0. Factor -1/2*g**f - 1/2*g + 1/2 + 1/2*g**3.
(g - 1)**2*(g + 1)/2
Let u(c) be the third derivative of -c**6/120 - c**5/40 + c**3/3 + 4*c**2. Let t(z) be the first derivative of u(z). Let t(w) = 0. Calculate w.
-1, 0
Suppose -2*p + 11 = 1. Determine t so that t + 3*t**2 - t**2 - 10*t**4 - t**p + 8*t**4 = 0.
-1, 0, 1
Let 7*f**5 + 24*f**4 + 35*f**3 + 2*f**3 - 5*f**3 - 24*f**2 + 4*f - 43*f**5 = 0. Calculate f.
-1, 0, 1/3, 1
Let x(d) be the third derivative of -d**8/80640 - d**5/12 + 5*d**2. Let r(j) be the third derivative of x(j). Factor r(v).
-v**2/4
Let h(v) = -v**2 - 7*v - 1. Let t(i) = -i. Suppose -36 + 11 = -5*x. Let p(o) = x*t(o) - h(o). Factor p(l).
(l + 1)**2
Let y(z) = 5*z**2 - 13*z - 11. Let u(h) = 3*h**2 - 7*h - 6. Let o(n) = 7*u(n) - 4*y(n). Let o(t) = 0. What is t?
-2, -1
Let m(d) = 5*d**2 - 6*d + 1. Let f be m(1). Determine p, given that 1/3*p**2 + 0*p - 1/6 + f*p**3 - 1/6*p**4 = 0.
-1, 1
Let v be (1 - (-5)/15)*-6. Let f be (-2)/v - 4/16. Factor 2/3*o**2 + f - 2/3*o.
2*o*(o - 1)/3
Let f = -895/2 - -4481/10. Let 0 - 1/5*x**2 + f*x = 0. Calculate x.
0, 3
Let x(k) be the first derivative of -k**9/12096 - k**8/6720 - 2*k**3/3 + 1. Let q(w) be the third derivative of x(w). Let q(b) = 0. Calculate b.
-1, 0
Factor 0 + 0*w**3 + 10*w**2 - 5/2*w**5 + 0*w - 15/2*w**4.
-5*w**2*(w - 1)*(w + 2)**2/2
Let l(s) be the first derivative of 1 - 1/3*s**3 - 4*s + 2*s**2. Solve l(t) = 0 for t.
2
Suppose -20 = -m - 0*m. Let t be (-1 - -16)*16/m. What is b in -27*b**3 + 44*b**2 + 8 + t*b**2 - 2*b**2 - 36*b = 0?
2/3
Let q(a) = -a**2 + 7*a + 3. Let n be q(7). Let y(k) be the first derivative of -3 + 0*k + 1/3*k**2 - k**n + 7/12*k**4. What is w in y(w) = 0?
0, 2/7, 1
Let l(p) = 3*p**2 + 1 - 4*p**2 - p - 2 + 2*p**2. Let y(d) = -d**2 + 3*d + 3. Let g(k) = -5*l(k) + y(k). Factor g(v).
-2*(v - 2)*(3*v + 2)
Let l = -47 - -471/10. Let k(x) be the second derivative of 0 - l*x**4 + 4/5*x**2 + 0*x**3 - 1/50*x**5 - 4*x. Factor k(u).
-2*(u - 1)*(u + 2)**2/5
Factor 1/3*j**3 - 1/3*j + 1/3 - 1/3*j**2.
(j - 1)**2*(j + 1)/3
Let d be 12 + -8 - (-2)/(-1). Let u(p) be the third derivative of -2*p**d - 1/30*p**5 + 0 - 1/3*p**4 + 0*p - 4/3*p**3. Factor u(l).
-2*(l + 2)**2
Let n be -1*(1 + 3/(-2)). Factor -1/2*j**2 - n*j**3 + 0 + 0*j.
-j**2*(j + 1)/2
Factor 8/21*b + 10/21*b**3 + 2/21*b**4 + 16/21*b**2 + 0.
2*b*(b + 1)*(b + 2)**2/21
Suppose 6*t - t = 10. Factor -8*b**t + 6*b**3 - 11*b**3 + b**3.
-4*b**2*(b + 2)
Let d(t) be the third derivative of -t**10/8064 - t**9/2520 - t**8/8960 + t**7/1680 + t**4/8 - t**2. Let y(o) be the second derivative of d(o). Factor y(k).
-3*k**2*(k + 1)**2*(5*k - 2)/4
Let s be ((-382)/7)/(10/(-185)). Let p = s - 1005. Find a, given that -38/7*a**2 - p*a**4 - 2/7 + 8/7*a**5 + 50/7*a**3 + 2*a = 0.
