. Factor 2/7*n**2 + p + 2/7*n.
2*n*(n + 1)/7
Let f = 6 - -13. Suppose -z + f = 4*s, -3 + 21 = 3*s + 2*z. Factor 0 + 2/9*y**2 - 4/9*y**3 + 2/9*y**s + 0*y.
2*y**2*(y - 1)**2/9
Let h(f) = f**3 + 4*f**2 + 2*f - 1. Let i be h(-2). Let w be (1/((-10)/4))/(3/(-5)). Factor 20/3*b**2 + 10/3*b + 10/3*b**4 + 2/3 + 20/3*b**i + w*b**5.
2*(b + 1)**5/3
Suppose 5*f + 9 = 3*o, -5*f - 15 = -5*o - 7*f. Let h(z) be the first derivative of 1/2*z**o + 1 - 3/2*z - 3/8*z**4 + 3/4*z**2. Factor h(j).
-3*(j - 1)**2*(j + 1)/2
Let m = 3/5 - 0. Factor 0 + m*x - 3/5*x**2.
-3*x*(x - 1)/5
Let z(c) = -c**3 - 2*c**2. Let j be z(-2). Let l(k) = -k**2 + 10*k - 24. Let w be l(4). Factor j*o - 2/5*o**2 + 2/5*o**3 + w.
2*o**2*(o - 1)/5
Let o(g) be the second derivative of g**5/70 + g**4/7 + 4*g**3/7 + 8*g**2/7 - 12*g. Find c, given that o(c) = 0.
-2
Let w = 28 - 17. Factor -a**3 - 9*a**2 - 1 + w*a - 26 - 38*a.
-(a + 3)**3
Let 2/5*w + 0 - 4/5*w**2 + 2/5*w**3 = 0. What is w?
0, 1
Let i(d) = -7*d**5 + 41*d**3 - 9*d**2 - 7*d. Let b(q) = 2*q**5 - 10*q**3 + 2*q**2 + 2*q. Let v(u) = -9*b(u) - 2*i(u). Factor v(t).
-4*t*(t - 1)**2*(t + 1)**2
Factor 39*k - 19*k - 2*k**2 - 2*k**2.
-4*k*(k - 5)
Let o(q) = -q**5 - q**4 + q**3 - 1. Let s(u) = 4*u**5 - 26*u**4 + 51*u**3 - 50*u**2 + 25*u - 6. Let f(t) = o(t) - s(t). Suppose f(n) = 0. Calculate n.
1
Suppose -4 = -t - a, 4*t = a - 2 + 8. Determine u, given that -4/3*u**2 + t*u + 4/3 - 2*u**3 = 0.
-1, -2/3, 1
Suppose 3*c = 44 - 17. Let a be (2/(-3))/((-2)/c). Factor -a - 2*n - 2*n - n**2 - 1.
-(n + 2)**2
Let n(a) be the second derivative of a**4/60 - a**3/30 - 14*a. What is s in n(s) = 0?
0, 1
Solve 24*s**3 - 3 + 0 + 48*s**2 + 3*s**4 + 3 = 0 for s.
-4, 0
Suppose 20 = -5*d, 3*y + 5*d + 0*d - 13 = 0. Suppose 2*i**2 - y*i**4 - i**3 - 4*i**4 + 13*i**4 + i = 0. Calculate i.
-1, -1/2, 0, 1
Let o(y) be the third derivative of -y**8/4200 - 5*y**3/6 - 3*y**2. Let h(j) be the first derivative of o(j). Factor h(i).
-2*i**4/5
Factor i**4 + 6*i**4 - 8*i**2 + 8*i**3 - 2*i - 2*i - 4*i**5 + 4 - 3*i**4.
-4*(i - 1)**3*(i + 1)**2
Factor -16/3*k - 4/3*k**2 - 4.
-4*(k + 1)*(k + 3)/3
Find n such that 302*n - 30*n**3 + 6*n**5 + 13*n - 2*n**5 + 18*n**4 - 150 - n**5 - 156*n**2 = 0.
-5, 1, 2
Find b, given that 3/5*b**2 + 1/5*b**4 + 0 - 4/5*b**3 + 0*b = 0.
0, 1, 3
Let s = -14 + 21. Suppose 0 = 5*d + s - 17. Factor -6/5*k**4 + 0*k + 2/5*k**5 - 2/5*k**d + 0 + 6/5*k**3.
2*k**2*(k - 1)**3/5
Let p = -4 + 8. Let g be (-3)/(-2) + 2/p. Suppose -j**2 + 0*j**2 - g*j**3 - j**2 = 0. Calculate j.
-1, 0
Let y(m) = m**2 - 8*m - 7. Let s be y(9). Factor -1/3*q**3 - 1/3 + 1/3*q + 1/3*q**s.
-(q - 1)**2*(q + 1)/3
Let v = 1/67 - -63/268. Suppose 1/4*u**2 - v*u + 0 = 0. What is u?
