*s. Let n be 42/18*(s/7)/5. Factor -10/3*q + n*q**4 - 6*q**2 - 2*q**3 + 0.
2*q*(q - 5)*(q + 1)**2/3
Let k = -184 + 186. Factor -25 + 13*n**k + 10*n**2 - 3*n**2 - 7*n - 88*n.
5*(n - 5)*(4*n + 1)
Let s = 496 + -493. Suppose 3*b - 23 = -2*b - 4*x, 15 = 3*b + s*x. Find k, given that 0*k + 0*k**b - 1/7*k**5 + 0 + 0*k**2 + 1/7*k**4 = 0.
0, 1
Find n, given that -143*n**2 + 3*n**4 - 2 - 140*n**2 + 2 + 229*n**2 - 51*n**3 = 0.
-1, 0, 18
Let f(p) be the third derivative of p**5/15 - 29*p**4/3 + 38*p**3 + 7080*p**2. Factor f(y).
4*(y - 57)*(y - 1)
Solve 2192 - 2204*d + 6584 - 212*d**2 + 3976 - 4*d**3 + 4068 = 0 for d.
-29, 5
Let y(s) be the third derivative of -1/1050*s**7 + 4*s - 4*s**2 + 2197/30*s**3 - 169/12*s**4 - 39/25*s**5 + 0 - 19/300*s**6. Solve y(z) = 0 for z.
-13, 1
Let o(d) = 3*d**2 - 411*d - 834. Let h(b) = -6*b**2 + 821*b + 1666. Let r(f) = 6*h(f) + 11*o(f). Factor r(y).
-3*(y - 137)*(y + 2)
Let a(f) be the third derivative of f**5/330 - 3*f**4/22 + 24*f**3/11 + 1366*f**2. Factor a(w).
2*(w - 12)*(w - 6)/11
Suppose 51*o - 21*o + 5940 = 0. Let m be 4 - (-64)/(-21)*(-231)/o. Factor 0 + 1/9*k**3 + m*k + 5/9*k**2.
k*(k + 1)*(k + 4)/9
Factor 1/4*f**2 + 21/2 - 17/4*f.
(f - 14)*(f - 3)/4
Suppose -502 = 2*y - 78. Let k = y + 214. Solve 0 + 2/9*f**4 - 4/9*f**3 - 2/9*f**k + 4/9*f = 0.
-1, 0, 1, 2
Let x(j) be the first derivative of 0*j + 0*j**2 - 1/16*j**4 + 1/6*j**3 + 41. Factor x(m).
-m**2*(m - 2)/4
Let q(o) be the first derivative of -o**4/24 - 29*o**3/18 - 10*o**2 - 13101. Factor q(n).
-n*(n + 5)*(n + 24)/6
Determine j so that 2*j - 1/2*j**3 + 3/2*j**2 - 6 = 0.
-2, 2, 3
Determine r, given that 224*r + 4704/11 + 2/11*r**4 - 40/11*r**3 - 32/11*r**2 = 0.
-6, -2, 14
Let j(o) be the second derivative of -2/5*o**5 + 0 + 0*o**2 - 2/15*o**6 + 4/3*o**4 + 16/3*o**3 - 41*o. What is w in j(w) = 0?
-2, 0, 2
Let c = 8253/4 - 24751/12. Factor 4*s - c*s**2 + 14/3.
-2*(s - 7)*(s + 1)/3
Let f be 0 + (-568)/(-156) + ((-1650)/(-45) - 38). Factor 2 + 2/13*z**3 + f*z**2 + 54/13*z.
2*(z + 1)**2*(z + 13)/13
Let y(c) be the first derivative of -2*c**3/15 - 2*c**2/5 + 16*c/5 - 1431. Factor y(u).
-2*(u - 2)*(u + 4)/5
Let h(f) be the first derivative of -f**3/12 + 703*f**2/4 - 494209*f/4 + 995. Suppose h(q) = 0. Calculate q.
703
Let m = 11042/2639 + -608/377. Suppose m*n + 0 - 6/7*n**2 = 0. What is n?
0, 3
Suppose -5*b - 3662 = -b + 5*f, 4*b - 3*f = -3646. Let g = b + 917. Let -2*s + 2/13*s**g + 8/13 + 30/13*s**2 - 14/13*s**3 = 0. Calculate s.
1, 4
Let b(j) be the first derivative of 35*j + 60 + 20*j**2 + 5/3*j**3. Factor b(s).
5*(s + 1)*(s + 7)
Let w = -15096 - -15099. Let v(h) be the third derivative of -3/70*h**5 + 1/14*h**4 + 0*h + 2*h**2 + 1/105*h**6 + 0 - 1/21*h**w. Factor v(l).
