*p*(p - 1)*(p + 1)
Factor 1/3*s**5 + 0*s**2 + 1/3*s**3 + 2/3*s**4 + 0 + 0*s.
s**3*(s + 1)**2/3
Factor -5*d**2 + 5*d**4 + 0*d**5 + 29*d**3 - 24*d**3 - d**5 - 4*d**5.
-5*d**2*(d - 1)**2*(d + 1)
Suppose -2*z - 3*v = -0*z + 1, -2*z + 2*v = -14. Factor 3*k**3 - 4*k**2 + k**5 - 2*k**5 - 6*k + k + k + 2*k**z.
-k*(k - 2)**2*(k + 1)**2
Let f(x) = 4 + 0 - 3. Let i = 55 + -33. Let n(c) = 2*c**2 - c + 11. Let p(t) = i*f(t) - 2*n(t). Factor p(g).
-2*g*(2*g - 1)
Let k be (5/90)/(20/6). Let q(v) be the third derivative of 4/3*v**3 - 2/3*v**4 - k*v**6 + 1/6*v**5 - 2*v**2 + 0*v + 0. Factor q(f).
-2*(f - 2)**2*(f - 1)
Let x = -2444/9 - -272. What is a in x - 2/9*a**2 - 2/9*a = 0?
-2, 1
Let v(z) be the second derivative of -z**8/1680 + z**7/840 + z**3/2 + 3*z. Let m(l) be the second derivative of v(l). Factor m(n).
-n**3*(n - 1)
Find n such that 10/3*n**5 - 4/3*n - 2/3*n**2 + 26/3*n**4 + 0 + 6*n**3 = 0.
-1, 0, 2/5
Suppose -1/2*n**2 + 1/2*n**4 + 0 - 1/2*n**3 + 1/2*n = 0. What is n?
-1, 0, 1
Let t be 1/2*(1 - -3). Factor 0 + 2 - 2*o**4 + 0 - 4*o**t + 4*o**4.
2*(o - 1)**2*(o + 1)**2
Let r(m) be the first derivative of 3/5*m**2 + 1/10*m**4 - 2/5*m - 2/5*m**3 - 5. Solve r(c) = 0.
1
Let a(n) be the second derivative of 0*n**3 + 0*n**2 + 1/50*n**6 + 1/20*n**4 + 0 - 6*n - 3/50*n**5. Factor a(s).
3*s**2*(s - 1)**2/5
Let y be (-2 - 1) + (-28)/(-147). Let a = -15/7 - y. Find u, given that -2/3*u - 2/9*u**3 + 2/9 + a*u**2 = 0.
1
Let l(p) be the first derivative of 0*p**2 - p + 2 + 1/3*p**3. Solve l(h) = 0.
-1, 1
Let g(l) be the second derivative of 5*l + 0 + 1/2*l**2 - 1/12*l**4 + 0*l**3. Factor g(i).
-(i - 1)*(i + 1)
Solve -81/7*a**5 + 27/7*a - 78/7*a**2 + 81/7*a**4 + 54/7*a**3 - 3/7 = 0 for a.
-1, 1/3, 1
Let h be 4 + (-3 + 3)/(-1). Factor h*n**2 + 6*n - 3*n**2 + 2*n**3 - 2 - 7*n**2.
2*(n - 1)**3
Let f = 15 - 13. Factor -f*x**2 - 3*x + x - 2*x.
-2*x*(x + 2)
Let m(v) be the third derivative of -v**8/224 + v**7/42 - v**6/20 + v**5/20 - v**4/48 + 11*v**2. What is u in m(u) = 0?
0, 1/3, 1
Let a = -66 - -44. Let n be 22/45 - a/55. Factor 2/9*v**2 + 8/9 - n*v.
2*(v - 2)**2/9
Let m(i) be the third derivative of -i**7/735 - i**6/105 - i**5/42 - i**4/42 - 31*i**2. Factor m(g).
-2*g*(g + 1)**2*(g + 2)/7
Factor -2*t**3 + 4*t**3 - 3 + 3*t**2 - 5*t**3 + 3*t + 0*t**2.
-3*(t - 1)**2*(t + 1)
Let h(f) = 6*f**4 + 10*f**3 - 20*f**2 - 72*f - 48. Let b(t) = 2*t**4 + 3*t**3 - 7*t**2 - 24*t - 16. Let y(j) = -8*b(j) + 3*h(j). Find x such that y(x) = 0.
-2, -1, 2
Let t be (-1)/(-1) + 412/(-36). Let k = 233/18 + t. Factor -5/2*a**3 - k*a**2 - 1/4 - 5/4*a**4 - 5/4*a - 1/4*a**5.
-(a + 1)**5/4
Let o = -30 - -35. Let v be 0/(2 - o) - -2. Factor 3*h**3 + 1/2*h**5 - v*h**4 + 1/2*h - 2*h**2 + 0.
h*(h - 1)**4/2
Let z(q) be the third derivative of 0*q + 0*q**3 + 0 + 0*q**4 + 1/270*q**5 + q**2. Factor z(u).