0, 1
Let l(h) be the third derivative of -h**5/60 + h**3/6 - 7*h**2. Let g(d) = 3*d**2 + 2*d - 5. Let j(b) = -2*g(b) - 4*l(b). Find q such that j(q) = 0.
-3, 1
Let c(t) be the second derivative of t**4/18 - 7*t**3/9 + 2*t**2 + t. Let c(d) = 0. What is d?
1, 6
Let s(a) be the first derivative of 2 - 2/5*a + 1/15*a**3 - 1/10*a**2. What is k in s(k) = 0?
-1, 2
Suppose -4 = -w - a, w + 0*a + 8 = 5*a. Let h(o) be the first derivative of -1/3*o**3 + 0*o**w + o - 2. Factor h(y).
-(y - 1)*(y + 1)
Determine t, given that 5*t + 7*t**2 + t**2 - 11*t**3 + 15*t**3 + 1 = 0.
-1, -1/2
Let z = -28 + 33. Let q(l) be the first derivative of 3/2*l**4 + 1/6*l**6 + 2 + 0*l - 4/5*l**z - 4/3*l**3 + 1/2*l**2. Let q(m) = 0. What is m?
0, 1
Let s(k) be the first derivative of -k**4/28 + 4*k**3/21 + 3*k**2/14 - 18*k/7 + 12. Factor s(r).
-(r - 3)**2*(r + 2)/7
Suppose i + 5*q = 8, 4*i + 2*q + 16 = 2*i. Let g be ((-16)/i)/((-2)/(-3)). Determine j, given that -3*j**4 + 2*j**4 - j**3 + j + 3*j**2 - g*j**2 = 0.
-1, 0, 1
Let x = -5 + 8. Suppose x*z + 21 = 5*g, -2*z = -4*g + 3*g + 7. Solve 0 + 2/5*p - 2/5*p**g + 0*p**2 = 0.
-1, 0, 1
Let z(w) = -w**5 - w**3 + w**2. Let o(j) = -6*j**5 - 9*j**4 - 9*j**3 + 9*j**2 + 9*j + 3. Let m(q) = -o(q) + 3*z(q). Solve m(a) = 0.
-1, 1
Let b = 24 + -21. Suppose b*n - 4*n - 3*d = 3, 2*d = 3*n - 2. Suppose 0 + 4/5*y**2 - 2/5*y + 2/5*y**5 - 4/5*y**4 + n*y**3 = 0. What is y?
-1, 0, 1
Let c(f) = 51*f**3 - 67*f**2 - 91*f + 37. Let s(m) = 26*m**3 - 34*m**2 - 46*m + 18. Let q(h) = -2*c(h) + 5*s(h). Suppose q(u) = 0. Calculate u.
-1, 2/7, 2
What is t in t**2 - 79 - 5*t + 0*t**2 + 83 = 0?
1, 4
Let a(y) be the first derivative of -y**5/20 + y**4/12 + y**3/6 - y**2/2 - 4*y - 2. Let u(d) be the first derivative of a(d). Factor u(s).
-(s - 1)**2*(s + 1)
Suppose 2*l + 7 - 31 = 0. Let s be (-3)/l - (-22)/24. Let s + 2/3*p - 2/3*p**2 - 2/3*p**3 = 0. What is p?
-1, 1
Let x be 22/99 - (-4)/(-18). Let z be (x - 1)*(-10 - -10). Factor 2/5*u**4 - 4/5*u**3 + 0*u + 2/5*u**2 + z.
2*u**2*(u - 1)**2/5
Let o be -1*12/18 + 1. Factor -1/3 - o*j**2 + 2/3*j.
-(j - 1)**2/3
Let t(y) = -120*y**2 - 4*y + 16. Let q(o) = 80*o**2 + 3*o - 11. Let z = -2 + 7. Let f(c) = z*t(c) + 8*q(c). Factor f(s).
4*(2*s + 1)*(5*s - 2)
Suppose -4*n = 2*h - 38, -2*n - 3*n - 3*h + 50 = 0. Find i, given that 10*i - 1 - 5*i - i**2 - n*i = 0.
-1
Suppose 8/3*r - 4/3*r**2 + 0 = 0. Calculate r.
0, 2
Let a be (-2)/(-10)*(-3 + (-115)/(-30)). Factor 5/6*t**3 + 1/6*t**2 - a*t**4 - 1/6*t**5 + 2/3 - 4/3*t.
-(t - 1)**3*(t + 2)**2/6
Let n(q) be the first derivative of -1/4*q**2 - 3 - 3/4*q**3 + 0*q - 3/4*q**4 - 1/4*q**5. Factor n(s).
-s*(s + 1)**2*(5*s + 2)/4
Let p(q) be the first derivative of -2*q**5/55 + 9*q**4/22 - 28*q**3/33 + 58. Factor p(b).
