
Let z be (12 - (-418)/(-33))/((-1)/6). Suppose 3 = 2*x - 2*o + 7, z*o - 16 = 0. Determine n, given that 0 + 4/7*n - 2/7*n**x = 0.
0, 2
Let g(y) be the first derivative of y**4/12 - 3*y**3/2 + 4*y**2 + 34*y + 47. Let b(r) be the first derivative of g(r). Factor b(u).
(u - 8)*(u - 1)
Let a(i) be the second derivative of -375*i**7/14 + 890*i**6 - 7741*i**5 - 3560*i**4 - 480*i**3 + 3104*i. Factor a(k).
-5*k*(k - 12)**2*(15*k + 2)**2
Suppose y = 2*y + 4. Let m(l) = -10*l**3 - 2*l**2 + 3*l + 16. Let k(v) = -3*v**3 - v**2 + v + 5. Let r(d) = y*m(d) + 14*k(d). Factor r(i).
-2*(i - 1)*(i + 1)*(i + 3)
Find i such that 18 - 7275*i**2 - 21*i + 3642*i**2 + 3633*i**2 + 3*i**3 = 0.
-3, 1, 2
Let r be ((-9)/4)/(3 - (-107)/(-36)). Let m = 93 + r. Factor 175*o**3 - 100*o - 108*o**2 + 49*o**4 + m + 15 - 43.
(o - 1)*(o + 4)*(7*o + 2)**2
Let i(y) be the first derivative of 67 + 0*y + 1/8*y**4 + 0*y**2 + 1/10*y**5 - 1/3*y**3. Factor i(u).
u**2*(u - 1)*(u + 2)/2
Let f = -436/5 - -88. Suppose -5*q + 50 = -b, -175*q + 5*b - 14 = -172*q. Determine t so that 20*t**3 - q*t**4 + 6*t - f + 14/5*t**5 - 16*t**2 = 0.
2/7, 1
Let r(n) = 2*n**2 + 67*n + 425. Let a be r(-25). Let b(j) be the second derivative of -3/100*j**5 + 1/20*j**4 + 0 - 18*j + 0*j**3 + a*j**2. Factor b(t).
-3*t**2*(t - 1)/5
Suppose 7*a - 4*a - 1104 = 0. Solve -840*t**2 - 450*t + 39*t**3 - 371*t**3 - a*t**5 + 366*t**5 + 56*t**4 = 0 for t.
-1, 0, 15
Let f = -441 - -439. Let j be (-22)/(-24) - f/(-8). Let 5/3*p - p**2 - j - 1/3*p**3 + 1/3*p**4 = 0. Calculate p.
-2, 1
Let t(c) be the first derivative of -3*c**5/10 + 11*c**4/6 + 8*c**3 - 20*c**2 - 104*c + 118. Let m(i) be the first derivative of t(i). Factor m(g).
-2*(g - 5)*(g + 2)*(3*g - 2)
Factor 5/3*m**4 + 16/3 - 8/3*m**3 - 8*m**2 + 32/3*m.
(m - 2)**2*(m + 2)*(5*m + 2)/3
Let a be (-29744)/936 + 37 - (1 + 4). Factor 22/9*t + 4/3 + a*t**3 + 4/3*t**2.
2*(t + 1)*(t + 2)*(t + 3)/9
Let g(m) be the first derivative of -m**4/8 + 19*m**3/6 + 13*m**2/4 + 76*m + 110. Let d(r) be the first derivative of g(r). Factor d(v).
-(v - 13)*(3*v + 1)/2
Let k(g) be the second derivative of -12/5*g**2 + 3/25*g**5 - 4/15*g**3 - 4 + 1/75*g**6 - 14*g + 3/10*g**4. Factor k(m).
2*(m - 1)*(m + 2)**2*(m + 3)/5
Suppose 216/7*c - 204/7 - 9*c**2 + 3/7*c**3 = 0. Calculate c.
2, 17
Let r(d) be the second derivative of -5 + 0*d**2 + 0*d**3 + 0*d**4 + 1/48*d**5 - 4*d - 1/360*d**6. Suppose r(c) = 0. Calculate c.
0, 5
Let q(v) be the first derivative of -v**4/2 - 102*v**3 - 2276. Find m, given that q(m) = 0.
-153, 0
Let t(a) = 121*a - 844. Let w be t(7). Let d(z) be the first derivative of 2/5*z**5 + 13 - 4*z**4 + 40*z**2 + 4*z**w + 50*z. Factor d(y).
