-16)/12). Let v(n) be the first derivative of 0*n - 2/9*n**6 + 2 + 1/9*n**3 - t*n**4 + 0*n**2 + 3/5*n**5. Solve v(d) = 0 for d.
0, 1/4, 1
Let s(d) = -d**3 - d + 1. Let l(v) = 5*v**5 - 25*v**4 + 20*v**3 - 50*v**2 - 5*v + 25. Let n(c) = l(c) - 30*s(c). Factor n(o).
5*(o - 1)**5
Suppose -4*w + 8 + 0 = 0. What is j in 4*j**4 - 2 + 0*j**3 - 4*j**3 - w*j**4 + 4*j = 0?
-1, 1
Let r = -1 + 3. Factor -1 + 7*h**3 - h**3 + 3*h - 6*h - r*h**3.
(h - 1)*(2*h + 1)**2
Let a(b) be the first derivative of -2*b**5/5 - b**4 - 2*b**3/3 - 4. Factor a(t).
-2*t**2*(t + 1)**2
Let y be (-20)/(-16)*(-6)/(-5). Let a(x) be the first derivative of 2 - 8/3*x**3 - x**2 + 0*x - y*x**4. Factor a(v).
-2*v*(v + 1)*(3*v + 1)
Factor 3/4*o - 3/2*o**2 + 0 + 3/4*o**3.
3*o*(o - 1)**2/4
What is x in -4*x**2 - 17*x**5 + 24*x**5 + 7*x**4 - 8*x**3 - 2*x**5 = 0?
-2, -2/5, 0, 1
Let s = -454/3 + 911/6. Factor s*f + 1/2*f**2 + 0.
f*(f + 1)/2
Let l be -11*(-16)/1056 - (-22)/12. Factor -1/8*u**l - 1/2*u + 0.
-u*(u + 4)/8
Find x such that -12 + 3/2*x**3 - 3/2*x**2 - 15*x = 0.
-2, -1, 4
Let p(t) be the second derivative of -5*t**7/63 - 2*t**6/45 + t**5/6 + t**4/9 + 34*t. Determine n, given that p(n) = 0.
-1, -2/5, 0, 1
Let f = 423 + -423. Factor 4/5*y**2 + 0*y - 6/5*y**3 + 2/5*y**4 + f.
2*y**2*(y - 2)*(y - 1)/5
Factor 4/7 + 26/7*k + 40/7*k**2 + 18/7*k**3.
2*(k + 1)**2*(9*k + 2)/7
Let y(c) be the first derivative of 0*c**2 - 1/2*c**3 - 3 + 0*c + 3/4*c**4 - 3/10*c**5. Factor y(q).
-3*q**2*(q - 1)**2/2
Let j(o) = o**2. Let z(s) = 2. Let u be ((-2)/(-5))/(2/(-10)). Let b(q) = u*j(q) + z(q). Find n, given that b(n) = 0.
-1, 1
Let a(k) = -8*k**4 + 32*k**3 - 59*k**2 + 32*k - 8. Let v(u) = 4*u**4 - 16*u**3 + 30*u**2 - 16*u + 4. Let m(d) = -6*a(d) - 11*v(d). Let m(b) = 0. What is b?
1
Let h(p) be the second derivative of p**4/54 + p**3/27 + 4*p. Factor h(y).
2*y*(y + 1)/9
Let u(x) be the third derivative of -x**8/1120 + x**7/560 + x**6/240 - x**5/80 + x**3/2 + 4*x**2. Let c(v) be the first derivative of u(v). Factor c(y).
-3*y*(y - 1)**2*(y + 1)/2
Let j(v) be the second derivative of -v**6/360 + v**5/120 + v**3/2 + v. Let q(w) be the second derivative of j(w). Factor q(t).
-t*(t - 1)
Let n(t) be the first derivative of -t**5/300 + t**4/60 - t**3/30 - 3*t**2/2 - 2. Let x(i) be the second derivative of n(i). Suppose x(d) = 0. What is d?
1
Let w(l) be the second derivative of 0*l**2 + 1/147*l**7 + 0 + 0*l**6 + 1/21*l**3 + 0*l**4 - 1/35*l**5 + 2*l. Factor w(s).
2*s*(s - 1)**2*(s + 1)**2/7
Factor -1/3 - 4*u**2 - 2*u - u**4 - 10/3*u**3.
-(u + 1)**3*(3*u + 1)/3
Determine y so that -2 + 2*y**2 + 2/7*y - 2/7*y**3 = 0.
-1, 1, 7
Suppose 0 = 5*s + v - 2 - 14, -10 = -3*s - v. Let d = 2 + -2. What is h in -1/6*h**s - 1/6*h + 1/3*h**2 + d = 0?
