 0 = t + 4*t - 15. Suppose t*b = b + 6. Factor 2*x**2 - 3*x**3 - 5*x**3 + 4*x**b.
-2*x**2*(2*x - 1)
Let q(m) be the second derivative of -m**4/54 + 10*m**3/27 - 25*m**2/9 + m. Factor q(y).
-2*(y - 5)**2/9
Let c(o) be the first derivative of o**8/5040 - o**6/540 + o**4/72 - 2*o**3/3 + 2. Let s(v) be the third derivative of c(v). Factor s(k).
(k - 1)**2*(k + 1)**2/3
Let z(u) be the first derivative of u**3/7 + 6*u**2/7 + 12*u/7 + 8. Determine n so that z(n) = 0.
-2
Let p be (-2)/6*90/(-50). Factor -3/5*s + 0 + p*s**3 + 0*s**2.
3*s*(s - 1)*(s + 1)/5
Let r be 50/(-30)*6/(-5). Find v such that -1/2*v + 1/2*v**3 + 1/4*v**r + 0 - 1/4*v**4 = 0.
-1, 0, 1, 2
Let a(c) be the first derivative of -c**6/150 + 7*c**5/100 - c**4/4 + 3*c**3/10 - 4*c - 1. Let l(o) be the first derivative of a(o). Solve l(m) = 0 for m.
0, 1, 3
Let w(v) = -3*v - 24. Let p be w(-9). What is m in -2/5 + 7/5*m**2 - 12/5*m**p + 7/5*m = 0?
-2/3, 1/4, 1
Let p(w) be the second derivative of 1/11*w**2 - 6*w - 1/66*w**4 - 1/33*w**3 + 0 + 1/110*w**5. Factor p(c).
2*(c - 1)**2*(c + 1)/11
Let i(d) be the first derivative of -d**4/20 + d**3/5 - 4*d/5 - 3. Factor i(l).
-(l - 2)**2*(l + 1)/5
Let l be 646/26 + 12/78. Suppose q - 23 = 5*i, 6*q - 4*i - l = 3*q. Factor -2*a**2 - 2/3 - 2/3*a**q - 2*a.
-2*(a + 1)**3/3
Let t(p) be the second derivative of -p**6/60 - p**5/40 + p**4/24 + p**3/12 - 4*p. Factor t(n).
-n*(n - 1)*(n + 1)**2/2
Let g(k) = 2*k**3 + 2 - 7*k**3 - 3*k**3 - 15*k + 11*k**2. Let x(s) = -24*s**3 + 34*s**2 - 44*s + 6. Let t(y) = 14*g(y) - 5*x(y). Factor t(i).
2*(i - 1)*(2*i - 1)**2
Let m(l) be the third derivative of 0*l**5 + 7*l**2 + 1/280*l**7 + 1/160*l**6 + 0 + 0*l + 0*l**4 + 0*l**3. Factor m(q).
3*q**3*(q + 1)/4
Let f be (-4)/(-2) + (-3)/2. Let k(r) = r**3 - 4*r**2 + 5*r - 6. Let x be k(3). Determine b so that 1/2*b + x*b**2 - f*b**3 + 0 = 0.
-1, 0, 1
Let b(v) be the second derivative of -v**4/8 - v**3/2 - 3*v**2/4 + 17*v. Determine c, given that b(c) = 0.
-1
Let n(y) = 16*y**3 + 6*y**2 - 12*y + 2. Let z(v) = 47*v**3 + 18*v**2 - 37*v + 6. Let q(t) = 7*n(t) - 2*z(t). Factor q(r).
2*(r + 1)*(3*r - 1)**2
Let k(w) be the third derivative of w**7/525 - w**6/100 + w**5/50 - w**4/60 - w**2. Factor k(b).
2*b*(b - 1)**3/5
Let g(p) be the third derivative of -5*p**8/168 + p**7/14 - p**6/24 - 12*p**2. Factor g(a).
-5*a**3*(a - 1)*(2*a - 1)
Suppose 84 = 5*g - g. Let d = -103/5 + g. Suppose -4/5 + 2/5*k**4 + 6/5*k**3 + d*k**2 - 6/5*k = 0. What is k?
-2, -1, 1
Let s be ((-557)/(-4))/((-135)/(-36)). Let b = s + -164/5. Factor 0 - b*g**4 - 3*g**3 + 2/3*g + 1/3*g**2 - 5/3*g**5.
-g*(g + 1)**3*(5*g - 2)/3
Suppose -3*h - 32 = -38. Let w(x) be the second derivative of x**3 + 1/10*x**5 + 1/2*x**4 + 4*x + x**h + 0. Solve w(z) = 0 for z.
