Let y(u) = u**5 + u**4 + u**3 - u. Let o(s) = -v(s) - 5*y(s). Factor o(m).
5*m**4*(m + 1)
Let v(u) = -u**3 + 9*u**2 - 13*u - 3. Let r be v(7). Determine x, given that -1 - r - 2*x**2 + 9*x - 1 - x**2 = 0.
1, 2
Let o(h) be the third derivative of h**5/100 + h**4/40 - h**3/5 - 51*h**2. Find l such that o(l) = 0.
-2, 1
Factor -94875*q + 16800*q**2 - 15*q**4 + 7*q**4 + 495*q**3 + 81970*q + 491520 + 13*q**4 + 222825*q.
5*(q + 3)*(q + 32)**3
Let -3/2*g**4 + 7/2*g**2 + 4 - 7/2*g**3 + 1/2*g**5 + 9*g = 0. What is g?
-1, 2, 4
Let y(f) = -4*f**2 - 36*f - 68. Let m(q) be the first derivative of -5 - q - 1/2*q**2. Let s(t) = -4*m(t) + y(t). Let s(u) = 0. What is u?
-4
Factor -44*d - 48*d - 1 + d**4 + 2*d**3 + 136*d - 46*d.
(d - 1)*(d + 1)**3
Suppose 5*s - 24*m = -23*m + 19, -5*s = 2*m - 22. Let 0 + 4/11*c**s - 4/11*c + 14/11*c**2 - 14/11*c**3 = 0. Calculate c.
0, 1/2, 1, 2
Suppose -81*s + 3*s**3 - 156 + 339*s**2 + 249*s - 390*s**2 = 0. What is s?
2, 13
Let s(t) be the second derivative of -10/3*t**4 + 0*t**3 + 1/4*t**5 + 0*t**2 - 18*t + 0. Solve s(r) = 0.
0, 8
Let n(b) be the first derivative of -b**3/12 - 15*b**2/4 - 14*b + 105. Find r, given that n(r) = 0.
-28, -2
Let i(q) be the third derivative of q**6/40 - q**5/5 + 190*q**2. Solve i(k) = 0.
0, 4
Let n = -200 + 202. Suppose u - 11*d + 13*d = 4, 3*u = n*d - 4. Find t, given that 0 + u*t + 1/3*t**2 = 0.
0
Let m = 46 + -44. Suppose 88 = m*p + 80. Solve -1/2*d + 0 - 2*d**p - d**2 + 7/2*d**3 = 0 for d.
-1/4, 0, 1
Let f(y) = 16*y**5 + 24*y**4 - 24*y**3 - 14*y**2 - 24*y. Let v(n) = n**5 + 2*n**4 + n**2 - n. Let g(u) = 2*f(u) - 28*v(u). Solve g(h) = 0.
-1, 0, 5
Suppose -4*l = -4*z - l - 4, 0 = z + l - 6. Suppose -y = -0*y - z. Factor -d**2 - 5*d**y + 9*d**2 - 7*d**2 + 16.
-4*(d - 2)*(d + 2)
Suppose 0 = 5*r - 225 - 25. Solve -5*w + 17*w**2 + 10 + 3*w**2 + r*w = 0.
-2, -1/4
Let x be 2 + 11 + 0 + 2. Let g be 2/(-4) - x/(-6). Find w such that -6*w**3 + 1 + 18*w + g + 4*w**2 - 27*w**4 - 10*w**5 + 20*w**2 - 2*w**5 = 0.
-1, -1/4, 1
Suppose 251*h = -10*m + 249*h + 28, -h - 6 = 0. Find o, given that 0 + 0*o - 8/7*o**2 - o**5 - 20/7*o**3 + 26/7*o**m = 0.
-2/7, 0, 2
Let z = 2453/1799 + -20/257. Suppose 3/7*s + z*s**2 - 9/7 - 3/7*s**3 = 0. Calculate s.
-1, 1, 3
Suppose 0 - 4/3*d - d**4 + 7/3*d**3 + 0*d**2 = 0. Calculate d.
-2/3, 0, 1, 2
Let q = -3 + 6. Suppose -4*f + 16*l - 12 = 12*l, -3 = -3*f - l. Factor -2/7*c**q + f*c + 4/7*c**2 + 0.
-2*c**2*(c - 2)/7
Let p(s) = -7*s + 304. Let b be p(43). Let o(n) be the first derivative of 2/21*n**b - 1/14*n**4 - 3 + 0*n + 2/7*n**2. Suppose o(u) = 0. Calculate u.
-1, 0, 2
Let p(s) = 3*s + 51. Let n be p(0). Factor -23*t**5 + 6*t**4 + n*t**5 - 25*t**5 + 3*t**3.
3*t**3*(t + 1)**2
Determine y so that 5*y**4 + 10 - 3 - 10*y**3 - 4*y**4 - 17*y**2 - 5*y**3 + 9 + 15*y = 0.
