*2*(y + 2)/3
Let i(t) be the third derivative of -t**6/1260 + t**4/84 + 5*t**3/3 + 3*t**2. Let u(q) be the first derivative of i(q). Factor u(f).
-2*(f - 1)*(f + 1)/7
Let f(s) = -s**3 + 7*s**2 - 6*s + 2. Let x be f(6). Suppose 0 = -3*u + 9, 2*u + 3 = 4*b + 1. Factor -28 - x*g**b + 32 + g - 2*g - g.
-2*(g - 1)*(g + 2)
Factor -48 + 41 + 5 + 12*d**2 - 132 - 62 + 584*d.
4*(d + 49)*(3*d - 1)
Let v = 4/7 + -41/70. Let f = v + 57/70. Factor 0*i + 0*i**2 + 0 + 2/5*i**4 - f*i**3.
2*i**3*(i - 2)/5
Let k(h) be the third derivative of 1/120*h**6 + 0*h**4 + 0*h - 1/60*h**5 + 0*h**3 + h**2 + 0. Factor k(y).
y**2*(y - 1)
Suppose z + 21 = -3*o, -2*z - 4*o = -6*z - 52. Let s be (-70)/(-25) + (-3)/z. Factor 7*h**2 - 5*h**2 + s*h - 5*h**3 + h**4 + 10*h**3 + 5*h**2.
h*(h + 1)**2*(h + 3)
Let k(h) be the third derivative of 5/6*h**4 - 1/42*h**7 + 5*h**2 - 1/12*h**6 - 10/3*h**3 + 1/4*h**5 + 0*h + 0. Find v, given that k(v) = 0.
-2, 1
Suppose 0 = -6*u + 11 + 1. Factor -2*d**u - 18*d**2 - 34*d**3 + 15*d + 90 + 29*d**3.
-5*(d - 2)*(d + 3)**2
Let n = -26 - -106. Let p be 1/8*n/30*1. Factor 1/3*j + 0 - p*j**3 + 1/3*j**2 - 1/3*j**4.
-j*(j - 1)*(j + 1)**2/3
Let w(g) be the third derivative of -1/40*g**6 + 0 + 0*g + 0*g**5 - g**2 + 1/8*g**4 + 0*g**3. Determine b, given that w(b) = 0.
-1, 0, 1
Let p = -33 - -36. Factor 3*s + s**p - 4*s**2 - 3*s + 5*s + 0*s - 2.
(s - 2)*(s - 1)**2
Let w(l) be the third derivative of -l**5/330 - l**4/22 - 8*l**3/33 + 48*l**2 - 3. Let w(c) = 0. What is c?
-4, -2
Suppose 3*k - r + 29 - 40 = 0, -4*k - 3*r - 7 = 0. Factor -4/3*q**3 + 8/3*q + 2*q**k - 2/3*q**4 - 8/3.
-2*(q - 1)**2*(q + 2)**2/3
Let s(u) = -2*u**4 - 55*u**3 - 221*u**2 - 297*u - 129. Let z(p) = 2*p**4 + 56*p**3 + 220*p**2 + 296*p + 130. Let t(q) = -4*s(q) - 3*z(q). Factor t(d).
2*(d + 1)**2*(d + 3)*(d + 21)
Let f = -21 - -25. Suppose 3*j = j - 4*w - 8, 5*j - 4*w - 22 = 0. Find x such that -2 + 2 - j*x - f*x**2 + 0*x**2 = 0.
-1/2, 0
Let a = -205 - -209. Let k(n) = 3*n**2 - 14*n + 10. Let s be k(a). Suppose 12/5*t**s + 0 + 2/5*t**3 + 18/5*t = 0. Calculate t.
-3, 0
Let g = -115 + 117. Factor 7*h**2 - 7*h**2 - 4*h**g - 6*h + 2*h.
-4*h*(h + 1)
Suppose 381 - 321 = 20*b. Factor 4/7*o**4 + 6/7*o**b - 2/7*o**5 - 8/7*o**2 + 0 - 8/7*o.
-2*o*(o - 2)**2*(o + 1)**2/7
Let c(g) be the third derivative of g**6/120 + g**5/15 - 5*g**4/24 + g**3/2 - 20*g**2. Let o be c(-5). Solve -2/7 + 2/7*l**o - 6/7*l**2 + 6/7*l = 0 for l.
1
Let i(r) be the first derivative of r**5/160 + r**4/32 - 3*r**3/16 + 27*r**2/2 + 32. Let u(d) be the second derivative of i(d). Factor u(b).
3*(b - 1)*(b + 3)/8
Let -4/7*g**2 - 24/7*g**3 + 12/7 + 2/7*g**5 - 8/7*g**4 + 22/7*g = 0. What is g?
