Suppose 6 = -3*n - c, n = -73*c + 72*c - 6. Factor 2/3*q**3 + 0*q + n*q**2 + 0.
2*q**3/3
Let m(g) be the third derivative of -1/540*g**6 + 0*g + 0*g**3 + 0 + 0*g**4 + 1/135*g**5 - 2*g**2. Determine d, given that m(d) = 0.
0, 2
Suppose 43862 = 4*v + 43854. Solve 0 + 1/2*w**3 - v*w - 3/2*w**2 = 0 for w.
-1, 0, 4
Let d(j) = j**3 - j**2 + j + 1. Let q(h) = -6*h**3 + 5*h**2 - 7*h - 5. Let i(c) = -39*d(c) - 6*q(c). Factor i(b).
-3*(b - 3)*(b - 1)*(b + 1)
Let s be 4/(-8) - (-14)/28. Let x(l) be the first derivative of s*l + 7 + 3/10*l**2 + 4/15*l**3. Let x(c) = 0. Calculate c.
-3/4, 0
Let i be (73/10)/(13/((-130)/(-12))) + -6. Factor 1/3 - 1/4*j - i*j**2.
-(j - 1)*(j + 4)/12
Let r = 909 + -2725/3. Let g(t) be the third derivative of 2*t**2 + 0 - 1/30*t**5 + 1/20*t**6 - 1/4*t**4 + 0*t + r*t**3 - 1/105*t**7. Factor g(v).
-2*(v - 2)*(v - 1)**2*(v + 1)
Let i(j) be the third derivative of -j**8/10080 - j**7/504 - 19*j**5/60 + 16*j**2. Let d(w) be the third derivative of i(w). What is m in d(m) = 0?
-5, 0
Let x = 4414/35 + -126. Let b(t) be the first derivative of 0*t + 1 + 0*t**4 + x*t**5 - 4/21*t**3 + 0*t**2. Solve b(o) = 0 for o.
-1, 0, 1
Suppose -3*r + 16 = 10. Let 9*o - 23*o**3 + 4*o**r - 17*o + 27*o**3 = 0. Calculate o.
-2, 0, 1
Let t(v) be the third derivative of 18*v**2 + 0*v**3 + 0*v + 0 + 0*v**5 - 1/805*v**7 + 1/1380*v**6 + 0*v**4. Let t(w) = 0. What is w?
0, 1/3
Let n = 14218 + -14213. Find k, given that -1/3*k**5 + k**4 + 17/3*k**2 + n*k**3 + 2*k + 0 = 0.
-1, 0, 6
Let z(x) be the second derivative of 5*x**4/12 + 205*x**3/6 - 215*x**2 - 9*x - 14. Factor z(s).
5*(s - 2)*(s + 43)
Let p be -6*(71/9 - 8). Factor 32/3 + p*k**2 + 16/3*k.
2*(k + 4)**2/3
Let r(p) be the third derivative of -p**6/30 - 7*p**5/60 - p**4/12 + p**3/6 - 4*p**2 - 2. Determine b so that r(b) = 0.
-1, 1/4
Let m(l) = -18*l + 12. Let p be m(-2). Let n be ((-1)/(-4))/(30/p). Let 0*a**3 + 2/5*a**2 - n*a**4 - 1/5*a**5 + 1/5*a + 0 = 0. What is a?
-1, 0, 1
Let m(z) be the first derivative of -z**5/40 - z**4/32 + z**3/4 + z**2/4 - z - 35. Determine f, given that m(f) = 0.
-2, 1, 2
Suppose 35*k + 64 = 67*k. Let t(w) = -w + 3. Let q be t(0). Find v, given that 0 + 2/5*v**q + 0*v - 4/5*v**k = 0.
0, 2
Let f(b) = -6*b**3 + 116*b**2 + 1674*b + 8. Let q(r) = r**3 + r - 1. Let v(y) = f(y) + 8*q(y). Suppose v(s) = 0. Calculate s.
-29, 0
Let f(t) = 66*t**2 + t - 1. Let g be f(-3). Let a = -21 + 24. Find l such that -20*l**2 - g*l**a + 1 + 602*l**3 - 1 + 8*l = 0.
0, 2/3, 1
Solve 18/7*n**3 - 24/7*n - 2/7*n**5 + 0 + 8/7*n**2 + 0*n**4 = 0.
-2, 0, 1, 3
Factor 20/9*g**2 - 2/3*g - 2/9*g**5 + 0 - 8/3*g**3 + 4/3*g**4.
-2*g*(g - 3)*(g - 1)**3/9
Factor 138*s + 1587 - 41*s**2 - 29*s**2 + 73*s**2.
3*(s + 23)**2
Suppose 5*r - 10 = 85. Let x = -16 + r. Factor -f**3 + 0*f**3 + x*f**3.
