*h**3 - 11*h + 28*h**5 = 0. What is h?
-70, -2, 0
Let d(v) be the third derivative of v**6/36 + 3*v**5/20 + v**4/3 - 55*v**3/3 + 139*v**2. Let u(s) be the first derivative of d(s). Factor u(l).
2*(l + 1)*(5*l + 4)
Let n be (37 - 9)/4 + 3 + (-1128)/114. Let -2/19*o + 0 + n*o**3 - 2/19*o**4 + 2/19*o**2 = 0. What is o?
-1, 0, 1
Let o be 2077/(-93) + 108/4. Factor -10*t**2 - 2/3*t**4 + o*t**3 + 6*t + 0.
-2*t*(t - 3)**2*(t - 1)/3
Suppose 13*g - 55 - 10 = 0. Let -87*s**5 - 8*s + 45*s**g + 45*s**5 + 12*s**4 - 12*s**2 + 6*s**3 - s = 0. Calculate s.
-3, -1, 0, 1
Let w(c) = -c - 14. Let n(s) = -s**2 - 716*s + 522. Let i(r) = n(r) - 13*w(r). Solve i(h) = 0.
-704, 1
Let j(u) be the second derivative of 4/15*u**3 - 6*u + 1/150*u**6 - 2/5*u**2 - 1/50*u**5 - 2 - 1/20*u**4. Solve j(r) = 0 for r.
-2, 1, 2
Find i such that -331086080/3*i + 110334016/3 - 63040*i**3 + 12*i**4 + 248503648/3*i**2 = 0.
2/3, 2626
Factor -2/21*n**4 + 4/21*n + 2/21 - 4/21*n**3 + 0*n**2.
-2*(n - 1)*(n + 1)**3/21
Suppose 2*m = 4*g + 46, -16*m + 102 = -12*m + 2*g. Factor 0*l**4 - 55*l**3 - 185*l**2 - 5*l**4 - 13 - 225*l - 52 - m.
-5*(l + 1)**2*(l + 3)*(l + 6)
Suppose -3722512/3*w - 2/9*w**3 + 9454/9*w**2 - 1241888 = 0. Calculate w.
-1, 2364
Let n(p) be the third derivative of p**7/840 - 37*p**6/120 + 293*p**5/240 - 73*p**4/48 + 6*p**2 - 56. Solve n(x) = 0.
0, 1, 146
Suppose 2*c - 5*b = -c - 13, 0 = -25*b + 28*b - 15. Let k(f) = f**2 - f - 3. Let s be k(3). Factor 1/2*y**c + 3/2*y**s - 3/2*y - 5/2*y**2 + 2.
(y - 1)**2*(y + 1)*(y + 4)/2
Let y(v) = -45*v**3 + 80*v**2 - 30*v + 10. Let p(a) = -a**2 - a - 1. Let j = -187 + 182. Let u(n) = j*p(n) - y(n). Find r, given that u(r) = 0.
1/3, 1
Let o(b) be the third derivative of b**5/20 - 375*b**4/4 + 140625*b**3/2 + 455*b**2. Find x such that o(x) = 0.
375
Let s(c) be the third derivative of -c**6/30 + 991*c**5/60 - 247*c**4/8 - 2895*c**2 + c. Factor s(l).
-l*(l - 247)*(4*l - 3)
Let f = -200847 + 200849. Factor -3/7 + 0*c**3 - 3/7*c**4 + 0*c + 6/7*c**f.
-3*(c - 1)**2*(c + 1)**2/7
Let y(m) = -2*m + 26. Let f(j) = 4*j + 3. Let d be f(2). Let i be y(d). Suppose -15*u**2 - i*u**4 - 4*u - 19*u**3 + 3*u**2 + 7*u**3 = 0. Calculate u.
-1, 0
Let m(o) be the second derivative of -9/17*o**2 + 2*o - 1/102*o**4 - 2/17*o**3 + 1. Factor m(g).
-2*(g + 3)**2/17
Factor 2819 + 3338 + 251 - 167 - 3*s**3 + 5712*s**2 + 11433*s - 523.
-3*(s - 1906)*(s + 1)**2
Let c(r) be the first derivative of 1/24*r**4 + 1/6*r + 2/9*r**3 - 1/72*r**6 + 213 - 1/30*r**5 + 7/24*r**2. Solve c(p) = 0 for p.
-1, 2
Let w be (-298)/(-138) - (8 - 322/42). Determine b, given that 8/23 + w*b**2 + 32/23*b + 18/23*b**3 = 0.
-1, -2/3
Let k(d) = 5*d**4 - 842*d**3 - 177199*d**2 + 12*d. Let b(w) = -4*w**4 + 842*w**3 + 177206*w**2 - 10*w. Let j(f) = -6*b(f) - 5*k(f). Solve j(y) = 0.