-1, 1, 6
Let u(r) be the second derivative of -r**5/70 + 3*r**4/14 - 20*r**3/21 + 12*r**2/7 + 114*r. What is q in u(q) = 0?
1, 2, 6
Let j = -9/49 + -97/539. Let q = j + 42/55. Find n such that -2*n - 8/5*n**2 - q*n**3 - 4/5 = 0.
-2, -1
Let a(g) be the third derivative of g**8/84 - g**6/15 + g**4/6 - 24*g**2. What is x in a(x) = 0?
-1, 0, 1
Suppose 231/2*b**2 + 10 - 49/4*b**3 + 69*b = 0. What is b?
-2/7, 10
Let j(b) = -5*b**2 + 12*b + 9. Let i(s) = -4*s**2 + 10*s + 8. Let k(w) = 4*i(w) - 3*j(w). Factor k(d).
-(d - 5)*(d + 1)
Let h(y) = 35*y**4 + 80*y**3 + 115*y**2 - 140*y + 90. Let j(b) = -b**4 - 4*b**3 - 1. Let k(q) = -h(q) - 30*j(q). Factor k(s).
-5*(s - 3)*(s - 2)**2*(s - 1)
Determine k, given that -3*k - 5*k**2 - 5 + 3 + 18 - 2 + 0 = 0.
-2, 7/5
Let x(g) be the second derivative of 25*g**4/12 - 20*g**3/3 + 8*g**2 - 19*g. Suppose x(k) = 0. What is k?
4/5
Let l(f) be the second derivative of -f**5/330 + 5*f**4/132 + 2*f**3/11 + f**2 + 7*f. Let p(q) be the first derivative of l(q). Find c such that p(c) = 0.
-1, 6
Determine x so that -8/5*x**2 - 12/5*x**3 - 8/5*x**4 + 0 - 2/5*x - 2/5*x**5 = 0.
-1, 0
Let i = -126/65 - -33/13. Determine f so that -i*f**2 + 0*f + 0 = 0.
0
Suppose -2 = -2*f - 4*s, -5*f - 27*s = -25*s - 13. Find h, given that -5/3*h**f - 10/3 + 0*h**2 + 5*h = 0.
-2, 1
Determine o, given that 0 - 148/7*o**2 - 4/7*o**3 + 312/7*o = 0.
-39, 0, 2
Let x(j) be the third derivative of -j**8/32 + 19*j**7/140 + 3*j**6/40 - 7*j**5/10 - j**4/2 + j**2 + 18. Suppose x(g) = 0. Calculate g.
-1, -2/7, 0, 2
Let x be (-5)/565*(-2)/(-1). Let p = x - -232/339. Factor 0 + 0*u + 2/9*u**5 + 4/9*u**3 + p*u**4 + 0*u**2.
2*u**3*(u + 1)*(u + 2)/9
Let f(d) be the first derivative of -3*d**5/5 + 15*d**4 - 118*d**3 + 270*d**2 - 243*d - 16. Find a, given that f(a) = 0.
1, 9
Factor 0 - 1/6*j - 49/6*j**3 - 7/3*j**2.
-j*(7*j + 1)**2/6
Determine a, given that -16/9*a**2 - 2/9*a**3 - 32/9 - 40/9*a = 0.
-4, -2
Let h(b) = -b**2 + 5*b - 4. Let o be h(3). Determine y so that -24*y**4 - 207*y**2 + 32*y**3 + 4*y**5 - 210*y**2 + 16 - 36*y + 425*y**o = 0.
-1, 1, 4
Let -2/5*d**3 - 2/5*d**4 + 6/5*d**2 + 2/5*d - 4/5 = 0. Calculate d.
-2, -1, 1
Factor 34/11*b**3 + 0*b + 0 - 4/11*b**2.
2*b**2*(17*b - 2)/11
Suppose 4*p - 173 - 159 = -320. Factor -3/4*y**5 + 9/4*y**p - 15/4*y**2 + 3/2*y + 0 + 3/4*y**4.
-3*y*(y - 1)**3*(y + 2)/4
Let s(g) be the first derivative of 455*g**4/4 - 1075*g**3/3 + 170*g**2 - 20*g - 35. Determine i so that s(i) = 0.
1/13, 2/7, 2
Let z(k) be the first derivative of k**4/20 - 73*k**3/5 + 15987*k**2/10 - 389017*k/5 - 117. Determine x so that z(x) = 0.
73
Factor -4/9*q + 2/3 - 2/9*q**2.
-2*(q - 1)*(q + 3)/9
Let q(j) = j**3 + j**2 + 2*j. Let p(x) = -2*x**5 + x**3 + 5*x**2 - 16*x. Let d(w) = 2*p(w) + 22*q(w). Let d(n) = 0. Calculate n.
