Let i be (1371322/714)/(-53) + 37. Factor 0*n**2 - 2/21*n**5 + 0*n + 6/7*n**4 + 0 - i*n**3.
-2*n**3*(n - 8)*(n - 1)/21
Suppose 664*l - 1882 = -277*l. Find j such that 64*j**l - 450/7 + 60/7*j + 2/7*j**4 - 60/7*j**3 = 0.
-1, 1, 15
Let z = -2986/39 + 6089/78. Solve 0 - z*j**3 + 9*j**2 + 21/2*j = 0 for j.
-1, 0, 7
Let v(g) be the second derivative of 11/2*g**3 - 11 - 1/10*g**6 + 2*g + 6*g**2 + 3/20*g**5 + 9/4*g**4. Factor v(x).
-3*(x - 4)*(x + 1)**3
Let b(n) be the first derivative of -n**5/15 - n**4/3 + 16*n**3/3 + 160*n**2/3 + 132*n + 18. Let w(k) be the first derivative of b(k). Factor w(z).
-4*(z - 5)*(z + 4)**2/3
Let w = 3265 - 3260. Let u(c) be the first derivative of 1/9*c**6 + 0*c + 3 - 4/9*c**3 + 0*c**2 + 0*c**w - 1/2*c**4. Suppose u(v) = 0. What is v?
-1, 0, 2
Determine m, given that -1/6*m**3 + 2/3*m**2 + 7/6*m - 5/3 = 0.
-2, 1, 5
Let t(u) be the third derivative of 5*u**8/448 - 37*u**7/840 + 7*u**6/160 + 3*u**5/80 - u**4/12 - 34*u**2 - 23*u. Let t(f) = 0. Calculate f.
-8/15, 0, 1
Let o(k) = k**3 + 41*k**2 - 48*k + 74. Let i be o(-42). Let j = i - 323. Factor -2*w**2 - 16/5*w**j - 2/5*w - 8/5*w**4 + 0.
-2*w*(w + 1)*(2*w + 1)**2/5
What is p in 96/5 + 7*p**3 + 289/5*p**2 + 70*p = 0?
-48/7, -1, -2/5
Let b = -542 - -660. Let t be b/35 - (-156)/(-195). Solve -t*h + 3/7*h**2 + 15/7 = 0.
1, 5
Let n(h) be the second derivative of h**5/50 + 22*h**4/15 + 163*h**3/15 + 24*h**2 + 3*h - 16. Suppose n(s) = 0. Calculate s.
-40, -3, -1
Let b(s) = -206*s + 20. Let q be b(-14). Factor -3*f**3 - q*f + 2904*f + 3*f**5.
3*f**3*(f - 1)*(f + 1)
Let x be -3 - (-15)/(-6)*(-10 + 8). Suppose -5*l = x*c, 8*l = 7*l - 3*c - 13. Let 3*f**l - 27/5*f**3 - 3*f**4 + 6/5*f + 0 + 21/5*f**5 = 0. Calculate f.
-1, -2/7, 0, 1
Let d(i) be the third derivative of -44*i**2 - 1 + 0*i**3 - 1/15*i**5 + 0*i + 1/3*i**4. Find u, given that d(u) = 0.
0, 2
Factor -132/7*f - 2/7*f**2 - 2178/7.
-2*(f + 33)**2/7
Let v = -3465/79 - -446532/395. Let b = v + -1086. Factor b + 1/10*h**2 - 7/10*h.
(h - 6)*(h - 1)/10
Let w(x) = -7*x**5 + 19*x**4 - 18*x**3 - 29*x**2 - 5. Let m(b) = -3*b**5 + 9*b**4 - 8*b**3 - 14*b**2 - 2. Let t(g) = 5*m(g) - 2*w(g). Solve t(p) = 0 for p.
-1, 0, 2, 6
Let r(h) be the first derivative of -2/3*h**3 - 1/26*h**4 + 29/13*h**2 - 30/13*h - 95. Factor r(m).
-2*(m - 1)**2*(m + 15)/13
Let x(m) be the second derivative of -3*m**5/20 + 363*m**4/4 - 723*m**3/2 + 1083*m**2/2 - 116*m - 6. Factor x(n).
-3*(n - 361)*(n - 1)**2
Suppose -63 = 27*c - 171. Let p(y) be the second derivative of 0 - 9/5*y**5 - 10*y - 40*y**2 - 19*y**c - 128/3*y**3. Factor p(v).
-4*(v + 5)*(3*v + 2)**2
Suppose 3*c + 0*x = -3*x + 9, -5*c - 20 = -2*x. Let k be (-1778)/(-210) + 5/6*c. Solve 26/5*n**2 + 8/5 - 22/5*n**3 - k*n**4 - 2*n**5 + 32/5*n = 0.