2*f**3
Let t = 9 - -2. Suppose -10*x = -t*x. Factor 0*q**2 + 0 + x*q - 1/2*q**3.
-q**3/2
Suppose 438 - 462 = -8*r. Let y(l) be the first derivative of 0*l + 6 + 0*l**2 - 1/6*l**r. Factor y(c).
-c**2/2
Let w(v) be the second derivative of 5/39*v**3 - 3/13*v**2 + 3/130*v**5 - 19*v + 0 + 11/78*v**4. Solve w(n) = 0 for n.
-3, -1, 1/3
Let g(b) be the first derivative of b**7/1470 - b**6/280 + b**5/140 - b**4/168 - 5*b**2/2 - 23. Let w(z) be the second derivative of g(z). Factor w(q).
q*(q - 1)**3/7
Let s(m) be the third derivative of m**7/84 - 31*m**6/240 - 37*m**5/60 + m**4/3 + 204*m**2. Factor s(l).
l*(l - 8)*(l + 2)*(5*l - 1)/2
Let p be -3 + 2 + 4 - (-74 - -77). Let v(u) be the first derivative of 3*u**6 - 42/5*u**5 + 0*u**2 - 1 + 8*u**4 + p*u - 8/3*u**3. Suppose v(r) = 0. What is r?
0, 2/3, 1
Factor 0 + 18*z**2 + 2/9*z**5 + 10*z**3 + 22/9*z**4 + 12*z.
2*z*(z + 2)*(z + 3)**3/9
Let n be (-10)/3*60/(-50). Let 10/9*a**n - 10/9*a**2 - 2/9*a**3 + 2/3*a**5 + 0 - 4/9*a = 0. Calculate a.
-1, -2/3, 0, 1
Suppose -s + 3*l = 1, -5*l + 10*l = s + 3. Let w be ((-2)/3)/((-14)/3). Factor -2/7*c - w*c**s - 1/7.
-(c + 1)**2/7
Let y be 5 - (-24)/(-42)*(-14)/(-4). Let p(u) be the third derivative of 0 - 1/6*u**4 + 0*u + 5*u**2 - 1/30*u**6 + 0*u**y + 2/15*u**5. Factor p(n).
-4*n*(n - 1)**2
Suppose 0 = 9*u - 6*u - 24. Let t(m) = -m + 11. Let r be t(u). Find x, given that -160*x**3 + 0 - x**2 + 159*x**r + x + 1 = 0.
-1, 1
Find m such that 0 + 485/2*m**4 - 39*m + 25/4*m**5 - 157*m**2 - 211/4*m**3 = 0.
-39, -2/5, 0, 1
Let i(l) be the second derivative of 0 + 12*l + 4/5*l**3 - 14/5*l**2 + 1/15*l**4. Factor i(f).
4*(f - 1)*(f + 7)/5
Suppose 0 = -8*w - 46 + 14. Let p = w - -7. Solve 0 - 2*x**p + 0*x + 5/4*x**4 + x**2 - 1/4*x**5 = 0 for x.
0, 1, 2
Let x(o) be the third derivative of -o**6/180 + 13*o**5/30 - 169*o**4/12 + 2197*o**3/9 + 2*o**2 - 12. Factor x(a).
-2*(a - 13)**3/3
Let j(d) be the third derivative of -8*d**7/105 + 7*d**6/10 - 29*d**5/15 + d**4 + 528*d**2. Determine v so that j(v) = 0.
0, 1/4, 2, 3
Let f(j) be the third derivative of 0*j - 1/6*j**3 - 1/60*j**5 + 1/12*j**4 + 2*j**2 + 0. Solve f(k) = 0.
1
Let h(v) be the third derivative of v**8/224 + v**7/42 - v**6/40 - 3*v**5/10 - 29*v**4/48 - v**3/2 - 3*v**2 + 3*v. Determine u, given that h(u) = 0.
-3, -1, -1/3, 2
Let k(f) be the second derivative of f**5/30 - f**4/6 - 8*f**3 - 176*f**2/3 + 419*f. Suppose k(b) = 0. Calculate b.
-4, 11
Let k = 47 + -47. Let l(d) be the third derivative of -10*d**2 + k*d**3 - 1/12*d**4 + 0 + 0*d + 1/105*d**7 - 1/30*d**5 + 1/60*d**6. Factor l(p).
2*p*(p - 1)*(p + 1)**2
Let y(u) = -u + 15. Let k be y(6). Let d(i) = -20*i**3 - 3*i**2 + 18*i + 3. Let v(g) = -81*g**3 - 12*g**2 + 72*g + 12. Let j(r) = k*d(r) - 2*v(r). Factor j(w).