1/2, 1
Let c(l) = l**5 + 4*l**4 + 9*l**3 + 2*l**2 + 4*l + 8. Let r(a) = a**4 + a**3 + a + 1. Let d(b) = -2*c(b) + 14*r(b). Determine x, given that d(x) = 0.
-1, 1
Suppose 0*g = 2*b + g - 6, b = 2*g - 2. Find s, given that s**4 - s - 2/3*s**b - 1/3 + 2/3*s**3 + 1/3*s**5 = 0.
-1, 1
Let t(n) be the third derivative of -n**8/7 - n**7/21 + 13*n**6/120 - n**5/30 + n**4/12 - 3*n**2. Let h(w) = -w**4 + w. Let s(z) = -2*h(z) + t(z). Factor s(o).
-o**2*(3*o + 2)*(4*o - 1)**2
Let i = 2472263363/500 - 4944525. Let f = 3/125 + i. Factor 3/4*c**2 - 3*c**3 + 1/2*c + 0 + f*c**4.
c*(c - 1)**2*(7*c + 2)/4
Let n be (-1 - -5)*(-26)/4. Let m be n/(-10) + 18/45. Factor 3 - 3*j**2 - 4*j - 2*j - m.
-3*j*(j + 2)
Suppose d - 6*d + 5 = 0. Let k(f) = -d + 2 + f**3 - f + 0*f + f**2. Let n(u) = -u**4 + 3*u**3 + 3*u**2 - 3*u + 2. Let l(t) = -2*k(t) + n(t). Factor l(o).
-o*(o - 1)**2*(o + 1)
Let x(i) be the third derivative of i**9/48384 + i**8/26880 - i**7/1680 + i**6/720 - i**5/15 + 2*i**2. Let a(q) be the third derivative of x(q). Factor a(t).
(t - 1)*(t + 2)*(5*t - 2)/4
Let v(w) be the second derivative of -w**7/336 - w**6/80 - w**5/80 - 23*w. Factor v(c).
-c**3*(c + 1)*(c + 2)/8
Find o such that 0*o - 1/2*o**4 - 3/2*o**3 + 0 - o**2 = 0.
-2, -1, 0
Let w(y) be the first derivative of -y**6/210 - 2*y**5/105 - y**4/42 + 3*y**2/2 - 2. Let q(r) be the second derivative of w(r). Solve q(f) = 0 for f.
-1, 0
Let q(r) be the first derivative of -2*r**3/9 - 2*r**2/3 + 2*r + 2. Factor q(v).
-2*(v - 1)*(v + 3)/3
Let u(s) be the second derivative of 2*s**7/63 - 4*s**5/15 - 2*s**4/9 + 2*s**3/3 + 4*s**2/3 - 10*s. Factor u(x).
4*(x - 2)*(x - 1)*(x + 1)**3/3
Let w(p) be the second derivative of 3*p**5/20 + p**4/2 - 5*p**3/2 - 9*p**2 + 39*p. Let w(f) = 0. What is f?
-3, -1, 2
Let s(p) = -p**3 - 3*p**2 + 3*p - 3. Let m be s(-4). Suppose -m - 1 = -q. Factor y**4 - 2*y**4 + y**3 - y + 0*y**4 + y**q.
-y*(y - 1)**2*(y + 1)
Suppose 12/13 + 10/13*c + 2/13*c**2 = 0. Calculate c.
-3, -2
Suppose 2 = 3*r + 4*c, -2*r - 1 = -3*r - c. Let n be 12*r/(-14) + 2. Determine z, given that n*z**3 - 2/7*z + 2/7*z**4 + 0 - 2/7*z**2 = 0.
-1, 0, 1
Let b be ((-240)/21)/4 - -4. Factor -8/7 - 2/7*s**2 - b*s.
-2*(s + 2)**2/7
Let b(a) be the second derivative of -a**4/42 + 3*a**3/7 - 19*a. Factor b(x).
-2*x*(x - 9)/7
Let d = 57 - 51. Let z(m) be the third derivative of -1/200*m**d + 1/50*m**5 + 0 - m**2 + 0*m + 0*m**3 - 1/40*m**4. Let z(h) = 0. What is h?
0, 1
Let s(l) = -5*l**3 - 5*l**2 + 5*l - 1. Let h(q) = -3 + 0*q**3 - 4*q**2 - 4*q**3 + 3 + 4*q. Let t(g) = -3*h(g) + 2*s(g). Factor t(m).
2*(m - 1)*(m + 1)**2
Let b(c) = -c**4 + 2*c**3 + 4*c**2 - 10*c - 3. Let w(h) = h**4 + h**3 - h**2 + h. Let y(p) = -b(p) - 4*w(p). Solve y(s) = 0.