-2, -1, -2/5, 1
Let y(r) be the first derivative of 3*r**4/8 - 107*r**3/2 + 312*r**2 - 618*r + 634. Factor y(t).
3*(t - 103)*(t - 2)**2/2
Determine s, given that 48 - 408/5*s - 3/5*s**4 + 87/5*s**3 + 87/5*s**2 - 3/5*s**5 = 0.
-4, 1, 5
Let m(u) be the third derivative of -u**7/20160 + u**6/2880 + u**5/64 + 77*u**4/24 + 2*u**2 - 73. Let f(t) be the second derivative of m(t). Factor f(r).
-(r - 5)*(r + 3)/8
Suppose 3623*p - 4144 = 6725. Factor -6/7*x**2 - 12/7*x + 24/7 + 3/7*x**p.
3*(x - 2)**2*(x + 2)/7
Let m(z) be the first derivative of z**4/4 + 11*z**3/3 + 8*z**2 + z - 18. Let h be m(-9). Solve -37 + 17 + h + 2*r**2 - 10*r + 13 = 0.
2, 3
Suppose 2*k = -8*k + 420. Let p be 21/9 - 35/k. Determine h, given that 1/2*h**4 + h + 1/2*h**5 - p*h**3 + 0 - 1/2*h**2 = 0.
-2, -1, 0, 1
Let f(z) = 115*z - 21735. Let b be f(189). Factor b*j**2 - 1/9*j**3 + 0*j + 1/9*j**5 + 0*j**4 + 0.
j**3*(j - 1)*(j + 1)/9
Let d(h) be the first derivative of h**6/3 - 342*h**5/5 + 7559*h**4/2 - 13998*h**3 - 7560*h**2 + 42336*h + 3489. Suppose d(j) = 0. What is j?
-1, 1, 3, 84
Let k(n) be the first derivative of -n**8/84 - 8*n**7/105 - n**6/10 - 15*n**2/2 + 7*n + 106. Let y(u) be the second derivative of k(u). Factor y(m).
-4*m**3*(m + 1)*(m + 3)
Find l, given that 1/2*l**2 + 2*l**3 - 3*l + 0 + 1/2*l**4 = 0.
-3, -2, 0, 1
Let x(u) = -14*u**2 + u - 1. Let q(j) = -3*j**3 - 9*j**2 + 6*j - 6. Let h(b) = q(b) - 6*x(b). Factor h(n).
-3*n**2*(n - 25)
Suppose 0 = -82*n + 62*n + 3920. Factor 96*y + 607 + 1064*y**3 - n*y**4 + 656*y**2 - 607.
-4*y*(y - 6)*(7*y + 2)**2
Let g(d) = -1218*d - 2432. Let l be g(-2). Let y(c) be the second derivative of 0 + 0*c**2 + 2/5*c**5 + 1/6*c**3 - 3/4*c**l - 4*c. Factor y(m).
m*(m - 1)*(8*m - 1)
Suppose 3*z - 90 = 21*z. Let a(d) = -d**2 - 7*d - 8. Let q be a(z). Factor -n**4 + n**q + 2/9*n**3 + 0 - 2/9*n.
-n*(n - 1)*(n + 1)*(9*n - 2)/9
Let v(j) = 9*j**4 + 36*j**3 + j**2 - 21*j - 23. Let k(a) = a**4 + 4*a**3 + a**2 + a - 1. Let d(b) = 7*k(b) - v(b). Factor d(g).
-2*(g - 2)*(g + 1)**2*(g + 4)
Let c(d) be the third derivative of -d**6/40 - 13*d**5/20 - 5*d**4/2 + 50*d**3 + 334*d**2. Determine u, given that c(u) = 0.
-10, -5, 2
Suppose 33 = 17*h - 1. What is x in -160*x - 149*x - 4*x**h + 321*x = 0?
0, 3
Find w such that 1/5*w**4 + 61/5*w**3 - 961/5*w + 899/5*w**2 + 0 = 0.
-31, 0, 1
Let c = 6511 - 6506. Let q(d) be the second derivative of 0 + 1/16*d**2 + 1/160*d**c - 1/48*d**3 + 26*d - 1/96*d**4. Factor q(y).
(y - 1)**2*(y + 1)/8
Suppose 2858 = -5*h - 2*q - 957, -15 = -3*q. Let x be (-6)/20 - h/300. Factor 2*i**3 - 11/2*i**2 + 6*i - x - 1/4*i**4.
-(i - 3)**2*(i - 1)**2/4
Factor 5/4*f**4 + 85/4*f + 0 - 5/4*f**2 - 85/4*f**3.