-1, 1, 16
Let x = -2408/5 - -482. Let r be 1/6 + (-33)/(-90). Factor x + r*l + 2/15*l**2.
2*(l + 1)*(l + 3)/15
Let f(q) be the first derivative of -q**6/3 - 8*q**5/5 + 4*q**4 + 20*q**3/3 - 23*q**2 + 20*q + 130. Determine v, given that f(v) = 0.
-5, -2, 1
Let m(l) = -l**2 + 14*l - 38. Let f(j) = -j**2 + 15*j - 39. Let a(h) = -2*f(h) + 3*m(h). Suppose a(n) = 0. What is n?
6
Let g = -201/10 - -103/5. Let x(p) be the third derivative of -g*p**4 + 0 - 1/60*p**6 + 11/60*p**5 + 0*p - 3/2*p**3 - p**2. Factor x(s).
-(s - 3)**2*(2*s + 1)
Let z(s) be the first derivative of 4*s**3/21 + 8*s**2/7 - 128*s/7 - 777. Suppose z(l) = 0. Calculate l.
-8, 4
Suppose 263/4*f**2 + 305/4*f**3 + 3/2 + 75/4*f**4 + 71/4*f = 0. Calculate f.
-3, -2/3, -1/5
Let i = -12 - -14. Factor -3*n**3 - n**2 - 3*n + 3*n**4 + 0*n**i + 6*n**3 - 2*n**2.
3*n*(n - 1)*(n + 1)**2
Let i = -2565 - -2567. Factor -39/2*g**i - 6 - 18*g - 9*g**3 - 3/2*g**4.
-3*(g + 1)**2*(g + 2)**2/2
Factor 40/7*d + 2/7*d**4 - 2/7*d**2 + 0 - 40/7*d**3.
2*d*(d - 20)*(d - 1)*(d + 1)/7
Suppose -7*w = -12*w. Let c(g) be the second derivative of 0 + 0*g**6 + 0*g**3 + w*g**4 + 3/40*g**5 - 1/28*g**7 + 0*g**2 + 3*g. Factor c(k).
-3*k**3*(k - 1)*(k + 1)/2
Suppose 5*f + 18 = -3*v, v + 3*f = 2*v - 8. Let g(q) = -8*q**2 + 8*q + 13. Let i(a) = a**2 - a - 1. Let p(y) = v*g(y) - 3*i(y). Suppose p(s) = 0. What is s?
-1, 2
Find k such that -42*k**4 + 0*k**3 + 12 + 111*k**2 - 37*k - 9*k**3 - 35*k = 0.
-2, 2/7, 1/2, 1
Let a(r) be the first derivative of r**4/12 - 2*r**3/3 + 2*r**2 - 9*r + 27. Let y(n) be the first derivative of a(n). Factor y(p).
(p - 2)**2
Let t be 1/(-1) - (0 - 3). Let f be (-301)/(-63) - t/(-9). Factor -4*q**2 - 2*q**3 + f*q**3 - q**3.
2*q**2*(q - 2)
Factor -570*i + 232324 + 9162*i**2 - 9158*i**2 + 226*i + 2272*i.
4*(i + 241)**2
Solve -16*y + 46/3 + 2/3*y**2 = 0.
1, 23
Let l be (-1)/2 - (4599/6)/7. Let p = l - -113. Factor 1/2*i**2 - 5/6*i**p + 0 + 1/3*i.
-i*(i - 1)*(5*i + 2)/6
Let m = -2/815 + 101/1304. Let t(n) be the second derivative of 0 - m*n**5 + 3/2*n**2 - 1/4*n**4 + 1/4*n**3 + 5*n. Factor t(u).
-3*(u - 1)*(u + 1)*(u + 2)/2
Let i = 582/427 - -4/61. Let v = 2/1383 - -8284/9681. Factor i*x**3 + 4/7*x**2 + 0*x + v*x**4 + 0.
2*x**2*(x + 1)*(3*x + 2)/7
Factor -720*k**3 + 399 + 1985*k**2 - 188 + 524 + 422*k - 2622*k + 205*k**2 - 5*k**4.
-5*(k - 1)**3*(k + 147)
Factor -11*v**3 - 378*v + 33*v**2 + 2*v**3 + 390*v.
-3*v*(v - 4)*(3*v + 1)
Let u(b) = b**2 - 40*b + 2. Let x be u(40). Let t(s) be the first derivative of 12 + 15/2*s**x - 5*s**3 + 10*s - 3*s**5 - 35/4*s**4. Factor t(j).
-5*(j + 1)**3*(3*j - 2)
Let i(o) = 9*o**3 + 55*o**2 + 130*o + 76. Let q(a) = a**3 - 1. Let f(c) = -i(c) + 4*q(c). Let f(d) = 0. Calculate d.