-1
Let t(y) be the second derivative of -y**7/28 - y**6/20 + 9*y**5/40 + 5*y**4/8 + y**3/2 + 22*y. Factor t(p).
-3*p*(p - 2)*(p + 1)**3/2
Let r(i) be the first derivative of 4*i**3/3 - 8*i**2 + 16*i - 6. Factor r(k).
4*(k - 2)**2
Suppose -5*x = -7 - 8. Solve 8*p**4 - 6 + 2*p + 4*p**2 - 14*p**x + 6 = 0 for p.
-1/4, 0, 1
Let m = -200 + 1404/7. Determine b, given that 0 + 81/7*b**4 + 40/7*b**2 + 117/7*b**3 + m*b = 0.
-1, -2/9, 0
Let z(h) = -h**2 + 7*h. Let t be z(6). Let r(g) be the third derivative of 1/135*g**5 - g**2 - 1/540*g**t - 1/108*g**4 + 0*g**3 + 0 + 0*g. Factor r(f).
-2*f*(f - 1)**2/9
Suppose -3*v - 133 + 28 = 0. Let y = 37 + v. Find u, given that 2/3*u - 1/3 + 0*u**y - 2/3*u**3 + 1/3*u**4 = 0.
-1, 1
Let a(l) = -12*l**2 + 26*l - 14. Let t(m) = 4*m**2 - 9*m + 5. Let x(b) = -3*a(b) - 10*t(b). Factor x(h).
-4*(h - 2)*(h - 1)
Let r = -1121/5 + 225. Let 0 + 1/5*w**3 + 4/5*w**2 + r*w = 0. Calculate w.
-2, 0
Let v(d) be the third derivative of -d**7/840 - d**4/12 - 5*d**2. Let u(w) be the second derivative of v(w). Factor u(i).
-3*i**2
Let a = -17 + 19. Let p(y) be the second derivative of 0 + 8/9*y**4 + 3*y + 1/3*y**a + 8/9*y**3. Determine l, given that p(l) = 0.
-1/4
Let k(r) be the second derivative of 0*r**4 - 1/14*r**7 - 3/20*r**5 + 0 - 1/5*r**6 + 0*r**3 - 6*r + 0*r**2. Factor k(f).
-3*f**3*(f + 1)**2
Let l = -1966 - -90463/46. Let s = l + -2/23. Factor 0 + 0*a + 1/2*a**5 - s*a**2 + 1/2*a**4 - 1/2*a**3.
a**2*(a - 1)*(a + 1)**2/2
Let z = 13/30 + -1/10. Let 1/3*n + 2/3*n**2 + z*n**3 + 0 = 0. Calculate n.
-1, 0
Let o(k) = -10*k**4 + 10*k**3 + 29*k**2 - 5*k - 6. Let j(a) = 9*a**4 - 9*a**3 - 30*a**2 + 6*a + 6. Let n(f) = 2*j(f) + 3*o(f). Find c such that n(c) = 0.
-1, -1/2, 1/2, 2
Let v(h) be the third derivative of -h**9/75600 + h**7/12600 - h**4/24 + 4*h**2. Let g(z) be the second derivative of v(z). Factor g(t).
-t**2*(t - 1)*(t + 1)/5
Let t = 141 + -139. Let p(y) be the first derivative of 3 - 1/3*y**6 - 8/5*y**5 + 0*y + 0*y**3 + 0*y**t - 2*y**4. Solve p(d) = 0 for d.
-2, 0
Suppose 4*b = -5*p - 4 + 6, 0 = -4*p - b + 6. Suppose 0 - 1/2*d - 3/2*d**p - d**3 = 0. What is d?
-1, -1/2, 0
Let q(i) be the third derivative of i**6/600 - i**5/100 + 2*i**3/15 - 41*i**2. Factor q(t).
(t - 2)**2*(t + 1)/5
Let d be 2/5 - (-1536)/(-135). Let k = d + 56/5. Find a such that 2/9 - 2/3*a + 2/3*a**2 - k*a**3 = 0.
1
Let j be (-45)/105*2/(-3). Factor -2/7*h**3 + 0 + j*h + 0*h**2.
-2*h*(h - 1)*(h + 1)/7
Let w(y) be the third derivative of y**5/30 + 5*y**4/6 + 25*y**3/3 + 18*y**2. Determine g, given that w(g) = 0.
-5
Let f(z) be the third derivative of z**8/840 + z**7/210 + z**6/300 + 12*z**2. Suppose f(r) = 0. What is r?
-2, -1/2, 0
Let o(u) be the third derivative of u**11/47520 - u**10/16800 + u**9/30240 - u**5/30 - 4*u**2. Let k(n) be the third derivative of o(n). Factor k(r).
r**3*(r - 1)*(7*r - 2)
Solve 3/2*a**3 - 3/2*a - 1/4*a**4 + 2 - 7/4*a**2 = 0 for a.