5*f*(f - 17)*(f - 1)*(f + 1)/4
Suppose -513*n + 398 + 745 = 117. Factor -6/7 - 2/7*j**n - 8/7*j.
-2*(j + 1)*(j + 3)/7
Let t(b) be the first derivative of -b**5/35 - 15*b**4/14 - 48*b**3/7 + 16*b**2/7 + 768*b/7 + 4588. Suppose t(f) = 0. What is f?
-24, -4, 2
Find t such that 2088*t**2 - 48*t**3 + 152*t**3 + 2084 - 4170*t - 53*t**3 - 53*t**3 = 0.
1, 1042
Let h be ((-6)/(-10))/((-15)/(-100)). Determine w so that 6*w**5 - 47*w**3 + 22*w**h + 8*w**2 + 46*w**3 + 25*w**3 = 0.
-2, -1, -2/3, 0
Let l = 376 + -368. Suppose 0 = -66*j + l*j + 116. What is p in 3/4*p**j + 45/8*p**3 + 9*p**4 + 0*p + 0 - 6*p**5 = 0?
-1/4, 0, 2
Factor 25/2*o**2 + 1/2*o - 3 + 23/2*o**3 + 5/2*o**4.
(o + 1)**2*(o + 3)*(5*o - 2)/2
Let j(a) be the first derivative of -69/2*a**2 + a**3 - 230 + 66*a. Factor j(m).
3*(m - 22)*(m - 1)
Let y = -6817 - -6817. Let i(t) be the second derivative of 3/16*t**4 - 7/80*t**5 + 0*t**2 - 1/12*t**3 - 17*t + y. What is c in i(c) = 0?
0, 2/7, 1
Let r(f) be the third derivative of 0*f**3 + 0*f - 1/210*f**7 + 0 + 1/40*f**6 + 36*f**2 + 1/24*f**4 - 1/20*f**5. Factor r(d).
-d*(d - 1)**3
Let f be 4*(-1 + (-68)/1840) + 4. Let c = f - -8/23. What is r in -c*r**2 + 8/5 - 7/5*r = 0?
-8, 1
Suppose -y = -22 + 2. Suppose 2*h + y = 6*h, 3*h = 4*o - 1. Factor 0*w**2 + o*w + 2*w + 0*w**2 - 3*w**2.
-3*w*(w - 2)
Suppose 74 - 74 = -34*r. Let f(x) be the second derivative of 34*x + 2/9*x**3 + r*x**2 + 0 - 1/9*x**4. Find z, given that f(z) = 0.
0, 1
Let g be (132/(-110))/((-2)/20*3). Suppose g*a + 5*d + 4 = -1, -5*a - 3*d - 3 = 0. Find p, given that 0 - 3/5*p**2 - 3/5*p**3 + a*p = 0.
-1, 0
Let g(n) = 82*n - 5 - n**3 - 95*n - 11*n**2 - 22. Let j be g(-10). Find b such that 0 + 2/9*b + 2/9*b**j - 4/9*b**2 = 0.
0, 1
Let r(v) be the first derivative of -3/2*v**2 + 1/3*v**3 - 10*v - 45. Let r(i) = 0. What is i?
-2, 5
Let p be (4/24)/((-75)/(-225)). Let k(a) be the first derivative of p*a**3 + 0*a + 31 + 3/8*a**4 + 0*a**2. Solve k(q) = 0.
-1, 0
Let m(q) be the first derivative of q**7/840 - q**6/240 - q**5/48 + q**4/16 - 55*q**2/2 + 47. Let t(j) be the second derivative of m(j). Factor t(y).
y*(y - 3)*(y - 1)*(y + 2)/4
Let k = -34566 + 34609. Let v(c) be the third derivative of 1/20*c**5 + 1/10*c**4 + 0*c**3 + 0 - k*c**2 + 1/200*c**6 + 0*c. Factor v(q).
3*q*(q + 1)*(q + 4)/5
Solve 2/11*f**5 + 72*f + 194/11*f**3 - 564/11*f**2 - 432/11 - 32/11*f**4 = 0 for f.
2, 3, 6
Let s(z) be the first derivative of 0*z**5 + 104 + 8/3*z - z**2 - 1/36*z**6 + 13/24*z**4 - 8/9*z**3. Solve s(l) = 0 for l.
-4, -1, 1, 2
Let p(k) be the second derivative of -k**5/190 + 25*k**4/57 - 503*k**3/57 + 814*k**2/19 - 7754*k. Determine l, given that p(l) = 0.
2, 11, 37
Determine b, given that 94*b + 1/2*b**3 + 67/2*b**2 - 128 = 0.
-64, -4, 1
Determine b so that -56/5*b**2 + 1/5*b**4 - 54/5*b + 54/5*b**3 + 11 = 0.
-55, -