-2*b**2*(b - 7)*(b - 2)/11
Suppose -4*z = 2*q + 4 - 24, -15 = 2*q - 3*z. Let w = -6/77 + 4/11. Determine m so that 0*m + 0 - 2/7*m**5 + q*m**2 + w*m**3 + 0*m**4 = 0.
-1, 0, 1
Find b such that 2/7 + 1/7*b**4 + 5/7*b**3 + b + 9/7*b**2 = 0.
-2, -1
Suppose 29 = 3*h - 4. Let f = -38 + 70. Factor 8*t**4 + 6*t**4 + 4*t + f*t**3 + h*t**2 + 11*t**2.
2*t*(t + 1)**2*(7*t + 2)
Let l(f) be the third derivative of -2*f**2 + 1/60*f**5 + 0*f**4 + 0*f**3 + 0*f + 0. Factor l(z).
z**2
Let h(d) be the first derivative of -1/5*d**5 + 1/12*d**6 - 5 - 1/4*d**2 + 0*d + 0*d**4 + 1/3*d**3. Factor h(t).
t*(t - 1)**3*(t + 1)/2
Let f(o) be the third derivative of 0*o + 0*o**3 + 0 - 1/84*o**4 - 2/735*o**7 + 1/105*o**5 + 1/1176*o**8 + 0*o**6 - 3*o**2. Let f(m) = 0. Calculate m.
-1, 0, 1
Let d(c) be the first derivative of -3 + 0*c**3 - 9/2*c**2 - 6*c + 3/4*c**4. Determine j so that d(j) = 0.
-1, 2
Let s(z) = -z**3 - z**2 - z. Let g(k) = -3*k**4 + 16*k**3 + 16*k**2 + 6*k - 2. Let u(n) = 2*g(n) + 22*s(n). Determine p, given that u(p) = 0.
-1, -1/3, 1, 2
Let w = -16 + 22. Suppose m + w = 4*m. Determine r so that -10*r**m + 11*r**2 + 2*r - r = 0.
-1, 0
Let m be 5 - 3*(-2)/(-3). Factor 2*n - n**m - 4*n**2 + 2 + 2 - n**3.
-2*(n - 1)*(n + 1)*(n + 2)
Let w = 16 + -11. Suppose 0 = u - w, -5*k + u = -2*u. Factor -p**2 + 0*p**k + p**3 - 4*p + 2*p.
p*(p - 2)*(p + 1)
Let x be (-1)/(-9)*12 + -1. Factor x*i**4 - 2/3 - i + i**3 + 1/3*i**2.
(i - 1)*(i + 1)**2*(i + 2)/3
Let k(l) be the second derivative of -l**5/120 - l**4/48 - 3*l**2/2 + 6*l. Let d(j) be the first derivative of k(j). Let d(f) = 0. Calculate f.
-1, 0
Let t(n) = -n**2 + 8*n + 2. Let f be t(8). Factor f*i + 1 + i + i**2 + 0*i**2 - i.
(i + 1)**2
Let v(h) = -h**5 - h**3 + h**2 - h. Let w(y) = 5*y**5 + 2*y**4 - y**3 - 7*y**2 + 5*y + 2. Let z(d) = 3*v(d) + w(d). Factor z(l).
2*(l - 1)**2*(l + 1)**3
Factor 2/9*k**2 + 1/9*k**3 + 0*k + 0.
k**2*(k + 2)/9
Let k(h) be the third derivative of -h**6/420 + h**4/84 - 14*h**2. Factor k(z).
-2*z*(z - 1)*(z + 1)/7
Let q be 1 - (-64)/(3 - 4). Let h be (-6)/27 - 230/q. Solve -2*b**2 + h*b + 8/7 = 0.
-2/7, 2
Factor 3/2*w**2 + 33/8*w - 9/8.
3*(w + 3)*(4*w - 1)/8
Suppose 2 = z + 10. Let l be z/(-12) + -2 - -2. Factor 0 + l*m + 2/3*m**2.
2*m*(m + 1)/3
Determine c, given that 4*c**2 - 6*c**3 + 2*c**3 + 3*c**3 - 3*c = 0.
0, 1, 3
Factor -8*c**2 - 7*c**2 + 2*c**3 + 23*c**2.
2*c**2*(c + 4)
Factor 52*x**3 + 12*x**4 - 44*x**3 - 17*x**4 - x**5 + 48*x**2.
-x**2*(x - 3)*(x + 4)**2
Let k(c) be the first derivative of 3/14*c**4 - 2/7*c**3 + 1 - 2/35*c**5 + 1/7*c**2 + 0*c. Factor k(a).
-2*a*(a - 1)**3/7
Let v be -2*3/6*-2. Suppose -2*g + 6 = 2*g + v*f, 4*f + 15 = g. Factor -2*d**3 + 3*d - 6*d**2 - 3*d**3 + 8*d**g.
3*d*(d - 1)**2
Let w(n) be the third derivative of 0*n + 0 + 0*n**4 + 0*n**3 - 1/120*n**6 + 3*n**2 + 0