2*u**2/9
Let j(b) = -12*b + 18. Let c(p) = p**2 + 24*p - 36. Let x(k) = -2*c(k) - 5*j(k). Determine u, given that x(u) = 0.
3
Suppose 3*q - 3*s + 30 = 0, -q - 3 - 9 = -2*s. Let n(p) = -2*p - 6. Let i be n(q). Factor -3*o - i*o**2 - o + 14*o**3 + 0*o**3.
2*o*(o - 1)*(7*o + 2)
Let b(j) = -3*j**3 + j**2 + j. Let q be b(-1). Let -2*h**q - 3*h**3 - h**2 + 4*h**3 = 0. Calculate h.
-1, 0
Let i(h) = 3*h**4 + 4*h**3 + 7*h**2 + h + 5. Suppose 7*v - 6*v = -4. Let d(w) = 2*w**4 + 4*w**3 + 6*w**2 + 4. Let s(r) = v*i(r) + 5*d(r). Factor s(p).
-2*p*(p - 2)*(p - 1)*(p + 1)
Suppose 16*u = 70 - 6. Suppose -1/3*w + 0 + 0*w**3 - 1/6*w**u + 1/2*w**2 = 0. Calculate w.
-2, 0, 1
Let u(n) be the second derivative of -2*n**6/45 + n**5/12 + n**4/12 - 5*n**3/18 + n**2/6 + n. Determine g so that u(g) = 0.
-1, 1/4, 1
Suppose -3*c - 40 = 2*l, 2*l - 5*l - c = 60. Let m be 1*4/l + 3. Let -m*q - 4/5 - 6/5*q**2 = 0. What is q?
-2, -1/3
Factor 79*i**2 + 127*i**2 + 160*i**2 + 85*i**4 - 400*i**3 - 5*i**5 - 46*i**2.
-5*i**2*(i - 8)**2*(i - 1)
Let k be (-3 - -6)*(-4)/(-30). Let m = 16/15 - 2/3. Find j, given that k*j - 4/5 + m*j**2 = 0.
-2, 1
Suppose 0*z**2 + 0*z + 0 + 1/4*z**3 + 1/4*z**4 = 0. Calculate z.
-1, 0
Suppose -2*o**5 + 0*o**5 - o**4 + 2*o**3 + o**4 = 0. What is o?
-1, 0, 1
Let g(w) be the third derivative of -w**8/56 - w**7/15 - w**6/12 - w**5/30 - 5*w**2. Factor g(x).
-2*x**2*(x + 1)**2*(3*x + 1)
Let w(z) be the first derivative of 10/27*z**3 + 1/27*z**6 + 0*z - 2/45*z**5 + 1 - 2/9*z**2 - 1/6*z**4. Factor w(m).
2*m*(m - 1)**3*(m + 2)/9
Suppose -u = -0*u - 1. Let g be (u + 0)*(7 - 5). Factor 0*q - 1/4*q**g + 1/4.
-(q - 1)*(q + 1)/4
Factor -2/3 + 2/3*o**2 + 2/3*o - 2/3*o**3.
-2*(o - 1)**2*(o + 1)/3
Let r(z) be the second derivative of 0*z**4 + z + 0 + 0*z**2 + 1/3*z**3 - 1/10*z**5. Find g, given that r(g) = 0.
-1, 0, 1
Let y(g) = 18*g**4 - 69*g**3 + 70*g**2 - 12*g. Let i(p) = -9*p**4 + 34*p**3 - 35*p**2 + 6*p. Let u(o) = 7*i(o) + 4*y(o). Factor u(n).
n*(n - 3)*(n - 1)*(9*n - 2)
Let j(a) be the first derivative of a**4/7 + 20*a**3/21 + 16*a**2/7 + 16*a/7 + 15. Factor j(d).
4*(d + 1)*(d + 2)**2/7
Let z be 1/1 - (8 + -2). Let p(b) be the first derivative of -4*b**3/3 + 9*b - 4. Let d(i) = 6*i**2 - 14. Let y(x) = z*d(x) - 8*p(x). Factor y(s).
2*(s - 1)*(s + 1)
Let g(q) be the second derivative of -q - 1/35*q**5 + 0*q**4 + 0 + 1/147*q**7 + 0*q**2 + 1/21*q**3 + 0*q**6. Factor g(t).
2*t*(t - 1)**2*(t + 1)**2/7
Suppose a - 4*a - 3*q - 6 = 0, 4*a = 3*q - 8. Let n = 5 + a. What is t in 0 + 0*t - 1/4*t**2 + 1/2*t**n - 1/4*t**4 = 0?
0, 1
Let n(k) be the second derivative of k**4/108 + k**3/18 + k**2/9 - k + 7. Factor n(c).