2*(y - 5)**2*(y + 1)**2
Suppose 0*b - 3*b - 3*p + 165 = 0, 4*p + 116 = 2*b. Let x = b + -54. Factor 2*t**x + 3*t**4 + 2*t**4 + 3*t**2 - 10*t**2 - 5*t**3 + 5*t.
5*t*(t - 1)**2*(t + 1)
Suppose 87 = 36*x - 129. Let f(o) = o**2 + 27*o - 193. Let i be f(x). Factor 2/17*r**4 + 0 + 2/17*r**i + 0*r - 10/17*r**3 + 6/17*r**2.
2*r**2*(r - 1)**2*(r + 3)/17
Suppose -9*j + 39 = 3. Let g be (j + -5)*-1*1*2. Factor 4/3*p**g + 0 + 0*p - 2/3*p**3.
-2*p**2*(p - 2)/3
Let z(t) be the second derivative of -4 + 147/4*t**2 + 161/24*t**3 - 5/16*t**4 - 30*t - 9/80*t**5 + 1/120*t**6. Determine m, given that z(m) = 0.
-3, -2, 7
Suppose 39*y = 28*y + 132. Factor -2*m**4 - 107 + 206 - y*m**3 + 32*m - 20*m**3 - 69 - 28*m**2.
-2*(m - 1)*(m + 1)**2*(m + 15)
Let w be 189/14*(-65)/(2535/(-26)). Let -3/2*o**3 - 15/4 + 3/4*o**4 - 21/2*o - w*o**2 = 0. What is o?
-1, 5
Let n(t) be the second derivative of t**6/30 - t**4/12 - t**3/2 + 274*t. Let m(r) = r**4 + 25*r**3 - r**2 - 13*r. Let q(y) = m(y) + 4*n(y). Factor q(x).
5*x*(x - 1)*(x + 1)*(x + 5)
Let c(x) be the third derivative of -x**6/60 + 2*x**5/15 + 20*x**4/3 + 64*x**3 + 17*x**2 + 169*x. What is r in c(r) = 0?
-4, 12
Let p(k) be the first derivative of 3*k**5/5 - 33*k**4/4 + 15*k**3 + 81*k**2/2 - 283. Factor p(j).
3*j*(j - 9)*(j - 3)*(j + 1)
Let u be (36/22)/(24 - 15210/660). Solve -u + 6/7*o**3 - 32/7*o**2 + 4/7*o**4 - 1/7*o**5 + 5*o = 0.
-3, 1, 4
Suppose 0 = 1984*k - 1488 - 4464. Find a such that 4/9*a**2 + 0 + 0*a + 2/9*a**k = 0.
-2, 0
Suppose -320/7 - 20/7*h**3 + 304/7*h - 48/7*h**2 + 4/7*h**4 = 0. What is h?
-4, 2, 5
Let k be ((-4590)/(-945))/(4 - 2 - 9/7). Factor 2/5*w**4 + 78/5*w - 8 - k*w**2 - 6/5*w**3.
2*(w - 5)*(w - 1)**2*(w + 4)/5
Let u(t) be the second derivative of -t**6/45 + t**5/2 - 23*t**4/6 + 65*t**3/9 + 50*t**2 + 2*t + 3. Solve u(p) = 0.
-1, 5, 6
Let r(a) be the first derivative of -5*a**3/3 + 5*a**2 + 40*a - 1425. Find d, given that r(d) = 0.
-2, 4
Let c(b) be the third derivative of b**6/780 + 7*b**5/390 - 2*b**4/3 + 80*b**3/13 - 1882*b**2 + b. Factor c(k).
2*(k - 4)**2*(k + 15)/13
Let d(c) be the third derivative of 0 + 1/630*c**6 + 0*c**5 + 0*c**3 + 3*c**2 - 36*c + 0*c**4 + 1/2205*c**7. Let d(k) = 0. Calculate k.
-2, 0
Find d such that -3/2*d**3 - 72*d**2 - 75 + 297/2*d = 0.
-50, 1
Let v = 377 + -71. Let q = -1526/5 + v. Solve 16/15 + 8/5*s + q*s**2 + 2/15*s**3 = 0 for s.
-2
Let a(q) = -q**2 + 23*q - 53. Let y be a(13). Suppose 33*b - 242 = -y. Factor -144/5 + 168/5*c + 1/5*c**3 - b*c**2.
(c - 12)**2*(c - 1)/5
Let x(v) be the third derivative of -v**5/135 + 11*v**4/54 + 52*v**3/27 - 149*v**2 + 7*v - 3. Factor x(p).
-4*(p - 13)*(p + 2)/9
Let d(f) be the third derivative of -f**5/12 + 35*f**4/4 + 220*f**3/3 - 994*f**2. Let d(z) = 0. What is z?