-1, 1
Let p(z) be the third derivative of -z**7/315 - 7*z**6/180 - z**5/5 - 5*z**4/9 - 8*z**3/9 - 2*z**2. Solve p(u) = 0 for u.
-2, -1
Factor -7*p**3 + 24*p**2 - 6*p**2 - 2*p**4 + 13*p**3 + 10*p.
-2*p*(p - 5)*(p + 1)**2
Let x(a) be the first derivative of -a**6/9 + 4*a**5/15 + a**4/3 - 16*a**3/9 + 7*a**2/3 - 4*a/3 + 15. What is d in x(d) = 0?
-2, 1
Let g be 96 - (3 - 14/6). Let u = g - 94. Suppose 8/9*f + u*f**2 + 2/9*f**4 + 2/9 + 8/9*f**3 = 0. Calculate f.
-1
Let a(l) be the second derivative of 0*l**2 - 1/2*l**4 - 1/2*l**3 + 0 + l. Factor a(b).
-3*b*(2*b + 1)
Let c = -1714/5 + 343. Determine r so that 1/5 - c*r**2 + 0*r = 0.
-1, 1
Let u = 80 - 238/3. Let -u*l - 1/3 - 1/3*l**2 = 0. What is l?
-1
Let 4/3*q**5 - 1/3*q**3 + 0*q + 0 - q**4 + 0*q**2 = 0. What is q?
-1/4, 0, 1
Suppose -2*y + 3 = -5*c - 6, y + 13 = -c. Let h be ((-18)/y)/(7/28). Factor h*k**2 - 2 + k + k**4 + 4*k**4 - 13*k**3 + 0*k.
(k - 1)**3*(5*k + 2)
Let s(a) be the second derivative of -4/9*a**3 + 2/63*a**7 + 2*a + 0 - 1/9*a**6 + 1/3*a**2 + 2/9*a**4 + 1/15*a**5. Find r such that s(r) = 0.
-1, 1/2, 1
Let f be 0/(4 + -1) - -4. Suppose f*p = -0*p + 8. Determine u so that -3*u**4 + p*u**3 + u**3 + u**2 - 2*u**3 + u**3 = 0.
-1/3, 0, 1
Let i = -7/37 + 58/111. Determine k so that -i*k**5 + 1/3*k**4 + 1/3*k**3 + 0 + 0*k - 1/3*k**2 = 0.
-1, 0, 1
Let t = 3 + -1. Factor 4*m**t - 2*m**2 - 3*m**4 + m**4 + 0*m**4.
-2*m**2*(m - 1)*(m + 1)
Let p(q) be the third derivative of q**8/420 - q**7/70 + q**6/45 - 2*q**3/3 - q**2. Let t(k) be the first derivative of p(k). Find g such that t(g) = 0.
0, 1, 2
Let b(n) = 2*n**2 - 3*n**2 + 0*n**2 - n. Let p(o) = 3*o**3 - 12*o**2 - 21*o + 6. Let k(u) = 12*b(u) - p(u). Factor k(l).
-3*(l - 1)**2*(l + 2)
Let g(u) be the third derivative of 0*u**5 + 2*u**2 + 1/270*u**6 + 1/945*u**7 + 0*u + 0 + 0*u**4 + 0*u**3. Factor g(b).
2*b**3*(b + 2)/9
Let x = -959/4 + 240. Determine p, given that p + 1 + x*p**2 = 0.
-2
Let d(h) be the first derivative of 1/3*h**3 - 1/2*h**2 + 3 - h + 1/4*h**4. Solve d(q) = 0.
-1, 1
Suppose -5/2*v + 3 + 1/2*v**2 = 0. What is v?
2, 3
Let b(n) be the third derivative of 0*n + n**2 - 1/70*n**5 + 0*n**3 + 0 + 1/42*n**4. Solve b(f) = 0 for f.
0, 2/3
Let d be (-21)/7 - 2*3. Let c = 11 + d. Factor 13/2*n**2 - c*n - 5/2*n**3 - 2.
-(n - 2)*(n - 1)*(5*n + 2)/2
Let c(p) be the first derivative of -6 - 5/8*p**2 - 1/2*p - 1/12*p**3 + 1/8*p**4. Solve c(b) = 0.
-1, -1/2, 2
Let d(a) be the third derivative of -a**8/3360 + a**7/560 - a**6/720 - a**5/80 + a**4/24 - a**3 - 6*a**2. Let p(v) be the first derivative of d(v). Factor p(t).
-(t - 2)*(t - 1)**2*(t + 1)/2
Let b(t) be the third derivative of -t**8/70560 + t**6/2520 - t**5/30 - 2*t**2. Let z(s) be the third derivative of b(s). Factor z(n).
-2*(n - 1)*(n + 1)/7
Le