(c + 1)*(c + 2)/9
Let u be (-535)/25 + (-2)/(-5). Let c = u + 21. Factor -1/2*l**4 + 0 + c*l + l**3 - 1/2*l**2.
-l**2*(l - 1)**2/2
Let i(z) = -z + 2. Let r be i(5). Let q be ((-9)/12)/(r/12). Determine k, given that q*k - 2*k**2 - 3 - 2*k**3 + 4*k**2 + 4 - k**5 - 3*k**4 = 0.
-1, 1
Suppose 267*g - 240*g - 54 = 0. Factor 0*u - 2/3*u**3 + 1/3*u**g + 1/3*u**4 + 0.
u**2*(u - 1)**2/3
Let i(l) be the first derivative of 7*l**3/3 + 15*l**2 + 8*l - 38. Determine s so that i(s) = 0.
-4, -2/7
Let j(a) be the first derivative of 0*a + 2/35*a**5 + 0*a**2 - 2 + 0*a**3 - 1/14*a**4. Let j(x) = 0. What is x?
0, 1
Let t = -20 + 24. Determine v, given that -2/5*v**3 + 4/5*v**t + 0 - 2/5*v**5 + 0*v**2 + 0*v = 0.
0, 1
Let i be ((-4)/50)/((-20)/25). Let h(l) be the second derivative of 0*l**4 - 1/15*l**3 + 0 - 1/150*l**6 + i*l**2 + 1/50*l**5 - 3*l. Factor h(w).
-(w - 1)**3*(w + 1)/5
Let w = 0 - 0. Suppose -k = -w*k + 4*d - 23, 2*d = 5*k - 5. Find g such that 10*g**3 - 10*g**2 + 4*g**2 + 0*g**k - 4*g = 0.
-2/5, 0, 1
Let i(l) = l**3 + 2*l**2 + 3*l. Let c(v) = -v**2 - 2*v**3 - 2*v + v**3 - 4*v**3 + 4*v**3. Let b(f) = 3*c(f) + 2*i(f). Find x, given that b(x) = 0.
0, 1
Let p = -268 - -489/2. Let o = 24 + p. Factor o*c**4 - c**2 + 0*c**3 + 0*c + 1/2.
(c - 1)**2*(c + 1)**2/2
Let x = 29/90 + -1/10. Factor 0 + 0*z + 0*z**2 + x*z**3.
2*z**3/9
Suppose 2*z = -6, k + 18 = 4*k - 4*z. Factor 0 - 4/5*d - 2/5*d**3 + 6/5*d**k.
-2*d*(d - 2)*(d - 1)/5
Let o(c) = -c**2 - 7*c + 5. Let r be o(-6). Let s = r - 8. Factor 1/2*z**2 - 1/2 + 1/2*z**s - 1/2*z.
(z - 1)*(z + 1)**2/2
Solve -6*h - 3/5*h**2 - 27/5 = 0.
-9, -1
Let g(v) = -2*v + 14. Let w be g(7). Factor 1/2*x**4 + w*x - 1/2*x**5 + 1/2*x**3 - 1/2*x**2 + 0.
-x**2*(x - 1)**2*(x + 1)/2
Let o(z) be the first derivative of 1/2*z**5 - 11/8*z**4 + 1/3*z**6 + 7/4*z**2 + z - 7/6*z**3 - 5. Let o(j) = 0. What is j?
-2, -1, -1/4, 1
Let k(c) = -9*c**3 - c**2 + 9*c + 1. Let v(z) = -5*z**3 - z**2 + 5*z + 1. Let s(g) = -3*k(g) + 5*v(g). Factor s(t).
2*(t - 1)**2*(t + 1)
Let y(u) = 10 - 2*u**3 - 11 - u + u**2 + u**3. Let h(w) = -5*w**3 - w**2 - 12*w - 8. Let k(v) = -3*h(v) + 12*y(v). Factor k(s).
3*(s + 1)*(s + 2)**2
Let b(i) = -8*i**4 - 16*i**3 + 5*i**2. Let r(c) = -52*c**4 - 104*c**3 + 32*c**2. Let q(n) = 32*b(n) - 5*r(n). Factor q(a).
4*a**3*(a + 2)
Let q(f) = -4*f**3 + 29*f**2 - 53*f + 27. Let m(x) = -6*x**3 + 44*x**2 - 80*x + 40. Let g(o) = -5*m(o) + 8*q(o). Suppose g(i) = 0. Calculate i.
2
Let q = -180 + 367/2. Let h be -6 + 22/4 - -3. Suppose -1/2*l**4 + h*l**3 - 1 - 9/2*l**2 + q*l = 0. What is l?
1, 2
Suppose -5*v - 5*x = -30, -3*x - x - 40 = -4*v. Let 0*t**2 - v + 0*t + 4*t**2 + 4*t = 0. Calculate t.
-2, 1
Let b(x) be the second derivative of x**7/1260 + x**6/360 + x**5/360 + 3*x**2 - x. Let z(s) be the first derivative o