0, 1
Let c(w) be the first derivative of w**6/45 - w**5/10 + w**4/18 + w**3/3 - 2*w**2/3 - 6*w + 2. Let z(l) be the first derivative of c(l). Factor z(g).
2*(g - 2)*(g - 1)**2*(g + 1)/3
Suppose 5*s - 25 - 215 = 0. Let u be (-2)/5 - s/(-60). Solve -2/5*y**2 + 4/5 + u*y = 0 for y.
-1, 2
Let l(k) be the second derivative of 3*k**5/80 - k**4/8 - 7*k**3/8 - 3*k**2/2 + 2*k + 33. Factor l(p).
3*(p - 4)*(p + 1)**2/4
Let a = -1 - -14/15. Let j = a + 17/30. Factor -q + j*q**2 + 1/2.
(q - 1)**2/2
Let b(z) be the third derivative of 0*z**4 + 0 + 0*z + 1/120*z**6 + 2*z**2 - 1/60*z**5 + 0*z**3. Factor b(m).
m**2*(m - 1)
Let 2*c + 4/7*c**3 - 2*c**2 - 4/7 = 0. Calculate c.
1/2, 1, 2
Let f(k) be the second derivative of 1/9*k**3 + 0 - 1/12*k**4 + 1/6*k**2 + 2*k. Factor f(a).
-(a - 1)*(3*a + 1)/3
Let c(f) be the second derivative of -f**6/150 + f**5/50 + f**4/60 - f**3/15 + 4*f. Find w, given that c(w) = 0.
-1, 0, 1, 2
Let k = 40741/60 - 679. Let c(b) be the second derivative of 1/12*b**4 - k*b**5 - 4*b + 0 - 1/6*b**3 + 1/6*b**2. Find m such that c(m) = 0.
1
Let x(d) = d**4 + d**3 + d**2 - d + 1. Let n(u) = 13*u**4 - 6*u**3 + 25*u**2 - 12*u + 7. Let h(f) = 2*n(f) - 18*x(f). What is t in h(t) = 0?
-1/4, 1, 2
Suppose 0 = 7*w - 2*w - 15. Let j(r) = -r**2 + 5*r + 2. Let n be j(5). Find a such that -a**2 + 0*a**w + a**2 + 4*a**n + a**3 + 4*a = 0.
-2, 0
Suppose -27*i = -35*i + 16. Factor -2/3 - 2*k**i - 2*k - 2/3*k**3.
-2*(k + 1)**3/3
Suppose 1/9*x**5 - 2/9*x**2 - 2/9*x**3 + 1/9*x + 1/9 + 1/9*x**4 = 0. Calculate x.
-1, 1
Let b(t) = -t**3 - 6*t**2 + 2*t + 14. Let j be b(-6). Suppose -10 = -5*u - 0. Factor -2*o**u - j*o**2 - o**4 + 5*o**2.
-o**2*(o - 1)*(o + 1)
Factor 0 + 2/3*a**3 + 0*a**2 - 1/3*a + 0*a**4 - 1/3*a**5.
-a*(a - 1)**2*(a + 1)**2/3
Let n(r) be the third derivative of r**6/1080 + r**5/540 - r**4/54 - 2*r**3/27 + 33*r**2. Factor n(y).
(y - 2)*(y + 1)*(y + 2)/9
Let r(c) be the first derivative of 6*c - 4*c + 0*c + 4*c**4 - 2 + 6*c**2 + 8*c**3. Factor r(t).
2*(2*t + 1)**3
Suppose -z + 4 + 0 = 0. Let a = 2 + 1. Factor 0*d**2 + 1/3*d**5 + 0*d**a + 0 + 1/3*d**z + 0*d.
d**4*(d + 1)/3
Suppose -3*f = -4*f + 2. Let b = 0 + 0. Factor -8/3*k**f + b - 4*k**3 - 2*k**4 - 1/3*k**5 + 0*k.
-k**2*(k + 2)**3/3
Let t(o) be the second derivative of o**6/120 + o**5/60 - o**2/2 + o. Let a(w) be the first derivative of t(w). Factor a(u).
u**2*(u + 1)
Suppose -3*n - 35*n + 114 = 0. Factor 0 + 1/5*a**n - 2/5*a + 1/5*a**2.
a*(a - 1)*(a + 2)/5
Let h(g) = -5*g**5 - 21*g**4 - g**3 + 9*g - 9. Suppose 27 = 2*q + q. Let j(y) = y**5 + 5*y**4 - 2*y + 2. Let o(b) = q*j(b) + 2*h(b). Factor o(s).
-s**3*(s - 2)*(s - 1)
Let t(u) be the third derivative of u**7/21 - u**6/15 - u**5/30 - 2*u**2. Determine q so that t(q) = 0.
