose u(k) = 0. Calculate k.
0, 24
Suppose 4*a - 24 - 8 = 0. Let i(w) = -4*w + 239*w**2 + 247*w**2 - 491*w**2 - 3. Let b(n) = -14*n**2 - 12*n - 8. Let m(o) = a*i(o) - 3*b(o). Solve m(j) = 0.
-2, 0
Determine l so that 31*l**4 - 15*l**3 + 35*l**4 - 102*l**4 + 377*l**2 - 97*l**3 - 2*l**5 - 1600 + 167*l**2 + 480*l = 0.
-10, -2, 2
Let r(c) be the first derivative of 2 - 5/2*c + 0*c**3 + 1/2*c**5 + 5/4*c**4 - 5/2*c**2. Factor r(j).
5*(j - 1)*(j + 1)**3/2
Let g(s) be the second derivative of -s**6/120 + 27*s**5/40 - 781*s**4/48 + 117*s**3/2 - 169*s**2/2 + 2*s - 43. Determine z, given that g(z) = 0.
1, 26
Let f(g) = -2*g**3 - 17*g**2 - 70*g - 45. Let j(r) = r**2 + 1. Let q(d) = 2*f(d) - 10*j(d). Factor q(l).
-4*(l + 1)*(l + 5)**2
Suppose 4*z + 0 = 16. Suppose 2 = -2*k + 3*k - z*q, 0 = -5*q + 25. Factor 8*s**4 - 4*s + 11*s**5 + 15*s**5 - 8*s**2 - k*s**5.
4*s*(s - 1)*(s + 1)**3
Suppose 16*i - 321 = -241. Suppose -4/3*s**3 + 0*s - 14/9*s**4 + 0*s**2 - 2/9*s**i + 0 = 0. Calculate s.
-6, -1, 0
Let f(z) be the third derivative of -2*z**7/105 + z**6/15 + z**5/15 - z**4/3 - 394*z**2. Factor f(m).
-4*m*(m - 2)*(m - 1)*(m + 1)
Let n = 2213/8 - 276. Let p = -3/8 + n. Let -1/2*c**2 + 1/4*c**4 + p - 1/2*c**3 + 1/4*c**5 + 1/4*c = 0. Calculate c.
-1, 1
Let m be 1 - 13/(-4) - 19/76. Let r be m/(-18) + 5/((-450)/(-56)). Factor 0 + r*v + 2/5*v**2.
2*v*(v + 1)/5
Let z(b) = -b**3 + 10*b**2 + b - 9. Suppose 36 + 4 = 4*k. Let c be z(k). Factor -4*j + c - 5 + 2*j**2 + 4*j**3 + 2*j**2.
4*(j - 1)*(j + 1)**2
Let n = 9965 + -9962. Find z, given that 9*z + 2 + 7/4*z**n + 15/2*z**2 = 0.
-2, -2/7
Factor -40*u + 39*u**2 + 2260*u**4 - 4*u**3 + 2*u**3 - 2262*u**4 - 7*u**2.
-2*u*(u - 2)**2*(u + 5)
Let t(x) = x + 12 + 7 - 17. Let g be t(13). Suppose 9*y**3 - y**3 + g*y**2 - 3 + 5*y - 2*y + y**3 = 0. What is y?
-1, 1/3
Suppose 13*b = -29*b - 29*b + 14*b. Suppose -40/3*j**3 + 12*j**2 + b + 4/3*j = 0. Calculate j.
-1/10, 0, 1
Let i = -15 + 18. Suppose -3*h - i*h = h. Suppose 0*k + h + 1/4*k**2 + 1/4*k**3 = 0. Calculate k.
-1, 0
Suppose -42*w + 25 = -46 - 13. Solve -8/5*x - 2 + 2/5*x**w = 0 for x.
-1, 5
Let u(b) be the second derivative of -1/10*b**5 + 2*b**2 - 6*b - 1/3*b**4 + 0 + 1/3*b**3. Find y, given that u(y) = 0.
-2, -1, 1
Let l be (-16)/(-44)*(-51)/(-2). Let t = l - 90/11. Factor t*i + 18/11 + 2/11*i**2.
