Let p(k) be the second derivative of k**4/54 + 125*k**3/27 - 128*k**2/3 - 429*k + 3. Factor p(a).
2*(a - 3)*(a + 128)/9
Let q be -7*(-717)/(-9) - (-4)/(-1). Let v = 565 + q. Factor 6*i - v - 8/3*i**2.
-2*(i - 1)*(4*i - 5)/3
Suppose -2*t = f - 10, 19*t = f + 20*t - 6. Suppose -4*v + w - 4*w + 11 = 0, 2*w + 2 = f*v. Factor -4/9*l + 1/9 + 4/9*l**v.
(2*l - 1)**2/9
Let i be ((-2)/(-6))/(-4*(-2)/48). Let -288*q + 1031*q**i - 432*q**3 - 963 - 27*q**2 + 979 = 0. What is q?
2/27, 1/4, 2
Suppose 34/3*h**4 - 148/3*h**3 + 16*h + 0 + 56/3*h**2 + 10/3*h**5 = 0. Calculate h.
-6, -2/5, 0, 1, 2
Let w = -8727 + 8745. Let a(c) be the first derivative of -6/85*c**5 + 2/17*c**3 + 1/51*c**6 + 1/34*c**4 - w - 2/17*c**2 + 0*c. Find p such that a(p) = 0.
-1, 0, 1, 2
Let m be 23/15 + (-1248)/(-4680). Suppose 1/5*j**2 + 0 - m*j = 0. Calculate j.
0, 9
Let l be (2 - 4)/(198/(-27) - -7). Let u(h) be the first derivative of 12 + l*h + 9/4*h**4 - 4*h**3 - 3/2*h**2. Factor u(q).
3*(q - 1)**2*(3*q + 2)
Suppose -5*o = 5, -k + 3*o + 28 = 2*o. Let y = k - 23. What is a in 5*a**y - 16*a**2 + 2*a**4 - a + 9*a**4 + 5*a - 4*a**3 = 0?
-1, 0, 1/4, 1
Let o = 36 + -32. Suppose 3*h = f - 27, 4*f = -0*f - o*h + 44. Solve 9*x**2 + 3*x**2 - 10 + 13*x**2 + 0 + f*x = 0 for x.
-1, 2/5
Let n(t) be the first derivative of t**4/4 + 44*t**3/3 - 46*t**2 + 511. Factor n(d).
d*(d - 2)*(d + 46)
Suppose -27/2 + 1/2*w**2 + 23/4*w = 0. What is w?
-27/2, 2
Let k(x) = x**4 - x**3 - 2*x**2 - x - 2. Let u(d) = -27*d**4 - 147*d**3 + 957*d**2 - 1269*d + 606. Let y(a) = 24*k(a) + u(a). Suppose y(m) = 0. What is m?
-62, 1, 3
Let i(k) = 2*k - 5. Let t be i(5). Let r be (-42)/231 + ((-9)/11 - -3). Factor w**3 + r*w**2 + w**2 + 5*w - t*w.
w**2*(w + 3)
Let h(t) be the third derivative of -8*t - 1/15*t**5 - 4*t**3 - 7/6*t**4 + t**2 + 0. Factor h(w).
-4*(w + 1)*(w + 6)
Let t(u) be the third derivative of -15*u**2 - 6*u**3 - 1/24*u**6 + 37/60*u**5 + 0*u - 3 + 19/6*u**4. Factor t(n).
-(n - 9)*(n + 2)*(5*n - 2)
Factor 2/3*k**2 + 16 - 20/3*k.
2*(k - 6)*(k - 4)/3
Let a(x) be the first derivative of -3/2*x**4 - 12*x - 140/9*x**3 + 249 + 97/3*x**2. Factor a(b).
-2*(b - 1)*(b + 9)*(9*b - 2)/3
Suppose 5*p - 417 = -337. Let x be 1 - (5 - 88/p). Let 375/2 - x*g**3 + 45/2*g**2 - 225/2*g = 0. Calculate g.
5
Suppose 79*q - 112 = 51*q. Let m(i) be the second derivative of 0 - 1/3*i**q + 0*i**2 + 3*i - 1/5*i**5 + 0*i**3. Factor m(j).
-4*j**2*(j + 1)
Let y(b) be the third derivative of -b**6/360 + 7*b**5/180 - b**4/36 - 20*b**3/9 + 698*b**2. Solve y(v) = 0 for v.
-2, 4, 5
Let c(b) = 15*b**3 - 51*b**2 - 24*b + 3. Let z = -304 - -302. Let f(k) = -15*k**3 + 52*k**2 + 24*k - 2. Let u(n) = z*c(n) - 3*f(n). Factor u(v).