-1, 0, 3
Let u(x) = -x**2 + 11*x + 14. Let d be u(12). Let s(o) be the second derivative of -1/5*o**5 + 0 - 2/3*o**3 + 0*o**d - 2/3*o**4 - 7*o. Factor s(y).
-4*y*(y + 1)**2
Suppose u - 3 + 1 = 0. Factor -b**3 - b**4 + 0*b + 2*b**3 + 4*b**u - 6*b + 2*b.
-b*(b - 2)*(b - 1)*(b + 2)
Let d be (106 + -1)*86/1548. Let n(v) be the first derivative of -3*v + d*v**3 + 1 - 11/4*v**2. Factor n(k).
(5*k - 3)*(7*k + 2)/2
Let z = 130 + -109. Let i(t) = -t**3 + 8*t**2 - 7*t + 2. Let b be i(7). Determine h, given that 2 + h - 23*h**b - 2 + z*h**2 + h**3 = 0.
0, 1
Let r(w) be the second derivative of 1/110*w**5 - 4/11*w**2 + 1/66*w**4 - 4/33*w**3 + 0 + 11*w. Factor r(c).
2*(c - 2)*(c + 1)*(c + 2)/11
Let v be 36*1*52/(-12). Let y = 321/2 + v. Factor 7/2*u**3 + 0 + y*u**2 + u.
u*(u + 1)*(7*u + 2)/2
Let q(g) be the first derivative of -20 - 1/2*g**4 + 2*g - 3*g**2 + 2*g**3. Factor q(u).
-2*(u - 1)**3
Determine a so that -1/3*a**2 - 2500/3 - 100/3*a = 0.
-50
Suppose 101*o - 3*n - 11 = 96*o, 3*o - 3 = 3*n. Let q(x) be the second derivative of 0*x**2 + 0 - 1/27*x**4 - o*x - 1/180*x**5 - 1/18*x**3. Factor q(h).
-h*(h + 1)*(h + 3)/9
Suppose 113 = 30*f - 37. Factor 8/19*o**2 + 12/19*o**3 + 8/19*o**4 + 2/19*o**f + 2/19*o + 0.
2*o*(o + 1)**4/19
Determine n, given that 204/7*n - 675/7*n**2 - 12/7 = 0.
2/25, 2/9
Let r(c) be the first derivative of c**5/10 - 9*c**4/4 + 17*c**3/6 + 685. Suppose r(o) = 0. Calculate o.
0, 1, 17
Let l = 33 + -39. Let k be (-10)/3 + (-2 - l). Suppose -k*w**2 + 0 - 2/3*w = 0. What is w?
-1, 0
Factor -36/23 - 22/23*p - 2/23*p**2.
-2*(p + 2)*(p + 9)/23
Suppose -12*x + 25 = -17*x + 5*o, -25 = -5*x - 5*o. Let -3/2*z**2 + 9/2*z**3 - 3*z - 3/2*z**5 + x + 3/2*z**4 = 0. What is z?
-1, 0, 1, 2
Factor 980 + 1032*h**2 + 2100*h + 233*h**2 - 4693*h**4 + 150*h**3 + 4698*h**4.
5*(h + 1)**2*(h + 14)**2
Let k = -33 - -50. Factor -k*d**3 - 10*d**3 + 24*d**3 - 15*d + 12*d**2 + 6.
-3*(d - 2)*(d - 1)**2
Let p(v) be the first derivative of -v**4/32 + 13*v**3/12 - 3*v**2 - 168. Suppose p(h) = 0. Calculate h.
0, 2, 24
Let u(b) = b**2 - b - 5. Let z be u(0). Let h(o) = 2*o + 13. Let i be h(z). What is y in i - 3*y**2 - 3/2*y + 3/2*y**3 = 0?
-1, 1, 2
Let c = 379/766 + 2/383. Suppose -2*n + 2*x + 9 = -3*x, 3*x + 13 = 5*n. Factor -1/2 + 1/2*d**3 - 1/2*d + c*d**n.
(d - 1)*(d + 1)**2/2
Let f = 2297/4 + -574. Let i(w) be the second derivative of -4*w + 0*w**3 + 3/10*w**6 + 1/14*w**7 + f*w**4 + 9/20*w**5 + 0 + 0*w**2. Find n such that i(n) = 0.
-1, 0
Let u(s) = s**3 + 11*s**2 + 8*s - 17. Let i be u(-10). Let d(y) be the first derivative of 0*y**2 - 2/21*y**3 + 0*y + i. Find p such that d(p) = 0.
0
Let p(h) be the third derivative of -h**6/180 - 2*h**5/9 - 19*h**4/36 - 149*h**2. Determine i, given that p(i) = 0.
-19, -1, 0
Let 2*h + 0 - 1/3*h**3 + 11/3*h**4 - 19/3*h*