-421, 0
Factor 281/9 - 1/9*q**2 + 280/9*q.
-(q - 281)*(q + 1)/9
Let w(p) = -2*p**2 - p - 1. Let o(u) be the third derivative of -4*u**5/15 - 15*u**4/4 + 41*u**3/3 + 32*u**2 - 2*u. Let k(h) = -o(h) + 6*w(h). Factor k(n).
4*(n - 1)*(n + 22)
Let b(u) = -u + 4. Let y be b(-3). Let f be (-71 + 65)/(-3 + 0). Factor -y*z**2 - 7*z + f*z + 4*z**2 - z - 3.
-3*(z + 1)**2
Let w(o) be the third derivative of o**8/84 - 2*o**7/105 - o**6/30 + o**5/15 + 407*o**2. Factor w(b).
4*b**2*(b - 1)**2*(b + 1)
Let u(k) be the third derivative of -k**6/180 + 4*k**5/9 + 92*k**4/9 + 256*k**3/3 - 781*k**2. Factor u(m).
-2*(m - 48)*(m + 4)**2/3
Suppose 0 = 2*f + 5*n - 40, 3*n - 7*n + 32 = 2*f. Let -6*p**5 + 2/7*p**3 + 0*p - 44/7*p**4 + 4/7*p**2 + f = 0. Calculate p.
-1, -1/3, 0, 2/7
Suppose -81*p = 81*p - 18*p - 720. Let o(c) be the third derivative of 1/3*c**3 + 1/75*c**p - 11/60*c**4 + 0*c - 32*c**2 + 0. Suppose o(h) = 0. What is h?
1/2, 5
Let d(c) = -3*c**3 - 2*c**2 + 38*c + 15. Let a(m) = m**3 + m**2 - 13*m - 5. Suppose 11*x + 6*x = 68. Let v(r) = x*d(r) + 11*a(r). Factor v(t).
-(t - 5)*(t + 1)**2
Suppose 155*o**4 - 38*o**3 + 280*o**2 + 1114*o**5 - 1109*o**5 + 137*o**3 + 331*o**3 = 0. Calculate o.
-28, -2, -1, 0
Let z = -24485/3 - -8170. Let i(w) be the first derivative of 15/2*w**2 + 5/4*w**4 + 0*w + z*w**3 - 6 - w**5. Let i(j) = 0. What is j?
-1, 0, 3
Factor 0 - 1/2*w**2 - w**3 + 1/2*w**4 + w.
w*(w - 2)*(w - 1)*(w + 1)/2
Let l = -385/36 + 103/9. Let u(m) be the second derivative of 0*m**3 + 5/6*m**4 - 5/6*m**7 - 2*m**6 + 0 + 22*m - l*m**5 + 0*m**2. Factor u(b).
-5*b**2*(b + 1)**2*(7*b - 2)
Let y(k) = -374*k**2 + 2628*k - 68. Let l be y(7). Factor -5*u + 1/10*u**4 + 9/2*u**l - 6/5*u**3 + 0.
u*(u - 5)**2*(u - 2)/10
Let y(x) be the first derivative of 1/70*x**7 + 0*x**3 + 0*x**6 + 0*x**2 + 0*x**4 + 25 + 0*x**5 - 13*x. Let o(g) be the first derivative of y(g). Factor o(b).
3*b**5/5
Find q, given that -2/11*q**2 - 78/11 + 80/11*q = 0.
1, 39
Let v = 57281/11 - 5207. Let a(l) be the first derivative of -10/11*l**3 - 23 - v*l**4 + 2/11*l - 6/11*l**2. Factor a(f).
-2*(f + 1)**2*(8*f - 1)/11
Let l be (-5491)/102 + (-2)/12. Let v be 5/((-105)/l) - (-156)/364. Factor 0 + 4/7*q**2 - 2/7*q**v - 2/7*q.
-2*q*(q - 1)**2/7
Factor 44/5*b + 1/5*b**2 + 84/5.
(b + 2)*(b + 42)/5
Factor -2/5*q**3 + 1152/5 - 1248/5*q + 98/5*q**2.
-2*(q - 24)**2*(q - 1)/5
Let n(o) be the first derivative of 1/12*o**4 + 11/9*o**3 - 11/3*o + 74 - 1/6*o**2. Suppose n(d) = 0. Calculate d.
-11, -1, 1
Let s(c) = 3*c**2 - 16*c + 13. Let u be s(6). Suppose -u*l + 6 = -23*l. Factor -l*p**3 - 17*p + 36*p - p**3 + 4*p**2 - 15*p - 4*p**4.
-4*p*(p - 1)*(p + 1)**2
Suppose -761*l = -759*l - 20. Factor -l - 48*j**2 - 13 - 17 + 55*j + 29*j + 4*j**3.