-2, 44
Suppose 2*z + s = 187, 2*s - 229 + 365 = z. Suppose -z*t - 1/2*t**5 - 36 - 89/2*t**3 - 103*t**2 - 8*t**4 = 0. Calculate t.
-6, -2, -1
Let r(q) be the first derivative of -q**5/5 - 18*q**4 - 70*q**3 - 104*q**2 - 24*q + 17. Let w(l) be the first derivative of r(l). Factor w(y).
-4*(y + 1)**2*(y + 52)
Factor 5/3 + 4/3*l - 1/3*l**2.
-(l - 5)*(l + 1)/3
Let x(s) be the second derivative of -5*s**4/12 - 1145*s**3/2 + 1720*s**2 + 11*s - 92. Factor x(b).
-5*(b - 1)*(b + 688)
Let k = 20876 + -20872. Let z(n) be the second derivative of 20*n - 1/48*n**k + 0 + 1/4*n**2 + 1/24*n**3. Determine x so that z(x) = 0.
-1, 2
Let l be 1 - (0 - (-1)/(-2)). Let i be (-4 - -9) + -15 + (15 - 5). What is c in -27/4*c**4 + 18*c**3 - 39/4*c**2 + i + l*c = 0?
0, 1/3, 2
Factor -809*m + 227*m + 332*m + 2*m**2 - 834*m - 356*m.
2*m*(m - 720)
Let g(o) be the second derivative of o**7/2520 + 23*o**6/720 + 11*o**5/60 + o**4 - o**3/3 + 73*o. Let t(y) be the third derivative of g(y). Factor t(j).
(j + 1)*(j + 22)
Let u(n) = -2*n**4 + 6*n**3 + 6*n**2 - 3*n + 9. Let j(w) = -18*w**4 + 54*w**3 + 52*w**2 - 26*w + 78. Let b(h) = -6*j(h) + 52*u(h). Factor b(p).
4*p**3*(p - 3)
Suppose -116*q - 8 = -114*q, 0 = -3*l - q + 23. Let n(j) be the second derivative of -l*j + 2/11*j**2 + 0 + 3/11*j**3 + 7/66*j**4. Factor n(u).
2*(u + 1)*(7*u + 2)/11
Let z = 333 - 331. Determine p so that -8*p**z - 7 + p**3 + 24*p - 8 - 6 + 3 - 3*p = 0.
2, 3
Let s(w) be the first derivative of -3*w**5/20 - 3*w**4/2 - 9*w**3/2 - 6*w**2 + 110*w + 107. Let a(d) be the first derivative of s(d). Factor a(g).
-3*(g + 1)**2*(g + 4)
Let i(n) be the third derivative of n**7/840 + n**6/240 - 3*n**5/80 - n**4/48 + n**3/3 + 1199*n**2. Suppose i(d) = 0. Calculate d.
-4, -1, 1, 2
Factor 1516/7*l + 2/7*l**2 + 287282/7.
2*(l + 379)**2/7
Solve -6/5*z**4 + 54/5*z**3 - 3/5*z**5 - 147/5*z + 12/5*z**2 + 18 = 0.
-5, -2, 1, 3
Suppose k = 3, 0*x - 4*k - 138 = -5*x - 90. Factor x + 15/2*l**2 + 39/2*l.
3*(l + 1)*(5*l + 8)/2
Let b(n) be the first derivative of n**6/6 - 21*n**5/5 + 9*n**4/2 + 40*n**3/3 - 687. Find o, given that b(o) = 0.
-1, 0, 2, 20
Let g(d) be the second derivative of -d**8/10080 - d**7/1008 - d**6/540 - 95*d**3/3 + d - 10. Let x(q) be the second derivative of g(q). Factor x(n).
-n**2*(n + 1)*(n + 4)/6
Suppose 4*b = 3*b + 7. Let r(q) = -5*q + 35. Let d be r(b). Find g, given that d - 6/11*g**2 + 6/11*g = 0.
0, 1
Let c(f) be the first derivative of f**4/14 + 380*f**3/21 + 748*f**2/7 + 1488*f/7 + 4035. Let c(u) = 0. What is u?
-186, -2
Let u(s) be the third derivative of -s**5/60 + 19*s**4/6 + 26*s**3 + s**2 - 993*s + 3. Factor u(l).
-(l - 78)*(l + 2)
Let g(j) be the second derivative of -1/8*j**4 + 0 + 1/20*j**5 - 2*j + 0*j**2 + 13/6*j**3 - 1/120*j**6. Let c(m) be the second derivative of g(m). Factor c(n).
-3*(n - 1)**2
Suppose 29241/7 + 1/7*l