3*v*(v - 4)*(5*v + 2)
Suppose -54*r + 38*r + 32 = 0. Suppose 3*t - 5*d - 6 = 3, 5*t - 46 = -2*d. Factor -29*k + 6 + 10*k**2 - 14*k**3 + 14*k**r + 5*k**3 + t*k.
-3*(k - 1)**2*(3*k - 2)
Suppose -4*z + 0*z = -4*n - 68, 5*n = 3*z - 55. Find r such that -23*r**4 + 15*r**2 - z*r**3 - 23*r**4 + 6*r + 4*r**5 + 31*r**4 + 5*r**5 = 0.
-1, -1/3, 0, 1, 2
Suppose 5*r + 110 = -0*r - b, 0 = r - 3*b + 38. Let f = r + 209/9. Factor 0 + 0*c**2 - 2/9*c + f*c**3.
2*c*(c - 1)*(c + 1)/9
Let a(x) be the third derivative of 13*x**6/60 - 733*x**5/10 - 156*x**4 + 340*x**3/3 + 13*x**2 + 206*x + 2. Factor a(r).
2*(r - 170)*(r + 1)*(13*r - 2)
Factor -80/9 + 2/9*h**2 + 26/3*h.
2*(h - 1)*(h + 40)/9
Suppose 4906 - 19242 = -16*t. Factor -160 - 33 + 78*a + a**2 + 818 + t.
(a + 39)**2
Let w(h) = 163*h + 447. Let c be w(-4). Let s be c/123*(-1)/(10/12). Factor 10/3*v + 25/6 - 5/6*v**s.
-5*(v - 5)*(v + 1)/6
Let p(u) be the second derivative of -u**8/3920 - 3*u**7/1960 + u**5/70 - 5*u**3/6 - 3*u**2/2 - u. Let m(q) be the second derivative of p(q). Solve m(j) = 0.
-2, 0, 1
Let k(t) = -4*t**4 - 65*t**3 + 314*t**2 - 10*t. Let o(p) = -2*p**4 - 32*p**3 + 156*p**2 - 4*p. Let c(l) = -2*k(l) + 5*o(l). Factor c(b).
-2*b**2*(b - 4)*(b + 19)
Factor 5*t**4 + 39690*t - 46305 + 367*t**3 - 57*t**3 + 1369*t**2 + 4862*t**2 + 69*t**2.
5*(t - 1)*(t + 21)**3
Let u be (-1)/(-5) + (-50578)/190. Let s = u + 269. Factor 0 - 1/3*t**5 + 2/3*t**2 - 2/3*t**4 + 0*t**s + 1/3*t.
-t*(t - 1)*(t + 1)**3/3
Let u(t) be the third derivative of -2*t**7/105 - 4*t**6/5 + 26*t**5/5 - 40*t**4/3 + 18*t**3 - 19*t**2 + 37*t. Suppose u(c) = 0. What is c?
-27, 1
Let a(s) be the first derivative of s**4/15 + 34*s**3/15 - 36*s**2/5 - 37*s - 23. Let g(n) be the first derivative of a(n). What is r in g(r) = 0?
-18, 1
Factor 476*x**2 - 17*x - 59*x - 44*x + 137*x**3 - 70*x**3 - 51*x**3.
4*x*(x + 30)*(4*x - 1)
Let -1/8*h**5 + 0 + 3/2*h - 1/8*h**4 + 13/8*h**3 + 25/8*h**2 = 0. What is h?
-3, -1, 0, 4
Let g(l) be the second derivative of l**4/6 - 16*l**2 - 612*l. Factor g(f).
2*(f - 4)*(f + 4)
Let j(i) = 5*i**2 + 291*i. Let b(m) = 14*m + 11. Let q be b(-1). Let n(p) = 10*p**2 + 579*p. Let k(t) = q*n(t) + 7*j(t). Let k(o) = 0. Calculate o.
-60, 0
Let y(c) = -c**4 + 14*c**3 - 47*c**2 + 56*c - 20. Let s(w) = -w - w + 2 - w**2 + 2*w - 176*w**3 + 177*w**3 - w. Let z(l) = 4*s(l) - 2*y(l). Factor z(v).
2*(v - 6)*(v - 4)*(v - 1)**2
Let u(t) be the third derivative of 0*t + 1/1680*t**7 + 2*t**2 + 1/12*t**3 + 13/480*t**5 - 29 + 1/16*t**4 + 1/160*t**6. Find y, given that u(y) = 0.
-2, -1
Let d(y) be the third derivative of y**6/120 - 173*y**5/60 + 64*y**4/3 - 170*y**3/3 - 11*y**2 + y - 49. Solve d(u) = 0.
1, 2, 170
Let l(k) be the third derivative of 0 - 51*k**2 + 0*k + 5/2*k**5 + 2500/3*k**3 + 1/24*k**6 + 125/2*k**4. Find b such that l(b) = 0.
