given that 3*h**4 - 3*h + 2*h - 3*h**3 - 2*h**4 + 0*h**3 + r*h**2 = 0.
0, 1
Let g be 2/((-2)/(-3)) + (-600)/216. Factor -2/9*u + 2/9*u**3 - g + 2/9*u**2.
2*(u - 1)*(u + 1)**2/9
Let f(n) = 3*n**5 + 5*n**4 - 3*n**3 - 5*n**2 - 2*n - 2. Let x(y) = -5*y**5 - 10*y**4 + 5*y**3 + 10*y**2 + 5*y + 5. Let i(p) = 5*f(p) + 2*x(p). Factor i(c).
5*c**2*(c - 1)*(c + 1)**2
Solve 8/5 + 8/5*a + 2/5*a**2 = 0 for a.
-2
Let l be 9 + 2/((-4)/6). Let n(g) be the third derivative of -1/525*g**7 - 1/150*g**l - 1/150*g**5 + 0*g**3 + 0 + 0*g**4 + 0*g - 2*g**2. Factor n(i).
-2*i**2*(i + 1)**2/5
Factor -1/2*c**2 - 1/2 - c.
-(c + 1)**2/2
Let o(z) be the first derivative of -z**6/2520 + z**5/840 + z**4/84 - 5*z**3/3 + 1. Let w(n) be the third derivative of o(n). Suppose w(a) = 0. What is a?
-1, 2
Let d = -5 + 3. Let h be (-56)/(-18) + (d - 0). Find x, given that -h*x**3 + 0*x + 2/3*x**4 + 0 + 4/9*x**2 = 0.
0, 2/3, 1
Let s(j) be the third derivative of 0 - 1/3*j**4 + 1/105*j**7 + 0*j + 1/3*j**3 + 1/5*j**5 - 1/15*j**6 - j**2. Factor s(c).
2*(c - 1)**4
Let z(s) be the third derivative of 1/15*s**5 + 1/60*s**6 - 3*s**2 + 1/12*s**4 + 0 + 0*s + 0*s**3. Solve z(x) = 0 for x.
-1, 0
Let m = 37 + -32. Let n(j) be the third derivative of 0*j**4 - 1/48*j**6 - 2*j**2 + 0*j**3 + 1/105*j**7 + 0 - 1/672*j**8 + 1/60*j**m + 0*j. Factor n(d).
-d**2*(d - 2)*(d - 1)**2/2
Let u be (12/(-15))/(1/(-5)). Factor -r + r + r**2 + u*r + r**2.
2*r*(r + 2)
Let c(q) be the third derivative of -q**6/900 + q**4/180 + 9*q**2. Let c(o) = 0. Calculate o.
-1, 0, 1
Let q(l) be the third derivative of 0*l**3 - 1/224*l**8 - 1/80*l**5 + 0 + 0*l + 0*l**4 + 1/80*l**6 - 4*l**2 + 1/280*l**7. Solve q(w) = 0 for w.
-1, 0, 1/2, 1
Let b = -3/142 + 389/4970. Let j(f) be the first derivative of 0*f**2 + 0*f**3 + 1/7*f**4 + 0*f - b*f**5 - 3. Suppose j(a) = 0. Calculate a.
0, 2
Let y = 22/5 + -2107/480. Let i(w) be the third derivative of y*w**4 + 2*w**2 + 1/120*w**5 + 0*w**3 + 0 + 0*w. Determine s, given that i(s) = 0.
-1/2, 0
Let k(c) = c**3 - 5*c**2 - 24*c + 5. Let p(f) = f**3 - 8*f**2 - 36*f + 8. Let s(l) = 8*k(l) - 5*p(l). Factor s(h).
3*h*(h - 2)*(h + 2)
Let n = 134 - 132. What is w in 0*w - 8/9 + 2/3*w**n - 2/9*w**3 = 0?
-1, 2
Factor -2*b**2 + 1/4*b**3 - 3*b + 1/4*b**4 + 0.
b*(b - 3)*(b + 2)**2/4
Suppose -484/3*b**2 - 2662/9*b**3 - 16/9 - 88/3*b = 0. What is b?
-2/11
Suppose 3*l - 15 = 3*z, 4*l + z - 10 = -0*z. Let o(a) be the first derivative of 2*a + 2/3*a**l + 2 + 2*a**2. Determine b, given that o(b) = 0.
-1
Suppose -2 = 5*q - 17. Let k(z) = -z**4 + z**4 + 7*z**3 - 1 - z**4 - 6*z**q. Let j(u) = -3*u**4 + u**3 + u**2 + u - 2. Let t(a) = j(a) - 2*k(a). Solve t(n) = 0.
-1, 0, 1
Let c = -184 - -184. Factor 2/7*z**2 + c - 2/7*z.