-3*(w - 1)*(w + 1)*(6*w + 1)
Let s(o) be the first derivative of -1 + 9/10*o**4 + 3*o**2 - 3/25*o**5 - 12/5*o**3 - 9/5*o. Factor s(v).
-3*(v - 3)*(v - 1)**3/5
Suppose -2*g + v + 7 = 0, -83*v = -2*g - 79*v + 16. Factor 3/8*y**5 + 3/4*y**g - 3/4*y**3 - 3/8 + 3/8*y - 3/8*y**4.
3*(y - 1)**3*(y + 1)**2/8
Let l(z) be the third derivative of 0*z + 7/60*z**6 - 5/8*z**4 + 0 - 1/30*z**7 - 3*z**2 - 1/30*z**5 + 3/2*z**3 + 1/336*z**8. Suppose l(d) = 0. What is d?
-1, 1, 3
Let x(c) = 2*c**3 + 2*c**2 - 82*c + 78. Let v(i) = -3*i**3 - 5*i**2 + 163*i - 155. Let y(q) = 2*v(q) + 5*x(q). Solve y(s) = 0.
-5, 1, 4
Let i(x) be the second derivative of 3*x**2 + 0 - 3/20*x**5 - 1/10*x**6 + 12*x + 5/2*x**3 + 3/4*x**4. Determine w, given that i(w) = 0.
-1, 2
Determine t, given that 74*t**4 - 112*t**3 - 56*t**4 + 84*t - 236*t + 222*t**2 + 24 = 0.
2/9, 1, 2, 3
Let u(f) be the second derivative of 2187*f**5/20 + 4617*f**4/4 + 9747*f**3/2 + 20577*f**2/2 + 451*f. Solve u(i) = 0.
-19/9
Let z = 1942 - 11875/6. Let a = -37 - z. Solve -1/6*p**3 + 0*p + 0 + 1/6*p**4 + a*p**5 - 1/6*p**2 = 0.
-1, 0, 1
Let s(i) be the third derivative of 0*i + 0*i**3 + 0 - 1/108*i**4 + 2/945*i**7 + 10*i**2 + 1/1512*i**8 - 1/135*i**5 + 0*i**6. Suppose s(o) = 0. Calculate o.
-1, 0, 1
Solve -22/13*x**4 + 12/13 - 70/13*x**3 + 70/13*x + 10/13*x**2 = 0.
-3, -1, -2/11, 1
Let k(u) be the third derivative of -14*u**2 + 0 + 0*u + 0*u**3 - 1/45*u**5 - 1/10*u**7 + 17/180*u**6 + 0*u**4 - 9/224*u**8. Factor k(z).
-z**2*(z + 2)*(9*z - 2)**2/6
Let v(u) be the third derivative of -u**6/80 + 13*u**5/20 + 29*u**4/16 - 27*u**3/2 + 17*u**2 + 8*u. Factor v(x).
-3*(x - 27)*(x - 1)*(x + 2)/2
Factor 33*v**3 - 73*v**3 + 15*v**3 - 16*v**2 - 39*v**2 - 3*v - 7*v.
-5*v*(v + 2)*(5*v + 1)
Let m(c) be the first derivative of 2*c**3/9 - 35*c**2/12 + 4*c + 257. Factor m(y).
(y - 8)*(4*y - 3)/6
Suppose -66*v - 35*v = -14*v. Let 3/4*z**2 - 1/4*z**4 + v + 0*z**3 - 1/2*z = 0. Calculate z.
-2, 0, 1
Let t(b) be the third derivative of -5*b**7/42 + b**6/6 + b**5 - 4*b**2 + 39*b. Factor t(s).
-5*s**2*(s - 2)*(5*s + 6)
Suppose 3*t + 5*j - 5 = 0, -3*t + j = -j + 2. Let z(f) be the first derivative of -6 + 0*f**2 + t*f - 1/2*f**4 - 4/3*f**3. Factor z(g).
-2*g**2*(g + 2)
Let c(s) = 130*s**2 + 10290*s + 305955. Let l(n) = -23*n**2 - 1816*n - 53992. Let d(g) = -8*c(g) - 45*l(g). Factor d(u).
-5*(u + 60)**2
Let s(z) = -z**3 + 14*z**2 + 16*z - 21. Let k be s(15). Let h(y) = y**3 + 7*y**2 + 6*y + 2. Let m be h(k). Factor -5/4*f + 1/4*f**3 - 1/4*f**m - 3/4.
(f - 3)*(f + 1)**2/4
Let r be (0 + 10 - 0)*-2. Let f be 2/2 - r/5. Find b, given that 4*b**5 - 8*b**4 - 3*b**3 + 14*b**4 - 6*b**2 - b**f = 0.
-2, -1, 0, 1
Solve -76/5*y**2 - 32/5 + 96/5*y**4 + 24*y