2*(i + 3)**2/11
Let m(f) be the second derivative of 0 + 3/20*f**4 + 1/5*f**3 + 0*f**2 + 3/100*f**5 - 13*f. Factor m(v).
3*v*(v + 1)*(v + 2)/5
Find s such that -139 + 6 - 9 + 795*s - 22 - 36*s**2 - 97 = 0.
1/3, 87/4
Let h(v) be the second derivative of -7/8*v**2 + 1/4*v**3 - 27*v + 1/48*v**4 + 0. Factor h(y).
(y - 1)*(y + 7)/4
Factor 8*m**4 + 20/3 + 86/3*m**3 + 27*m + 124/3*m**2 + 1/3*m**5.
(m + 1)**4*(m + 20)/3
Suppose -w + 3*a = -34, -27 = 4*w + 4*a - 83. Factor 4*u**3 - w*u - 3*u**2 - 16 - 9*u**2 + 51*u - 8*u**2.
4*(u - 2)**2*(u - 1)
Let b = 2737/5 + -547. Factor -b*f**3 - 2/5 - 6/5*f**2 - 6/5*f.
-2*(f + 1)**3/5
Suppose 2/7*f + 0 + 4/21*f**2 + 2/21*f**5 - 8/21*f**3 - 4/21*f**4 = 0. What is f?
-1, 0, 1, 3
Suppose -5*w = -2*b - 1269, -3*b = 3*w + 93 + 1800. Let z be (b/(-96) + -7)*(-4)/10. Factor z*t**2 + 0*t - 1/6*t**4 + 0*t**3 + 0.
-t**2*(t - 1)*(t + 1)/6
Find u such that -21/2*u + 45/2*u**2 - 27/2*u**3 + 0 + 3/2*u**4 = 0.
0, 1, 7
Suppose -19 = 9*q - 55. Let y be (-1)/(-5) + (-112)/10. Let a(k) = -14*k**2 - 5*k. Let p(u) = -5*u**2 - 2*u. Let f(h) = q*a(h) + y*p(h). Factor f(b).
-b*(b - 2)
Suppose 14*h = 9*h + 5. Let w(i) = 3*i**2 - 1. Let a be w(h). Factor 4*x + 2*x**2 - x + 4*x**4 - 7*x**3 + 0*x**4 - a*x.
x*(x - 1)**2*(4*x + 1)
Factor 7/5*t**2 - 12/5 - 4/5*t - 1/5*t**3.
-(t - 6)*(t - 2)*(t + 1)/5
Let m(n) be the third derivative of -n**8/1008 + n**7/504 + n**6/216 - n**5/72 - n**3/2 + 9*n**2. Let o(d) be the first derivative of m(d). Factor o(f).
-5*f*(f - 1)**2*(f + 1)/3
Let j(s) be the first derivative of 0*s + 0*s**2 + 2*s**3 + 9/4*s**4 + 18 + 3/5*s**5. What is o in j(o) = 0?
-2, -1, 0
Let a(z) be the second derivative of -z**5/5 + 5*z**4/3 - 60*z. Solve a(x) = 0.
0, 5
Let n(w) = -4*w**2 + 21*w - 20. Let r(o) = -2*o**2 - o. Let i(t) = 2*n(t) - 2*r(t). What is z in i(z) = 0?
1, 10
Let n(v) be the second derivative of v**5/140 - 5*v**4/84 + v**3/7 + 2*v - 46. What is t in n(t) = 0?
0, 2, 3
Let l(v) be the second derivative of -v**6/540 - v**3/3 - 7*v. Let t(a) be the second derivative of l(a). Factor t(q).
-2*q**2/3
Solve 19*d + 419*d**3 + 20*d - 398*d**3 - 15*d + 12*d**4 - 102*d**2 = 0.
-4, 0, 1/4, 2
Let k(w) be the second derivative of -4*w**7/21 + 17*w**6/15 - 2*w**5 + 2*w**4/3 + 30*w + 1. Determine t so that k(t) = 0.
0, 1/4, 2
Factor -116483 + 27*t**3 + 99*t + 90*t**2 + 116555 + 33*t + 3*t**4.
3*(t + 2)**3*(t + 3)
Le