4*(j - 10)*(j - 1)**2
Determine z, given that 0 + 1/4*z**3 + 18769/4*z - 137/2*z**2 = 0.
0, 137
Let o(y) be the second derivative of y**6/195 + y**5/130 - y**4/78 - y**3/39 - 20*y - 33. Solve o(a) = 0.
-1, 0, 1
Let j = -4038 - -12149/3. Let r(u) be the first derivative of 5/4*u**4 + 17 + j*u**3 + 25*u + 55/2*u**2. Factor r(q).
5*(q + 1)**2*(q + 5)
Let u(s) = 6*s**3 - 211*s**2 + 2*s - 133. Let r be u(37). Solve -3/4*y**5 - 13500*y + 63/2*y**4 + r - 510*y**3 + 3900*y**2 = 0.
2, 10
Let i = -54615/8 + 6827. Let q(w) be the third derivative of -i*w**3 + 0*w**4 - 4*w**2 + 0*w + 1/80*w**5 + 0. Let q(j) = 0. What is j?
-1, 1
Suppose 2*o + 7 = -3*r - 16, 0 = -o + 2*r - 29. Let u be -12*(o/(-4))/(-19). Factor 10/3*l**2 - 2/3*l**u - 8/3*l + 0.
-2*l*(l - 4)*(l - 1)/3
Let s(x) be the second derivative of -1/40*x**6 - 1/168*x**7 - 2*x + 0*x**5 - 32 + 1/12*x**4 + 0*x**3 + 0*x**2. Factor s(p).
-p**2*(p - 1)*(p + 2)**2/4
Let w = -679 - -681. Suppose -2*p = 3*c - 9, 2*p - w*c = -3*c + 7. Let -9/7*m**p + 3/7*m**2 + 9/7*m + 3/7*m**4 - 6/7 = 0. What is m?
-1, 1, 2
Let c(d) be the third derivative of 1/12*d**5 + 75/2*d**3 + 115/12*d**4 + 0*d + 0 - 25*d**2. Factor c(y).
5*(y + 1)*(y + 45)
Let x be (258/(-1892) + 216/11)/((-4)/(-234)). Factor 117/2*g + 3/4*g**2 + x.
3*(g + 39)**2/4
Let n be 12/130*1*((-16669)/237 + 72). Factor n*p**2 - 2*p + 24/13.
2*(p - 12)*(p - 1)/13
Suppose 4*u - 5*m = 212 - 229, 0 = 3*u - m + 10. Let l be 2*-2*(u + (-105)/(-36)). Find p, given that l + 1/6*p**3 + 5/6*p + 2/3*p**2 = 0.
-2, -1
Let a be 46*3/36 - (-63)/378. Suppose -3*s + 5*m = -0*m - 32, a = -3*s - 4*m. Factor 0 + 2/7*x**s - 1/7*x**3 - 1/7*x**5 + 0*x**2 + 0*x.
-x**3*(x - 1)**2/7
Let f be ((-12)/(-10))/((-18)/(-40)). Let c = 17428 - 17426. What is k in 4/3*k**3 - 4*k + 0*k**c - f = 0?
-1, 2
Let z be -2 - (26/(-6) + 2). Let b be (2 + (-60)/33)/(510/1870). Suppose b + l + z*l**2 = 0. Calculate l.
-2, -1
Let c = 242350 - 2665844/11. Factor 2/11*z**2 + c*z - 20/11.
2*(z - 2)*(z + 5)/11
Suppose 50*s = 36*s + 28. Factor -2*a**3 - 8*a**s + 28*a**2 + 112 - 54*a - 76.
-2*(a - 6)*(a - 3)*(a - 1)
Let l(n) be the third derivative of 0*n**3 + 1/180*n**6 + 1/12*n**4 + 2/45*n**5 - 229*n**2 + 0 - 2*n. Factor l(u).
2*u*(u + 1)*(u + 3)/3
Let o be (-16)/(-24)*27 + 1560/(-96). Suppose -33/4*b - 47/4*b**3 - o*b**4 - 91/4*b**2 + 9/2 = 0. What is b?
-3, -1, 2/7
Let n = 17 - 3. Let l = n - 12. Determine v so that -42*v**2 + v - 4*v**3 + 45*v**l + 3*v**3 - 3 + 0*v = 0.
-1, 1, 3
Let w be 46098/1144 + 3 + 33/(-12). Let d = 1949/44 - w. Factor d*f**2 + 0 + 3/4*f**3 + 9/2*f.
3*f*(f + 2)*(f + 3)/4
Let o(l) = l - 29. Let z be o(7). Let u be (-26 - -32) + z/4. Factor 1/2*v**3 + 0*v**2 + 0 - u*v.
v*(v - 1)*(v + 1)/2
Let m(s) = -