-10
Solve 212/11*r - 210/11 - 2/11*r**2 = 0 for r.
1, 105
Let k be (570/60)/(-1) + 11 + 1 - 2. What is w in 0*w**2 - 1 + k*w**3 - 3/2*w = 0?
-1, 2
Let r(f) be the second derivative of -f**4/4 + 55*f**3 - 963*f**2/2 - 14*f + 6. Determine p so that r(p) = 0.
3, 107
Let j be -1*1 + -70 + 19. Let q(z) = -18*z**2 - 72*z - 28. Let c(b) = 2*b**2 + 8*b + 3. Let k = -7 + 1. Let o(p) = j*c(p) + k*q(p). Factor o(l).
4*(l + 1)*(l + 3)
Suppose 0 = 2*f + f - 2*x - 15, 2*x = -3*f + 15. Suppose y - f*b = 2*y - 9, -3*y = b - 13. Factor 0 + 0*p + 13/7*p**y + 4/7*p**5 + 0*p**2 + 3/7*p**3.
p**3*(p + 3)*(4*p + 1)/7
Suppose 0 = 5*g + 5, -2*o + 6*g + 9 = 3*g. Let -96*i + 15 - o*i**2 + 8*i**2 + 116*i = 0. Calculate i.
-3, -1
Suppose 0 = -9*u + 42 + 372. Factor -27*z - 63 + u*z - 31*z + 3*z**2.
3*(z - 7)*(z + 3)
Find f such that 21 + 411 + 64*f**3 + 166*f**2 + 2*f**4 + 738*f + 162*f**2 - 2*f**3 + 38*f**2 = 0.
-24, -3, -1
Let l(w) be the first derivative of -2*w + 121 - 1/2*w**3 - 5/3*w**2 - 1/24*w**4. Determine d so that l(d) = 0.
-6, -2, -1
Let v(s) be the third derivative of -12*s - 25/24*s**4 - 1/24*s**6 + 2*s**2 - 5/3*s**3 + 0 - 1/3*s**5. Find i such that v(i) = 0.
-2, -1
Let x(t) be the second derivative of 9/10*t**6 + 0*t**2 - 21/20*t**5 + 0 + 0*t**3 - 145*t - 1/2*t**4. Factor x(q).
3*q**2*(q - 1)*(9*q + 2)
Suppose 44 - 127 = 125*h - 833. Let t(a) be the first derivative of 22/5*a**5 + 0*a**2 + h*a**4 + 31 + 8/3*a**3 + 0*a + a**6. Determine i so that t(i) = 0.
-2, -1, -2/3, 0
Let b(i) be the third derivative of i**6/900 + 22*i**5/75 + 484*i**4/15 + 229*i**3/6 + 5*i**2 - 3*i. Let n(y) be the first derivative of b(y). Factor n(a).
2*(a + 44)**2/5
Suppose -8*b + 6*b = -16. Solve -4*o**2 - 9*o - 28 - b*o + 30*o + 19*o = 0.
1, 7
Let t = -111 + 87. Let k = -11 - t. Factor -27*f**2 + k*f**2 + 13*f**2 - 196 - 28*f.
-(f + 14)**2
Let m(n) = n**2 - 32*n + 75. Let i(u) = u**2 - 4*u - 1. Let h = -411 - -413. Let l(y) = h*m(y) - 6*i(y). Factor l(x).
-4*(x - 3)*(x + 13)
Let y(f) = 6*f**2 + 23*f + 81. Let c(k) = -5*k**2 - 22*k - 81. Let h = -11 + 7. Let l(d) = h*y(d) - 5*c(d). Factor l(r).
(r + 9)**2
Let l(a) be the first derivative of a**5/10 - 6*a**3 + 8*a**2 + 96*a + 787. Suppose l(n) = 0. What is n?
-6, -2, 4
Let r(l) be the first derivative of -l**4/2 - 512*l**3/3 - 16637*l**2 - 64516*l + 1176. Factor r(t).
-2*(t + 2)*(t + 127)**2
Let t(q) be the second derivative of 1/30*q**6 + 0*q**2 - 2*q - 1/4*q**5 - 11 + 1/3*q**4 + 0*q**3. Factor t(s).
s**2*(s - 4)*(s - 1)
Let o(p) be the second derivative of 0*p**2 - 1/10*p**5 - 1/60*p**6 - 52*p + 0 - 5/24*p**4 - 1/6*p**3. Factor o(a).
-a*(a + 1)**2*(a + 2)/2
Let p(s) = 72*s - 61. Let x be p(2). Suppose -14*y = -83 + x. Let y + 3/2*z + 3/4*z**2 = 0. Calculate z.
-2, 0
Factor 