0 + 114*x**2. Factor y(u).
-3*u**2*(u - 3)**2*(u + 1)
Let i(h) be the second derivative of 5*h**7/42 - 7*h**6/6 + 15*h**5/4 - 65*h**4/12 + 10*h**3/3 + 48*h. Factor i(o).
5*o*(o - 4)*(o - 1)**3
Let c(u) be the second derivative of -3*u**4/2 + 11*u**3/6 + 7*u**2/2 - 497*u. Suppose c(g) = 0. What is g?
-7/18, 1
Let d(l) be the third derivative of -225*l**6/32 - 105*l**5/8 - 55*l**4/8 - 5*l**3/3 - 72*l**2. Factor d(s).
-5*(3*s + 2)*(15*s + 2)**2/4
Suppose 5*b - 33 = -t, 6*b + 7*t - 8*t - 22 = 0. Suppose 10/3*l**3 - 3 - 3*l + 10/3*l**2 - 1/3*l**4 - 1/3*l**b = 0. Calculate l.
-3, -1, 1, 3
Suppose -20*z + 21 = -19. Let y be (21 - 23) + 0 + z. Factor i + 1/2*i**3 + 3/2*i**2 + y.
i*(i + 1)*(i + 2)/2
Let n(m) be the first derivative of 3*m**4/16 + 15*m**3/4 + 39*m**2/4 + 210. Suppose n(t) = 0. What is t?
-13, -2, 0
Let x = 55/36 + -7/9. Let i = 13769/2036 - 13/1018. Solve 0*a + 0 - 81/4*a**2 - 81/4*a**3 - i*a**4 - x*a**5 = 0 for a.
-3, 0
Let h(s) = -15*s**3 + 115*s**2 - 20. Let g(r) = r**3 - r**2 + 2. Let q(m) = 10*g(m) + h(m). Factor q(j).
-5*j**2*(j - 21)
Let s(c) be the third derivative of 1/96*c**4 - 1/60*c**5 + 0 + 0*c**3 + 1/80*c**6 + 1/1344*c**8 - 1/210*c**7 - 11*c**2 + 0*c. Factor s(k).
k*(k - 1)**4/4
Let n(i) = -i**3 + 6*i**2 + 10*i - 16. Let c be n(7). Factor -20*o**3 + 5*o**4 - 30*o**4 - 10*o**5 + c*o**5.
-5*o**3*(o + 1)*(o + 4)
Factor 1/4*s**4 - 43/4*s**2 - 36 + 0*s**3 + 75/2*s.
(s - 3)**2*(s - 2)*(s + 8)/4
Factor 0*s + 0*s**2 - 2/7*s**3 + 0 + 6/7*s**4.
2*s**3*(3*s - 1)/7
Let j be 351/(-36) + ((-24)/2 - -22). Factor 2*b**3 - 5/4*b**4 - b**2 + 0 + j*b**5 + 0*b.
b**2*(b - 2)**2*(b - 1)/4
Let p = -425519/180 - -2364. Let u(x) be the third derivative of 0 + 0*x + p*x**5 - 5*x**2 + 0*x**3 + 0*x**4. Solve u(w) = 0.
0
Let r(o) = -o**3 - 43*o**2 + 110*o - 52. Let a(j) = j**2 + j. Let w(z) = 28*a(z) - 4*r(z). Factor w(y).
4*(y - 1)**2*(y + 52)
Factor 191*b**2 + 151*b**2 + 12*b**3 - 137*b**2 - 7*b**3.
5*b**2*(b + 41)
Let z(w) be the third derivative of w**6/828 - w**5/690 - w**3/3 + 13*w**2. Let v(u) be the first derivative of z(u). Factor v(r).
2*r*(5*r - 2)/23
Let w = -51 - -87. Let h be (-6)/w - (-26)/12. Solve 10*l**3 + 8*l**3 + 20*l**3 + 5*l**h - 23*l**3 = 0 for l.
-1/3, 0
Determine y, given that 6 - 1/5*y**2 + 29/5*y = 0.
-1, 30
Let h(a) be the third derivative of 7*a**6/660 + 8*a**5/165 + a**4/33 + 461*a**2. Factor h(u).
2*u*(u + 2)*(7*u + 2)/11
Let h be -9 - -12 - (-4 + 1). Let j(y) = 11*y**2 + 2 - 2*y**4 - 17*y**2 - h. Let q(d) = -d**4 - d**2 - 1. Let i(k) = -j(k) + 4*q(k). Factor i(s).
-2*s**2*(s - 1)*(s + 1)
Let t(g) be the second derivative of 2/45*g**6 - 1/9*g**4 - 2/27*g**3 - 16*g + 1/45*g**5 + 0*g**2 + 0. Let t(f) = 0. Calculate f.
