0*x + 0 + 2/3*x**2 - 2/3*x**a.
-2*x**2*(x - 1)/3
Let f = -328 - -1315/4. Solve -9/4*a**3 + f*a**4 - 3/2*a + 3/4*a**5 + 0 - 15/4*a**2 = 0.
-1, 0, 2
Let o(n) be the first derivative of n**6/6 + 4*n**5/5 + 3*n**4/2 + 4*n**3/3 + n**2/2 + 5. Factor o(u).
u*(u + 1)**4
Suppose 3*f + 2*f**2 - 1 - 5*f + 1 = 0. Calculate f.
0, 1
Let v(t) be the first derivative of 0*t - 1/8*t**2 - 1/6*t**3 - 2 - 1/16*t**4. Suppose v(j) = 0. What is j?
-1, 0
Let z(b) be the third derivative of -b**5/150 + 2*b**4/15 - 16*b**3/15 + 2*b**2 - 19*b. Factor z(c).
-2*(c - 4)**2/5
Let m(q) = -q**3 - 3*q**2 + 4*q + 5. Let z be m(-4). Determine t so that -4*t**5 - t - 2*t**2 + z*t**5 - 5*t**4 + 7*t**4 = 0.
-1, 0, 1
Let g(x) be the first derivative of x**5/25 + x**4/20 - x**3/5 - x**2/10 + 2*x/5 + 2. What is u in g(u) = 0?
-2, -1, 1
Let h(b) = -6*b**2 - 58*b - 5. Let k(d) = 3*d**2 + 30*d + 3. Let t(u) = 3*h(u) + 5*k(u). Find f such that t(f) = 0.
-8, 0
Let d(x) = -49*x**2 - 30*x - 6. Suppose 0 = -5*a + 3*a + 4. Let l(z) = 196*z**2 + 121*z + 25. Let v(f) = a*l(f) + 9*d(f). Factor v(r).
-(7*r + 2)**2
Suppose 0 = y + 6*y + 2*y. What is f in 2/3*f**3 - 1/3*f**5 + 0*f**2 + y + 0*f**4 - 1/3*f = 0?
-1, 0, 1
Factor -5/4*d - 1/4 - d**2.
-(d + 1)*(4*d + 1)/4
Let r be (12/15)/(6/15). Factor 7*a**2 + 6 - 4*a**2 + a**2 - r - 8*a.
4*(a - 1)**2
Let b(k) = -7*k + 114. Let y be b(16). Factor 2/7*r + 4/7 - 2/7*r**y.
-2*(r - 2)*(r + 1)/7
Factor 3/5*d**5 + 9/5*d**3 + 0*d + 0*d**2 + 0 - 12/5*d**4.
3*d**3*(d - 3)*(d - 1)/5
Let g(q) be the third derivative of q**6/540 - q**5/30 + q**4/4 + q**3/6 - q**2. Let u(z) be the first derivative of g(z). Factor u(p).
2*(p - 3)**2/3
Let c(x) = -x**3 + 4*x**2 - 3*x. Let s(n) = -2*n - 2*n**3 + 5*n**2 - n + 24 - 24. Let u(a) = 5*c(a) - 4*s(a). Suppose u(p) = 0. Calculate p.
-1, 0, 1
Let j(u) = u**3 - u**2 - u + 1. Let p(q) = 3*q**3 + q**2 - 8*q - 6. Let s(d) = 2*j(d) - p(d). Factor s(c).
-(c - 2)*(c + 1)*(c + 4)
Let z be 2 + (2 + -2)*1. Factor -o - 2*o + 0*o + o**2 + z.
(o - 2)*(o - 1)
Suppose 162 = b + 26*b. Determine y, given that -6 - 3/2*y**2 - b*y = 0.
-2
Let q(i) be the first derivative of -i**6/3 - 2*i**5/5 + i**4/2 + 2*i**3/3 + 4. Factor q(f).
-2*f**2*(f - 1)*(f + 1)**2
Suppose 4*x + 5*m + 17 = 0, 2*x + 0*x + 5*m + 21 = 0. Solve 2*w + 2/3*w**3 - x*w**2 - 2/3 = 0 for w.
1
Let q = 21 + -10. Suppose 4*g = q - 3. Solve 8/5*c - 2/5*c**g - 8/5 = 0.
2
Suppose 2*m - 4*x - 200 = 7*m, 4*m + 139 = x. Let j = m + 38. Factor 3*d**4 - 6*d**3 - 3/2*d - 1/2*d**5 + 5*d**j + 0.
-d*(d - 3)*(d - 1)**3/2
Let f(c) be the second derivative of -c**5/90 + c**3/27 + 9*c. Factor f(p).
-2*p*(p - 1)*(p + 1)/9
Let w = 193/2460 - -1/205. Let k(i) be the second derivative of -4*i + 0 - i**2 + 1/6*i**3 + w*i**4. Factor k(a).
