*(n + 1)**2*(3*n + 2)
Factor 4/3 + 2/3*d**2 + 2*d.
2*(d + 1)*(d + 2)/3
Let s be (-52)/(-182) - 61/(-7) - 6. Factor 0*c + 0 - 3/4*c**2 - 1/4*c**s.
-c**2*(c + 3)/4
Suppose 0 = -2*r + h + 3, r - 9 = 7*h - 4*h. Factor r*f**2 + 2/3*f**5 + 2/3*f**3 + 4/3*f**4 + 0*f + 0.
2*f**3*(f + 1)**2/3
Let g be (-1)/(-2)*(-10 + 4). Let p(q) = 7*q**3 - 3*q**2 - 7*q - 3. Let v(i) = 8*i**3 - 4*i**2 - 8*i - 4. Let k(r) = g*v(r) + 4*p(r). Let k(f) = 0. What is f?
-1, 0, 1
Let -72/7 + 6/7*h**2 + 6/7*h = 0. What is h?
-4, 3
Let p be (-16)/(-10) + 8/20. Factor 6*l - p*l - 1 + 4*l**3 - 5*l**2 - l**2 - l**4.
-(l - 1)**4
Let p be (-3 + 2 + -2)*-12. Let f be 8/p + (-2)/(-18). Factor -1/3*z**3 + 1/3*z**2 + 1/3*z - f.
-(z - 1)**2*(z + 1)/3
Let o = 49 - 44. Let q be (-2)/(-56) + 2/8. Factor -2/7*w**o + 0 + q*w**3 + 0*w - 2/7*w**2 + 2/7*w**4.
-2*w**2*(w - 1)**2*(w + 1)/7
Suppose -2*l - x + 50 = 0, 2*l - 2*x + 4*x - 50 = 0. Suppose -5*i - l = 0, -3*z - 4*i - 5 = 9. Factor 7*w - 3*w - 2 + 0*w - 2*w**z.
-2*(w - 1)**2
Let f be 23 + -29 + (-88)/(-10). Determine a so that 4/5 - f*a + 2*a**2 = 0.
2/5, 1
Let n(x) be the first derivative of 2*x**3/27 + x**2/9 - 6. Solve n(i) = 0.
-1, 0
Let x(f) = -f + 12. Let y be x(0). Let j = -9 + y. Factor -2/3 - 2*z - 2*z**2 - 2/3*z**j.
-2*(z + 1)**3/3
Suppose 1 = 3*v - 5. Let r(l) be the second derivative of 2*l + 4/9*l**3 - 1/3*l**v + 0 - 1/6*l**4. Determine c so that r(c) = 0.
1/3, 1
Suppose -8*h + 18*h - 6*h - 8*h**2 + 4*h**3 = 0. What is h?
0, 1
Let w = -376/925 + 18/37. Let f(a) be the first derivative of w*a**5 - 2/5*a**2 + 0*a**3 + 2 - 2/5*a + 1/5*a**4. Solve f(r) = 0.
-1, 1
Factor -v**2 - 4*v**2 + 8 - 2*v**2 + 26*v.
-(v - 4)*(7*v + 2)
Let h(s) be the third derivative of 7*s**8/16 + 17*s**7/10 + 67*s**6/40 - 23*s**5/20 - 2*s**4 + 2*s**3 - 9*s**2. What is n in h(n) = 0?
-1, 2/7
Let d = 531 + -527. Factor -1/3*b**3 - 1/3*b**d + 0*b + 0 + 0*b**2.
-b**3*(b + 1)/3
Suppose 2*r - 95 = -3*r. Let o = r + -37/2. Find h such that o + h + 1/2*h**2 = 0.
-1
Let s(m) be the second derivative of m**5/30 + m**4/6 + 2*m**3/9 - 6*m. Factor s(n).
2*n*(n + 1)*(n + 2)/3
Let w = -2555/9 + 283. Let o = w + 14/9. Factor 2/3*n + 2/9*n**3 - o*n**2 - 2/9.