-1, 1, 2, 4
Let y = -500/3 - -168. Factor 0*l + 2/3*l**4 + 0 + 2/3*l**3 - y*l**2.
2*l**2*(l - 1)*(l + 2)/3
Let h(s) = 98*s**2 - 86*s + 18. Let n(v) = -98*v**2 + 87*v - 18. Let p(j) = 6*h(j) + 4*n(j). Factor p(z).
4*(7*z - 3)**2
Let h(b) be the third derivative of -b**6/60 - b**5/30 + b**4/6 - b**2. Let h(x) = 0. Calculate x.
-2, 0, 1
Suppose 6*w = -w + 21. Factor 0 + 1/3*o**w + 1/3*o - 2/3*o**2.
o*(o - 1)**2/3
Let a(n) = 3*n + 9. Let m be a(-3). Suppose 0 + m*v + 1/3*v**3 + 1/3*v**4 + 0*v**2 = 0. What is v?
-1, 0
Suppose -2*c**4 - c - c**4 - 2*c**4 + 10*c**3 - 9*c + 5*c**2 = 0. What is c?
-1, 0, 1, 2
Let q(c) be the third derivative of 0 - 1/18*c**4 - 6*c**2 + 2/45*c**5 + 0*c**3 + 0*c - 1/90*c**6. Suppose q(b) = 0. What is b?
0, 1
Suppose 2*s - 2*a = 3*a - 4, -4*s + 6 = -3*a. Let 2*c**3 + 3*c**2 - 3*c**4 + c - 5*c**3 + s*c**5 - c = 0. Calculate c.
-1, 0, 1
Let f(n) = 4*n**2 + 0 + 5*n + 0*n**2 - 5*n**2 - 2. Let g be f(3). Factor g*d**2 + d**4 - 5*d**2 + 2*d**2 + 0*d**3 + 2*d**3.
d**2*(d + 1)**2
Let l(y) be the first derivative of 5/16*y**4 - 2 + 0*y**2 + 0*y - 1/12*y**3 - 1/5*y**5. Find h, given that l(h) = 0.
0, 1/4, 1
Let a = -25/3 + 53/6. Factor a*k**4 + 0*k**3 + 0*k**2 + 0 + 0*k - 1/2*k**5.
-k**4*(k - 1)/2
Let m(v) = 15*v**3 - v**2. Let l be m(1). Let a be 40/l + 6 + -8. Find j such that 2/7*j**3 + 2/7 + 6/7*j**2 + a*j = 0.
-1
Let y(r) = -r**3 + 7*r**2 - 4*r - 6. Let f be y(6). Let s be (f/(-3))/(-8 + 2). Solve 0*t + 4/3*t**3 + s*t**2 + 0 = 0 for t.
-1/4, 0
Let q be (-26)/(-10) + -3*4/20. Let -8/3 - 2/3*g**q + 8/3*g = 0. What is g?
2
Let j(z) = -z**3 + 19*z**2 - 19*z + 20. Let f be j(18). Let b(l) be the first derivative of 1/3*l**3 + 1 - 1/4*l**4 + l**f + 0*l. Find m such that b(m) = 0.
-1, 0, 2
Let s(y) be the third derivative of -y**8/672 - 11*y**7/420 - 23*y**6/120 - 3*y**5/4 - 27*y**4/16 - 9*y**3/4 - 12*y**2. Factor s(d).
-(d + 1)**2*(d + 3)**3/2
Let g(k) be the third derivative of -k**8/84 + k**6/10 - 2*k**5/15 + k**2 + 18*k. Determine w, given that g(w) = 0.
-2, 0, 1
Let c be 9/(-12) - (-23)/4. Suppose -2 = w - c. Factor 0 + 0*o**w + 6/5*o**4 + 0*o - 4/5*o**5 - 2/5*o**2.
-2*o**2*(o - 1)**2*(2*o + 1)/5
Let l(s) be the first derivative of s**5/15 + s**4/3 + s**3/3 - 2*s**2/3 - 4*s/3 + 11. Factor l(x).
(x - 1)*(x + 1)*(x + 2)**2/3
Factor -9/2*d - 3/4 - 15/4*d**2.
-3*(d + 1)*(5*d + 1)/4
Solve -5*s**4 + 30*s - 25*s**3 + 4 - 50*s - 40*s**2 - 4 = 0.
-2, -1, 0
Let h(a) be the third derivative of 1/315*a**7 - 4*a**2 + 0*a**4 - 1/180*a**6 + 0*a + 0*a**5 + 0 + 0*a**3. Factor h(z).
2*z**3*(z - 1)/3
Let a = 31 - 9. Let p = a - 22