2*(l - 1)**2*(4*l - 1)/7
Let u(x) be the second derivative of x**5/50 - 8*x**4/15 + x**3 + 2124*x. Factor u(i).
2*i*(i - 15)*(i - 1)/5
Let q be 165/(-44)*-4*5. Solve q*r + 4*r**2 + 22 + r**2 - 102 = 0 for r.
-16, 1
Let t(o) be the second derivative of o**7/49 - 8*o**6/35 + 36*o**5/35 - 16*o**4/7 + 16*o**3/7 + 12*o + 26. Let t(p) = 0. Calculate p.
0, 2
Let u(y) be the first derivative of -2*y**3/27 + 86*y**2/9 - 170*y/9 + 985. Factor u(q).
-2*(q - 85)*(q - 1)/9
Let w(y) be the second derivative of y**6/210 - 13*y**5/28 - 137*y**4/84 + 67*y**3/14 + 241*y + 7. Factor w(n).
n*(n - 67)*(n - 1)*(n + 3)/7
Let h(l) be the third derivative of l**5/570 - 295*l**4/228 - 1178*l**2. Factor h(t).
2*t*(t - 295)/19
Suppose 0 = -3*p + 3*f - 2*f - 40, -4*p + 4*f - 64 = 0. Let l be 512/(-32)*1/p. Factor 1/3*v**2 - l + v.
(v - 1)*(v + 4)/3
Suppose -32*n + 4*n = 196. Let g be (1 - 3)/(n - -3 - -3). Factor -8/9*i**g + 2/9*i**4 + 0 + 8/9*i - 2/9*i**3.
2*i*(i - 2)*(i - 1)*(i + 2)/9
Let r(f) = -f**2 - 3*f + 200. Let j be r(-15). Suppose 2*q = -j*q - 7*q. Factor q - 9/10*u**2 + 1/5*u + 7/10*u**3.
u*(u - 1)*(7*u - 2)/10
Suppose -10*k + 6450 = 1230. Let b be (-112)/(-58) + 36/k. Determine y so that 4*y - 28/3*y**3 + 0 - 16/3*y**b = 0.
-1, 0, 3/7
Let f = 3068/53 + -15234/265. Let p(w) = w**3 + 7*w**2 + w + 10. Let d be p(-7). Factor 2/5*b + 2/15*b**d + f*b**2 + 2/15.
2*(b + 1)**3/15
Let o(y) = -5*y**2 + 8*y - 1. Let p be o(2). Let m = 9 + p. Factor 2/3*j**5 + 6*j + 0 + 44/3*j**3 + 16*j**2 + 16/3*j**m.
2*j*(j + 1)**2*(j + 3)**2/3
Let m = -133 - -147. Determine p so that 120*p + 50 + 75*p**2 + 2*p**4 + 12*p**3 + 11*p**2 - m + 20 + 12*p**3 = 0.
-7, -2, -1
Suppose 5*m - 7*m = 8. Let h(p) = 3*p**2 + 10*p - 6. Let d be h(m). Suppose -4*w**d - 5*w - 11*w + 32 - 48 = 0. What is w?
-2
Let l(f) = 50*f + 550. Suppose 183*h - 188*h = 55. Let q be l(h). What is u in -2/3*u + 2/3*u**4 + 2/3*u**3 + q - 2/3*u**2 = 0?
-1, 0, 1
Let p(k) be the third derivative of -k**7/630 - k**6/90 + 3*k**5/20 + 17*k**4/36 - 28*k**3/9 + 14*k**2 + k - 32. Determine z, given that p(z) = 0.
-7, -2, 1, 4
Let g(v) be the second derivative of v**7/2016 + 7*v**6/576 + 5*v**5/48 + 43*v**4/12 + v**2/2 - 12*v - 4. Let x(m) be the third derivative of g(m). Factor x(k).
5*(k + 2)*(k + 5)/4
Suppose 19*s = -m + 25*s - 26, 0 = -2*m + 2*s - 2. Find w, given that 0*w**2 + 0*w - 15*w**3 - 1/2*w**m + 0 = 0.
-30, 0
Let r = 334 - 3. Solve 371*q**2 + 3*q - 13*q + 5*q**3 - 727*q**2 + 27 + r*q**2 + 93 = 0.
-2, 3, 4
Let q(u) be the second derivative of u**7/14 + 3*u**6/5 - 9*u**5/10 - 7*u**4 + 45*u**3/2 - 27*u**2 - 1033*u. Factor q(p).
3*(p - 1)**3*(p + 3)*(p + 6)
Let t(p) be the second derivative of 3*p**5/20 - 6*p**4 + 95*p**3/2 + 12454*p. Suppose t(d) = 0. What is d?