(a - 1)*(a + 2)
Let j(x) = -2*x - 3. Let o be j(-4). Let q be o/3 - (-1)/3. Suppose -c**3 + 4*c**3 - 2*c**3 + c**q = 0. Calculate c.
-1, 0
Suppose -4*c - 12 = -2*t, 0*t = 2*t + c - 2. Factor 11*g**2 - 1 - 5*g**t - 5 - 3*g**3 + 3*g.
-3*(g - 2)*(g - 1)*(g + 1)
Let k = 0 - 1. Let b = -7 - -6. Let q(n) = 1. Let a(g) = g**2 + 2*g - 1. Let h(o) = b*q(o) + k*a(o). Find c, given that h(c) = 0.
-2, 0
Let x = -148 + 297/2. Let j(o) be the first derivative of 0*o**2 + 2*o + 1/8*o**4 + 4 - x*o**3. Factor j(h).
(h - 2)**2*(h + 1)/2
Let d = 4 - 0. Suppose 0 = -d*m - 1 + 9. Find b such that 0*b**m - 1/4*b**4 - 3/2*b**5 + 0*b + 1/4*b**3 + 0 = 0.
-1/2, 0, 1/3
Solve 1/7*c**3 - 9/7 + 5/7*c**2 + 3/7*c = 0.
-3, 1
Let s(c) = -18*c**4 + 57*c**3 - 42*c**2 + 6*c + 3. Let u(t) = -t**4 - t**2 - t + 1. Let f(o) = s(o) + 3*u(o). Suppose f(g) = 0. Calculate g.
-2/7, 1
Let u(k) be the second derivative of 4/21*k**7 + 0 - k**4 - 1/5*k**5 + 0*k**2 + 8*k + 2/5*k**6 - 2/3*k**3. What is l in u(l) = 0?
-1, -1/2, 0, 1
Let l = 3114/7 + -444. Factor 0 + 2/7*s**2 - l*s.
2*s*(s - 3)/7
Let z(a) = -a**3 - 4*a**2 + 4*a - 5. Let n be z(-5). Let g = n - -3. Find d, given that -d**g - d + 0*d**3 - d**2 + 2*d**3 + 0*d + 1 = 0.
-1, 1
Let n(c) be the first derivative of -c**6/6 + c**5/5 + 3*c**4/4 - c**3/3 - c**2 + 3. Factor n(p).
-p*(p - 2)*(p - 1)*(p + 1)**2
Let x(h) be the second derivative of -1/21*h**3 + 0 + 1/21*h**4 + 1/70*h**5 - 2/7*h**2 + 3*h. Factor x(d).
2*(d - 1)*(d + 1)*(d + 2)/7
Let m = -6 - -10. Suppose m*h + 0 = 12. Factor -4*y**3 + y**h + 4*y**3.
y**3
Let q(u) be the third derivative of u**7/105 - u**6/30 - 2*u**5/15 + u**4/6 + u**3 + 8*u**2. Factor q(f).
2*(f - 3)*(f - 1)*(f + 1)**2
Suppose 4*h = 2*b + 10, -20 = -5*h - b + 5*b. Let z(t) be the third derivative of 1/20*t**5 + 1/4*t**4 + 0*t**3 + h - t**2 + 0*t. Factor z(w).
3*w*(w + 2)
Suppose 5*x - 37 = 73. Suppose 0*n = 3*n - 3*m - 15, 0 = -4*n + 5*m + x. Solve 1/3*c**n + 0 - 2/3*c**2 + 0*c = 0 for c.
0, 2
Let m be (-208)/104*((-30)/(-4))/(-3). Let v be 1/(-2) - 42/(-20). Solve 2/5*l + 6*l**3 + 0 - 14/5*l**2 - 26/5*l**4 + v*l**m = 0.
0, 1/4, 1
Let p(z) be the first derivative of -2*z**3/3 + 2*z**2 + 6*z + 20. Solve p(l) = 0.
-1, 3
Let o be (-2 + 0 + -1)*1/(-1). Factor -3/5*t**4 - 3/5*t**5 + 6/5*t + 9/5*t**o + 0 + 3*t**2.
-3*t*(t - 2)*(t + 1)**3/5
Suppose 4*z + 2*z = 12. Determine k so that 13 + 6*k**2 - 4*k - 4*k**z + 2*k**2 - 21 = 0.
-1, 2
Let o(r) be the second derivative of r**5/20 - r**4/12 - r**3/3 - 5*r. Factor o(s).
s*(s - 2)*(s + 1)
Let b(l) = -l**4 - 12*l**3 + 3*l**2 - 5. Let f(d) = 6*d**3 - 2*d**2 + 2. Let m(j) = 4*b(j) + 10*f(j). Factor m(v).
-4*v**2*(v - 2)*(v - 1)
Let g(z) be the first derivative of 2 - 1/3*z**3 - 2/3*z**2 - 3*z - 1/18*z**4. Let o(s) be the first derivative of g(s). Factor o(v).