-1, -1/3, 0, 1
Let m(x) be the third derivative of 2*x**7/945 - 2*x**6/135 - 2*x**5/45 + 2*x**4/27 + 10*x**3/27 + 50*x**2. Factor m(o).
4*(o - 5)*(o - 1)*(o + 1)**2/9
Let g = -237/31 - -1371/155. What is k in 24/5*k**3 + 3/5 - 6/5*k**2 + g*k**5 - 21/5*k**4 - 6/5*k = 0?
-1/2, 1
Let d(m) be the third derivative of m**6/420 - 8*m**5/105 - 19*m**4/84 + 34*m**3/21 - 82*m**2. Determine b, given that d(b) = 0.
-2, 1, 17
Factor -49/4 - 7/2*c - 1/4*c**2.
-(c + 7)**2/4
Let x(v) be the first derivative of -v**5/240 - v**4/96 + v**3/12 + 11*v**2 + 18. Let d(r) be the second derivative of x(r). Determine b so that d(b) = 0.
-2, 1
Solve -2/3*h**2 - 38/3 + 40/3*h = 0 for h.
1, 19
Let q(b) be the second derivative of -18*b + 0*b**2 + 0 - 2/9*b**3 - 1/60*b**5 + 1/9*b**4. Let q(h) = 0. What is h?
0, 2
Let g(n) = n**2 - 5*n + 6. Let d be g(3). Suppose d = 219*p - 214*p. Solve -2/7*t**4 + 0*t + p*t**3 + 0*t**2 + 0 = 0.
0
Factor -27/5*k + 18/5*k**2 - 42/5 + 3/5*k**3.
3*(k - 2)*(k + 1)*(k + 7)/5
Let m be ((-3)/40)/(1/(-12)) + (-86)/215. Let 0 - 3/2*y + m*y**2 = 0. Calculate y.
0, 3
Let o = 18001177/385 - 46756. Let x = -1/55 + o. Factor 4/7*u**2 + 2/7*u + 0 + x*u**3.
2*u*(u + 1)**2/7
Suppose -28 = -4*l + 16*z, -7*z = 3*l - 11*z - 13. Solve 1/6*n + 0 + 1/6*n**l + 1/3*n**2 = 0 for n.
-1, 0
Let o(z) = -z**2. Let x(j) = -3*j**2 - 7*j + 3. Let b(a) = 4*o(a) - x(a). Let w be b(6). Determine g so that 2*g**w + 5*g**2 - 2*g + g**3 - g**3 - 5*g**3 = 0.
0, 2/3, 1
Let x be ((-332)/(-8))/(5/(-10)). Let h = 251/3 + x. Factor 3*u**2 + 13/3*u**3 + 5/3*u**4 - h - 1/3*u.
(u + 1)**3*(5*u - 2)/3
Factor -3*w - 9 + 9/4*w**2 + 3/4*w**3.
3*(w - 2)*(w + 2)*(w + 3)/4
Let x(v) = -2*v**4 - 34*v**3 + 24*v**2 + 76*v - 22. Let i(q) = q**4 + 11*q**3 - 8*q**2 - 26*q + 7. Let z(s) = 14*i(s) + 5*x(s). Suppose z(o) = 0. Calculate o.
-1, 1, 3
Determine x so that -44944/5 - 848/5*x - 4/5*x**2 = 0.
-106
Let z(v) be the second derivative of -v**7/315 - 2*v**6/225 + v**5/50 - v - 31. Suppose z(x) = 0. What is x?
-3, 0, 1
Let w = 721/10 - 72. Let c(x) be the first derivative of 0*x**2 - 1/8*x**4 + 0*x + 3 + 1/3*x**3 - w*x**5. Solve c(h) = 0 for h.
-2, 0, 1
Let s = -987/46 + 43/2. Let p = 389/46 + s. Solve 9*v**3 - 5/2*v**4 + 0*v - p*v**2 + 2 = 0 for v.
-2/5, 1, 2
Factor -216 + 331*q - 7*q**2 + 3*q**2 - 447*q.
-4*(q + 2)*(q + 27)
Let n(o) be the first derivative of o**3/2 + 7*o**2/4 + o - 41. Factor n(t).
(t + 2)*(3*t + 1)/2
Let k(i) = -201*i - 6. Let h be k(1). Let t = 2279/11 + h. Solve 0*y**3 - 2/11*y**5 + 4/11*y**2 + 0 + t*y - 4/11*y**4 = 0 for y.
-1, 0, 1
Let r = 1279 + -1277. Let -12/7 + 4/7*p**r + 8/7*p = 0. Calculate p.
-3, 1
Suppose -2*u = -k + 2*u + 15, -85 = -2*k - 3*u. Factor k + y**2 - 2*y**2 - 3*y**2 + 5 + 12*y.