2*z*(z - 1)/7
Let v(q) = -2*q**2 - 5*q - 3. Let f(s) = 10*s**2 + 26*s + 16. Let g(p) = -3*f(p) - 16*v(p). Determine k so that g(k) = 0.
-1, 0
Let m = -52 - -52. Let j(g) be the third derivative of 1/24*g**3 + 1/240*g**5 + 0*g + 1/48*g**4 + m - 2*g**2. Factor j(c).
(c + 1)**2/4
Let x(t) be the second derivative of 0*t**3 + 0 + 0*t**2 - 1/15*t**5 - 1/126*t**7 - 4*t + 2/45*t**6 + 0*t**4. Factor x(c).
-c**3*(c - 2)**2/3
Let t(l) be the third derivative of -l**8/168 - l**7/105 + l**6/20 + l**5/6 + l**4/6 + 3*l**2. Factor t(f).
-2*f*(f - 2)*(f + 1)**3
Let f(c) = -c**5 - c**3 - c**2 + c - 1. Let z(r) = -4*r**4 + 6*r**3 + 18*r**2 + 12*r + 6. Let k(m) = -4*f(m) - 2*z(m). Factor k(w).
4*(w - 2)*(w + 1)**4
Find d such that d**2 - 228*d**3 - 10*d**2 + 231*d**3 + 4*d + 2*d = 0.
0, 1, 2
Let t(q) be the third derivative of q**5/210 - q**4/42 + q**2 + 29. Solve t(y) = 0.
0, 2
Let f(a) be the third derivative of a**7/945 - a**6/135 + a**5/90 + a**4/27 - 4*a**3/27 - 8*a**2. Find h, given that f(h) = 0.
-1, 1, 2
Suppose 1 - 7*a**3 - a - a + 9*a**3 - a**4 = 0. Calculate a.
-1, 1
Let u = 581 + -578. Factor 0 - 1/2*c**u + 1/2*c + 0*c**2.
-c*(c - 1)*(c + 1)/2
Solve 4/3*h**3 + 0 + 8/3*h**2 + 0*h - 4/3*h**4 = 0.
-1, 0, 2
Let r(m) = -m**4 + 2*m**3 + 2*m**2 + 2*m + 1. Let w(t) = t**4 - 3*t**3 - 2*t**2 - 3*t - 2. Let z be (-4)/(-2) + -2 - 3. Let s(u) = z*r(u) - 2*w(u). Factor s(p).
(p - 1)**2*(p + 1)**2
Let i(a) be the second derivative of -a**5/10 - a**4/6 + a**3/3 + a**2 + 18*a. Factor i(k).
-2*(k - 1)*(k + 1)**2
Let q = -32 + 16. Let s be q/12 - (-3 - -1). Factor 4/3*m + s + 2/3*m**2.
2*(m + 1)**2/3
Let x(o) be the third derivative of -o**8/1680 - o**7/1050 + o**6/100 + 3*o**2 - 5. Determine h so that x(h) = 0.
-3, 0, 2
Let v be (-2)/4 + (-21)/(-6). Let k(g) = 1 + 3*g**v + g**4 - 1. Let t(f) = -3*f**4 - 8*f**3. Let o(s) = 8*k(s) + 3*t(s). Factor o(n).
-n**4
Let c(b) be the third derivative of -b**5/15 + b**4/2 + 8*b**3/3 + 33*b**2. Factor c(l).
-4*(l - 4)*(l + 1)
Let a(s) be the first derivative of s**4 + 4*s**3/3 - 2*s**2 - 4*s + 12. Find u such that a(u) = 0.
-1, 1
Suppose -2*b + w + 29 = 0, -5*b + 32 = 4*w - 8. Factor -4 - 5*a**3 + 9*a**3 - 5*a**2 + a**3 + 2*a**2 - b*a.
(a - 2)*(a + 1)*(5*a + 2)
Let r(d) = 3*d**2 - 3*d - 3. Let b(v) = 2*v + 2 - 3*v + 4*v + 0*v - 2*v**2 + v**3. Let c(h) = 3*b(h) + 4*r(h). Solve c(s) = 0 for s.
-2, -1, 1
Let x = -14 + 17. Suppose -8 = -5*g + 22. Factor -33*h**2 - 8*h**4 + 75*h**3 - 61*h**4 - 6*h**2 + 21*h**5 + 6*h**x + g*h.
3*h*(h - 1)**3*(7*h - 2)
Suppose -d + 3*s - 16 = -4, -3*d = 2*s + 91. Let r = -53/2 - d. Factor 1/2 + 1/2*a**4 + 1/2*a**5 - a**2 - a**3 + r*a.
(a - 1)**2*(a + 1)**3/2
Let p(y) be the third derivative of -y**6/180 + y**5/90 + y**4/9 - 4*y**3/9 - 42*y**2. What is t in p(t) = 0?
-2, 1, 2
Let g(v) be the third derivative of -v**5/15 + v**4/6 - 18*v**2. Factor g(y).