-8, -2, -1
Let i(v) be the second derivative of -v**5/80 - v**4/8 + 7*v**3/24 + 183*v + 3. Determine l so that i(l) = 0.
-7, 0, 1
Let h(w) be the second derivative of -3*w**5/20 + 15*w**4/4 + 8*w**3 + 400*w. Factor h(m).
-3*m*(m - 16)*(m + 1)
Factor -2*o**2 - 71*o - 4*o**3 - 33*o - 53*o**2 - 38*o**2 - 15*o**2.
-4*o*(o + 1)*(o + 26)
Let y = -107409 + 107412. Suppose -2*r = 2 - 6. Determine b, given that -1/2*b**r + 1 - 3/2*b**y - 1/2*b**4 + 3/2*b = 0.
-2, -1, 1
Suppose -3*k - 5*c + 2 = 0, -k = -3*c + 7*c + 4. Factor 30 - 2*q**2 - 2*q - 30 + 2*q**3 + 2*q**k.
2*q*(q - 1)*(q + 1)**2
Let z**2 + 25*z**2 + 0*z - 24 + 5*z - 2*z**4 + 0 - 8*z**3 + 3*z = 0. Calculate z.
-6, -1, 1, 2
Let a(y) = -6*y + 31. Let p(m) = 7*m - 32. Let o(s) = -4*a(s) - 3*p(s). Let x be o(10). Factor 4/3*r**3 - 16/3 + 4*r**x + 0*r.
4*(r - 1)*(r + 2)**2/3
Suppose 54 = -n + 4*n. Suppose 4*c - 11 - 29 = -5*a, -2*a - 2*c + n = 0. Let -4*k**2 - 12*k**3 + 15*k + 14 - 6 - a*k**4 - 3*k = 0. Calculate k.
-2, -1, 1
Let g be (-130)/(-39) + -7 + 4. Let w(o) be the second derivative of 1/12*o**4 - 2*o + g*o**3 + 0 - 3/2*o**2. Factor w(x).
(x - 1)*(x + 3)
Let b(w) be the third derivative of -5/66*w**4 + 0*w + 25/33*w**3 + 8*w**2 + 0 + 1/330*w**5. Factor b(c).
2*(c - 5)**2/11
Suppose -17*j + 156 - 37 = 0. Let i(a) be the first derivative of 0*a**5 - 1/3*a**4 - j + 1/18*a**6 + 2/9*a**3 + 1/2*a**2 - 2/3*a. Factor i(b).
(b - 1)**3*(b + 1)*(b + 2)/3
Let 9/7*z**5 + 6/7*z - 33/7*z**4 - 27/7*z**2 + 45/7*z**3 + 0 = 0. Calculate z.
0, 2/3, 1
Let v(q) = q**3 - 7*q**2. Let n(x) be the first derivative of -x**3/3 + 10. Let d(g) = 14*n(g) - 2*v(g). Factor d(w).
-2*w**3
Let a(o) = -385*o + 1927. Let m be a(5). Factor 289/3 + 34/3*r + 1/3*r**m.
(r + 17)**2/3
What is d in d**4 - d**4 + 28*d**3 - 12*d**4 + 28*d**2 + 40*d**3 + 0*d**4 - 16 - 36*d**5 - 32*d = 0?
-1, -2/3, 1
Let d(l) be the second derivative of -l**6/24 + l**5/6 - 5*l**4/24 - l**2 - 3*l. Let h(i) be the first derivative of d(i). Factor h(y).
-5*y*(y - 1)**2
Let i(m) be the third derivative of m**5/30 - m**4/12 - 4*m**3 + 118*m**2. Factor i(p).
2*(p - 4)*(p + 3)
Let f(i) be the first derivative of -4*i**3/3 - 88*i**2 - 1936*i + 614. Suppose f(r) = 0. What is r?
-22
Let r(z) = -9*z**5 + 20*z**4 - 23*z**3 + z**2 + 27*z - 11. Let u(p) = -p**5 + p**3 + p**2 - p + 1. Let j(g) = -r(g) + 5*u(g). Find b, given that j(b) = 0.
-1, 1, 2
Let s(c) = -4*c**4 + 12*c**2 + 26*c + 14. Let d(n) = 9*n**4 - n**3 - 23*n**2 - 52*n - 29. Let x(g) = -2*d(g) - 5*s(g). Solve x(p) = 0 for p.
-2, -1, 3
Let d = 1 - 84. Let v = d + 585/7. Let 11/7*s + 2/7 + 13/7*s**2 + v*s**3 = 0. What is s?
-2, -1, -1/4
What is i in 156/5*i**2 + 54/5*i**3 + 1/5*i**4 + 51/5 + 154/5*i = 0?
-51, -1
Let a(p) = -5*p**2 + 20 - p*