-4*(y - 5)*(y + 2)
Suppose -4*w + 330 - 342 = 0, 0 = -2*f + 3*w + 9. Factor 8/7*t + f + 2/7*t**3 - 10/7*t**2.
2*t*(t - 4)*(t - 1)/7
Let b(m) be the third derivative of m**10/2016 + m**9/756 + m**8/1344 + 11*m**4/24 - 18*m**2. Let c(q) be the second derivative of b(q). Factor c(r).
5*r**3*(r + 1)*(3*r + 1)
Let g(i) be the second derivative of 2*i**6/15 - 2*i**5/5 - 15*i + 3. Solve g(c) = 0.
0, 2
Let o = -2/63569 - -63573/127138. Factor -2 - o*a**2 + 5/2*a.
-(a - 4)*(a - 1)/2
Let b(j) be the third derivative of 0*j + 1/4*j**5 + 42*j**2 + 0 + 3/4*j**4 + 1/2*j**3. Let b(q) = 0. What is q?
-1, -1/5
Let t = -24605/136 + 3082/17. Determine s, given that 3/4*s + t*s**4 + 3/2*s**3 + 0 + 15/8*s**2 = 0.
-2, -1, 0
Let u(v) = -4*v**2 - 5*v - 1. Let r(y) = -2*y**2 - 2*y. Let t(z) = -3*z + 50. Let c be t(15). Let h(a) = c*r(a) - 2*u(a). Factor h(w).
-2*(w - 1)*(w + 1)
Let z(y) be the first derivative of 3*y**4/2 - 23*y**3 + 72*y**2 - 81*y - 122. Factor z(r).
3*(r - 9)*(r - 1)*(2*r - 3)
Factor -48/7*q**3 + 0 - 96/7*q**2 - 6/7*q**4 + 0*q.
-6*q**2*(q + 4)**2/7
Let m(r) be the second derivative of -r**6/45 + r**5/3 - 16*r**4/9 + 32*r**3/9 - 5*r + 4. Factor m(u).
-2*u*(u - 4)**2*(u - 2)/3
Let q(k) be the second derivative of k**5/70 - 85*k**4/42 + 1763*k**3/21 + 1849*k**2/7 - 33*k - 3. Factor q(l).
2*(l - 43)**2*(l + 1)/7
Let g(w) be the third derivative of 1/360*w**5 + 1/720*w**6 + 0*w**3 - 21 - w**2 + 0*w - 1/72*w**4. Let g(k) = 0. Calculate k.
-2, 0, 1
Let t be (-11 - -1)*(15/(-10) - (7 - 8)). Factor 0*b**2 + 0*b + 8/5*b**4 - 8/5*b**3 - 2/5*b**t + 0.
-2*b**3*(b - 2)**2/5
Let r(t) be the first derivative of 3/5*t**3 + 12/5*t - 12/5*t**2 - 11. Factor r(i).
3*(i - 2)*(3*i - 2)/5
Let b(t) = -t**2 + t - 1. Let y(x) = -4*x**4 + 17*x**3 + 15*x**2 - 4*x - 1. Let d(f) = -b(f) + y(f). Determine n so that d(n) = 0.
-1, 0, 1/4, 5
Factor -1014 - 52*t - 2/3*t**2.
-2*(t + 39)**2/3
Let v(a) be the second derivative of -2/7*a**3 + 0 + 0*a**2 + 3*a + 5/28*a**4 - 3/140*a**5. Let v(k) = 0. Calculate k.
0, 1, 4
Let t(g) = -g**4 + 7*g**3 + 8*g**2 - 18*g + 6. Let h(z) = -z**3 + z - 1. Let w(o) = 6*h(o) + t(o). Suppose w(p) = 0. What is p?
-3, 0, 2
Let g(p) be the third derivative of 0*p + p**3 - 8*p**2 + 0 + 1/3*p**4 + 1/30*p**5. What is s in g(s) = 0?
-3, -1
Suppose 6*x - 2*x + 16 = 0. Let f(m) = 4*m**3 + 2*m**2 - 8*m - 14. Let u(s) = 17*s**3 + 7*s**2 - 32*s - 55. Let g(t) = x*u(t) + 18*f(t). Factor g(i).
4*(i - 2)*(i + 2)**2
Let i(a) = 3*a**3 + 6*a**2 - 3*a - 6. Let b(k) = -51*k**2 - 39*k - 115 + 39*k**3 + 129*k**2 + 37. Let w(z) = -2*b(z) + 27*i(z). Factor w(y).
3*(y - 1)*(y + 1)*(y + 2)
Let d(u) = -u**3 + 14*u**2 - 17*u - 17. Let i be d(13). Let h = i + 72. Factor 1/9*n**5 + 0*n**h + 0*n + 0*n**2 + 2/9*n**4 + 0.
n**4*(n + 2)/9
Let h(o) = -3*o**3 - o**2 + 4*o. Let c(g) = -17*g**3 -