-4*y*(y - 1)
Let y be 9/18*8 + (-64)/18. Factor -2/9*i - 2/9*i**3 + y*i**2 + 0.
-2*i*(i - 1)**2/9
Let s = 433/5 + -86. Factor 0 + 6/5*d**3 + 3/5*d**4 + 0*d + s*d**2.
3*d**2*(d + 1)**2/5
Let o(f) be the first derivative of 4*f**3/9 - 16*f**2/3 + 64*f/3 + 11. Solve o(y) = 0 for y.
4
Factor 4/5 - 6/5*r - 2*r**2.
-2*(r + 1)*(5*r - 2)/5
Find w, given that 2/5*w**2 + 18/5 + 12/5*w = 0.
-3
Suppose 1 = x - 1. Factor -2*v**4 + 2*v**x - 2*v + 3*v**4 + 5*v**3 - 3*v**3 - 3*v**4.
-2*v*(v - 1)**2*(v + 1)
Let k(l) = l**2 + l + 1. Let d(c) = -c**3 + 7*c**2 + 2*c + 6. Let h(t) = d(t) - 4*k(t). Let m be h(2). Determine a so that -m*a**2 + a + 3*a - 6*a = 0.
-1, 0
Let x(k) = k**5 - k**4 + k**2 - 1. Let o(b) = 6*b**5 + 6*b**4 + 6*b**3 + 3*b**2 - 3. Let j(a) = o(a) - 3*x(a). Determine h so that j(h) = 0.
-2, -1, 0
Let g be (-72)/(-10) + ((-156)/15 - -10). Solve -3*q + 2/5 + g*q**2 - 21/5*q**3 = 0.
2/7, 1/3, 1
Let j be (1 - (-22)/(-14))/(6/(-21)). Solve 2/5 - 1/5*c - 2/5*c**j + 1/5*c**3 = 0.
-1, 1, 2
Let q(p) = p**2 + 3*p - 7. Let r be q(-5). Factor -j + 3*j**3 + 3*j**r - 5*j**3 - 2 + 2*j**2.
(j - 1)*(j + 1)*(j + 2)
Determine w, given that 12/5*w**3 - 2*w**2 + 0*w + 0 - 2/5*w**4 = 0.
0, 1, 5
Let y(p) be the second derivative of 0 - 1/150*p**6 + 0*p**3 + 0*p**2 + 0*p**4 - 2*p - 1/100*p**5. Suppose y(g) = 0. Calculate g.
-1, 0
Let s(i) = i**3 - 2*i**2 + 2*i + 2. Let d be s(0). Determine v, given that 0*v**d - 3*v**2 - v**2 + 12*v = 0.
0, 3
Suppose -3/2*c**3 + 0 - 1/2*c**2 + 0*c - 1/2*c**5 - 3/2*c**4 = 0. Calculate c.
-1, 0
Let u(l) = -l**3 - 3*l**2 - 2*l - 2. Let i be u(-3). Factor f**2 + 7*f**3 - 2*f**4 + 3*f**3 + 11*f**2 + 4*f**i - 16 - 8*f.
2*(f - 1)*(f + 2)**3
Let h(n) be the third derivative of 3/110*n**5 + n**2 + 1/660*n**6 + 0*n + 2/11*n**4 + 0 + 16/33*n**3. Factor h(c).
2*(c + 1)*(c + 4)**2/11
Let t(l) be the first derivative of -l**4/4 + l**3/3 + l**2 - 4. Solve t(f) = 0.
-1, 0, 2
Determine s, given that 8 + 2/3*s**2 + 14/3*s = 0.
-4, -3
Factor -8 - 6*w**2 + 17 - 3 - 3*w + 3*w**3.
3*(w - 2)*(w - 1)*(w + 1)
Factor 2/5*b**2 - 2/5*b + 0.
2*b*(b - 1)/5
What is t in 1 - 19/4*t**3 + 9/4*t**4 + 3*t - 13/4*t**2 + 7/4*t**5 = 0?
-2, -1, -2/7, 1
Let b(n) be the second derivative of -27*n**5/70 + 9*n**4/14 - 3*n**3/7 + n**2/7 - 2*n - 5. Factor b(h).
-2*(3*h - 1)**3/7
Let x be 2/(-12) + 155/30. Factor 8*i**2 - i**3 + i**3 + i**4 - x*i**3 - 4*i.
i*(i - 2)**2*(i - 1)
Find o, given that -13/4*o**2 + 7/8*o**3 + 5/2*o + 1 = 0.
-2/7, 2
Suppose -2*v - k + 12 = -5*k, 3*v - 16 = 5*k. Let x be (-3)/(-2)*(1 - -1). Factor 2*w**2 - 2*w**5 - 2*w**2 + v*w**x.
-2*w**3*(w - 1)*(w + 1)
Let o(g) be the third derivative of -g**10/151200 - g**9/30240 + g*