-1/5, 0, 1
Suppose -2*w + w + 2 = 0. Suppose d - o - 3 = 0, 2*d + 4*o - 4 = -w*d. Factor -3*q**3 + q**4 - 2*q**5 + 2*q**4 + q**5 + q**d.
-q**2*(q - 1)**3
Let w(z) be the third derivative of 0*z**4 + 0*z - 1/1365*z**7 + 0*z**5 + 1/2184*z**8 + 0*z**3 + 0*z**6 + 3*z**2 + 0. Find n, given that w(n) = 0.
0, 1
Let r(d) be the second derivative of -d**7/5040 - d**6/720 - d**5/240 + d**4/6 + 3*d. Let j(q) be the third derivative of r(q). Factor j(y).
-(y + 1)**2/2
Let f(o) be the first derivative of o**7/147 + o**6/105 + 5*o + 3. Let n(g) be the first derivative of f(g). Factor n(p).
2*p**4*(p + 1)/7
Let k(y) = 139*y**4 + 115*y**3 - 32*y**2 - 12*y - 4. Let z(h) = -h**4 - h**3 - h**2 + 1. Let x(n) = k(n) + 4*z(n). Solve x(v) = 0.
-1, -2/9, 0, 2/5
Let o(b) be the first derivative of b**6/180 + b**5/60 - b**4/6 - b**3 + 2. Let d(l) be the third derivative of o(l). Solve d(u) = 0 for u.
-2, 1
Factor 2/5 - 1/5*y**4 - 1/5*y**3 + 3/5*y**2 + y.
-(y - 2)*(y + 1)**3/5
Suppose 2*u + 8 = 5*o + 4*u, 3*u = -2*o + 1. Suppose -o - 2 = -2*s. Factor -4*l - 2 + 0 - 2*l**s + 0*l**2.
-2*(l + 1)**2
Let c(n) = -3*n**2 + n - 4. Let f be 2/(-1 - (-21)/15). Let j(a) = -a + 4*a**2 + f + 0 + 0*a. Let u(r) = -5*c(r) - 4*j(r). Solve u(y) = 0.
-1, 0
Let v be 1 + 1 + (17 - 1). Suppose 3*h - 25 = 2*x - 10, 3*h - 3*x - v = 0. Solve -6*t**2 - t - t**3 - 2 - 5*t - t**h = 0 for t.
-1
Let p(w) be the first derivative of -3 - 3*w + w**3 + 3/2*w**2 - 3/4*w**4. Determine f, given that p(f) = 0.
-1, 1
Let g = -878 - -880. Find u, given that -3/2*u**g + 9*u - 27/2 = 0.
3
Let q(s) be the first derivative of -6*s**5/5 + 51*s**4/8 - 12*s**3 + 39*s**2/4 - 3*s + 2. Suppose q(z) = 0. Calculate z.
1/4, 1, 2
Let m(i) be the first derivative of i**6/120 - i**5/80 - i**4/48 + i**3/24 + 3*i + 2. Let w(c) be the first derivative of m(c). Factor w(g).
g*(g - 1)**2*(g + 1)/4
Let n = -8 - -12. Factor 3*f**2 + 0*f + 2*f - f**2 - n*f**2.
-2*f*(f - 1)
Let b(z) = z. Suppose -6*v + 7*v = 0. Let r be b(v). Solve r - 2/7*f**4 + 2/7*f**2 - 2/7*f + 2/7*f**3 = 0 for f.
-1, 0, 1
Let b = -9746/15 - -650. Factor -14/15*f**2 - b*f + 0 - 2/5*f**3.
-2*f*(f + 2)*(3*f + 1)/15
Let x(f) be the first derivative of -5*f**4/4 - 10*f**3 - 30*f**2 - 40*f + 15. Let x(r) = 0. Calculate r.
-2
Let u(f) = f**2 + 1. Let p(h) = h**3 - 10*h**2 + 3*h - 8. Let n(d) = -3*p(d) - 21*u(d). Determine w so that n(w) = 0.
1
Let b(w) = 13*w**3 - 2*w**2 + 7*w + 6. Let p(m) = -15*m**3 + 2*m**2 - 8*m - 7. Let y(f) = -7*b(f) - 6*p(f). Suppose y(x) = 0. Calculate x.
0, 1
Suppose 5*g + 1 = -0*t - t, 3*g = 2*t + 2. Let u(z) = 2*z**2 + 2*z - 1. Let q be u(1). Factor g*i - 2*i**q + 1 - 3*i**2 + 0*i.
-(i + 1)**2*(2*i - 1)
Let a(z) be the first derivative of -10*z**3/3 - 12*z - 1. Let o(u) = u**2 + 1 + 0 + 0. Let j(n) = -a(n) - 12