0, 5, 19
Let u(g) be the second derivative of g**5/10 - 229*g**4/6 + 12995*g**3/3 + 13225*g**2 - 370*g - 4. Determine y so that u(y) = 0.
-1, 115
Let g(x) be the first derivative of x**6/1260 + x**5/21 - x**4/4 + x**3 - 3*x + 137. Let r(o) be the third derivative of g(o). Let r(t) = 0. What is t?
-21, 1
Let g be (-3)/(-9)*(-11 - -26774). Find p such that -38*p**2 + g*p**3 - 8926*p**3 - p**5 + 9*p**4 - p**4 - 3*p - 21*p = 0.
-1, 0, 4, 6
Let j(d) = d**3 - 28*d**2 - 91*d - 53. Let i be j(31). Suppose 4*r - 17 + i = 0. Factor -2/3*u + u**r - 1/3*u**4 + 0*u**3 + 0.
-u*(u - 1)**2*(u + 2)/3
Suppose 0 = 3*b + 6147 - 6147. Let z(q) be the first derivative of 2/57*q**3 + b*q + 18 + 0*q**2 + 1/38*q**4. Factor z(c).
2*c**2*(c + 1)/19
Let h(x) be the third derivative of 33*x**7/140 - 5*x**6/4 + 3*x**5/40 - 3234*x**2. Determine r so that h(r) = 0.
0, 1/33, 3
Let b(m) = 43*m - 208. Let k be b(6). Let o be (-10)/k*((-84)/9)/2. Solve -8/15 - 4/15*r**2 - o*r + 2/15*r**3 = 0.
-1, 4
Let w(a) = 5200*a**2 + 135*a + 5390. Let b(x) = -297*x**2 - 8*x - 317. Let c(o) = 35*b(o) + 2*w(o). Factor c(p).
5*(p - 9)*(p + 7)
Let o(c) be the third derivative of c**8/672 + c**7/30 + 41*c**6/240 - 7*c**5/15 + 173*c**2. Suppose o(q) = 0. What is q?
-8, -7, 0, 1
Let s = 660742/117 + -69510/13. Factor -208/9*j - s - 4/9*j**2.
-4*(j + 26)**2/9
Let p(f) be the third derivative of -f**6/1800 + f**4/120 + 16*f**3/3 + 18*f**2 - 2. Let h(t) be the first derivative of p(t). Factor h(b).
-(b - 1)*(b + 1)/5
Suppose -c + 20 = 3*h, 2*h + 9*c = 40 + 15. Let w be 12/27*(h + 21/(-6)). Factor 0*m + 1/6*m**2 - w.
(m - 2)*(m + 2)/6
Let a be ((-60)/(-25)*210/(-63))/(-3 - 2). What is i in 2/5*i**2 - 6/5*i - a = 0?
-1, 4
Let z(w) be the second derivative of -w**7/21 - 28*w**6/15 + 13*w**5 + 26*w**4/3 - 131*w**3 - 288*w**2 + 266*w - 1. Determine v, given that z(v) = 0.
-32, -1, 3
Let l(q) be the second derivative of -q**5/35 + 269*q**4/21 - 1710*q**3 - 36450*q**2/7 - 3387*q. Let l(t) = 0. Calculate t.
-1, 135
Let f(c) be the second derivative of 0*c**3 + 0*c**2 - 2/9*c**6 + 10/3*c**5 + 1/189*c**7 - 500/27*c**4 - 2 + 52*c. Factor f(k).
2*k**2*(k - 10)**3/9
Let f(k) = -k**3 - 3*k**2 + 13*k + 7. Let l be 5 - (6 + (-17)/((-34)/(-12))). Let b(y) = -y**3 - 4*y**2 + 14*y + 11. Let n(g) = l*f(g) - 4*b(g). Factor n(j).
-(j - 3)*(j - 1)*(j + 3)
Let o(q) be the third derivative of q**7/1680 + 131*q**6/960 + 897*q**5/80 + 13225*q**4/48 - 85169*q**3/6 - 2313*q**2. Factor o(u).
(u - 7)*(u + 46)**3/8
Let z be 0 + (-24)/120 + (-194)/(-270). Let w(k) be the first derivative of -10 + 16/9*k + z*k**3 + 2*k**2. Factor w(n).
2*(n + 2)*(7*n + 4)/9
Let z = 2633/294 - 747/98. Suppose 0 + 4/15*h**3 + z*h - 2/15*h**4 + 26/15*h**2 = 0. What is h?
-2, -1, 0, 5
Let j(p) be the first derivative of -p