-2*(v + 1)*(v + 2)/3
Suppose -w**4 + w**4 + 2*w**5 + 3*w**4 - w**4 = 0. What is w?
-1, 0
Let r be 2 - ((-4)/(-2) - 0). Let u be -1*(r - -4)*-1. Solve -g**2 - g**5 - 4*g**3 - 3*g**u - 2*g**3 + 3*g**3 = 0.
-1, 0
Let k = -4319/3 - -1441. Suppose k - 2/3*f**3 + 2*f + 0*f**2 = 0. Calculate f.
-1, 2
Let i = -103 + 107. Let r(w) be the first derivative of 2/5*w**5 + 1/2*w**i - w**2 - 2/3*w**3 + 0*w + 4. Solve r(h) = 0.
-1, 0, 1
Let d = -10 - -17. Factor d*q**4 - 8*q**3 - 4*q**5 + q**4 + 4*q**4.
-4*q**3*(q - 2)*(q - 1)
Suppose 3*t - 4*v = -t + 180, -4*v = -20. Suppose 0 = x - 4, -p + x = 3*p - 4. Find z, given that -14*z**3 - z + 9*z - 26*z**2 + t*z**p = 0.
-2/7, 0, 2
Let p(c) be the first derivative of 9*c**5 - 12*c - 1 + 7/4*c**6 - 11*c**3 + 87/8*c**4 - 27*c**2. Solve p(u) = 0.
-2, -1, -2/7, 1
Let m = 7 - 4. Let i(h) = 4*h - 3*h**3 + h**3 - 3*h**2 + 11 - 7*h - 3*h**3. Let t(o) = 2*o**3 + o**2 + o - 4. Let c(l) = m*i(l) + 8*t(l). Factor c(y).
(y - 1)**2*(y + 1)
Factor -1/2*j**3 - 16 + 0*j + 3*j**2.
-(j - 4)**2*(j + 2)/2
Let 3*d + 8*d**4 - 4*d**2 + 0*d - 3*d - 4*d**3 = 0. What is d?
-1/2, 0, 1
Let u = -26 + 28. Factor -2/5*j + 0 - 2/5*j**u.
-2*j*(j + 1)/5
Determine d so that 10*d**3 + d**4 - 24*d**3 + 11*d**4 - 3*d**5 + 2*d**3 = 0.
0, 2
Let h = 22 + -19. Suppose 0 = h*t - 5*t + 6. Factor 0*j + 1/5*j**t + 1/5*j**5 + 0*j**2 - 2/5*j**4 + 0.
j**3*(j - 1)**2/5
Let t = 3706/5 + -741. Factor t*u**4 + 0*u**3 + 2/5*u - 3/5*u**2 + 0.
u*(u - 1)**2*(u + 2)/5
Let r be 40/36*3 + -1*3. Let a(k) be the first derivative of 0*k**2 - k + r*k**3 - 3. Let a(y) = 0. What is y?
-1, 1
Let k = 10 - 24. Let s(p) = -p**3 + p**2 - 3*p - 3. Let n(g) = -2*g**3 + 3*g**2 - 7*g - 7. Let q(i) = k*s(i) + 6*n(i). Let q(f) = 0. Calculate f.
-2, 0
Let h(j) = 65*j**5 + 55*j**4 - 60*j**3 + 25*j - 25. Let n(b) = -11*b**5 - 9*b**4 + 10*b**3 - 4*b + 4. Let y(p) = 4*h(p) + 25*n(p). Find i, given that y(i) = 0.
-1, 0, 2/3
Factor 2/15*j**5 + 2/5*j**3 - 2/15*j**2 - 2/5*j**4 + 0*j + 0.
2*j**2*(j - 1)**3/15
Let s(z) be the second derivative of -z**6/105 - z**5/35 + z**4/14 + 4*z**3/21 - 4*z**2/7 + 6*z. Suppose s(d) = 0. What is d?
-2, 1
Let p(d) be the second derivative of 0 + 1/9*d**4 - 2/45*d**6 + 0*d**2 + 1/63*d**7 + 0*d**5 - 1/9*d**3 - 3*d. Let p(v) = 0. What is v?
-1, 0, 1
Let l be 1/(-3) - (-152)/(-12). Let v be l/(-4) - (-2)/(-8). Let -6*w**3 + 3*w**v - w**4 + w**2 + 0*w**4 + 3*w**5 = 0. What is w?
-1, 0, 1/3, 1
Let q(u) = u - 6. Let o be q(6). Suppose v - 2*v + 2 = o. Suppose -4*b**2 - b**5 + b + 2*b**2 + v*b**4 + 0*b**2 = 0. What is b?
-1, 0, 1
Let j(n) = 3*n**3 - 2*n**2 + 3*n. Let o(h) = 13*h**3 - 8*h**2 + 13*h. Let r be (3/(-5))/(3/(-45)). Let p(t) = r*j(t) - 2*o(t). Determine m, given tha