2*(n - 1)**3/9
Let n(l) = l**2 + 8*l. Let x be n(-8). Suppose z + x*h - 8 = 2*h, -3*z = -4*h - 16. Factor -1/3*b**5 + z*b**2 + 0 - 1/3*b**3 + 2/3*b**4 + 0*b.
-b**3*(b - 1)**2/3
Suppose 56 = 13*a + 17. Let r(i) be the third derivative of 0*i - 1/9*i**3 + a*i**2 - 1/180*i**5 + 0 - 1/24*i**4. Let r(d) = 0. What is d?
-2, -1
Let l be 0/(2 - (4 - 1)). Let v(d) be the second derivative of 1/48*d**4 + l*d**3 - 1/8*d**2 + d + 0. Suppose v(o) = 0. What is o?
-1, 1
Let r(h) be the second derivative of 3*h**4/2 + 11*h**3/3 + 2*h**2 - 8*h. Determine k so that r(k) = 0.
-1, -2/9
Let w = 167/4 - 1137/28. Suppose 2*f - 2 = j, 5*j = -2*f + 9 + 5. Factor w*u**3 + 6/7*u**4 + 0*u + 2/7*u**j + 0.
2*u**2*(u + 1)*(3*u + 1)/7
Let f(c) be the first derivative of c**5 - 5*c**3/3 + 46. Find j such that f(j) = 0.
-1, 0, 1
Let v(r) be the second derivative of r**6/120 - 3*r**5/20 + 9*r**4/8 - 3*r**3/2 + 8*r. Let x(k) be the second derivative of v(k). Factor x(f).
3*(f - 3)**2
Let m(v) be the second derivative of -1/12*v**4 - 2*v**2 + 0 - 7*v + 2/3*v**3. Factor m(c).
-(c - 2)**2
Let o(r) be the first derivative of -r**3/2 - 3*r**2/4 - 23. Factor o(l).
-3*l*(l + 1)/2
Let i(t) be the first derivative of -t**6/48 + t**5/40 + 3*t**4/32 - 5*t**3/24 + t**2/8 - 58. Factor i(a).
-a*(a - 1)**3*(a + 2)/8
Let u(n) = -n**3 - 7*n**2 - 5*n + 6. Let i be u(-6). Suppose 4*s = -4*h, i = 5*s - 5*h + h - 27. What is a in -3*a**4 - s*a**3 - a**2 + 27*a - a**5 - 27*a = 0?
-1, 0
Let i(g) be the first derivative of g**8/4200 - g**7/700 + g**6/450 + 2*g**3 + 1. Let d(c) be the third derivative of i(c). Solve d(q) = 0.
0, 1, 2
Let j(s) be the first derivative of -3/2*s**2 + 8 + 0*s + 1/4*s**4 + 2/3*s**3. Determine q so that j(q) = 0.
-3, 0, 1
Let t be 2 - ((-45)/(-50))/(3/5). Suppose -m - t - 1/2*m**2 = 0. What is m?
-1
Suppose 2*c = 1 + 5. Let b = -14/5 + c. Solve 1/5*r - b*r**3 - 3/5*r**2 + 1/5 + 2/5*r**4 = 0 for r.
-1, -1/2, 1
Suppose 11*m - 5*y = 6*m - 15, -4*m + 2*y - 4 = 0. Let a(v) = 9*v**4 - 21*v**3 + 6. Let s(h) = h**3 + h**2 - 1. Let x(u) = m*a(u) + 6*s(u). Factor x(w).
3*w**2*(w - 1)*(3*w - 2)
Let d be 6/48 - (-2)/(-16)*-1. Suppose d*l**4 - 1/2*l + 0 - 3/4*l**2 + 0*l**3 = 0. Calculate l.
-1, 0, 2
Let v(i) be the second derivative of 2*i**6/15 + 3*i**5/5 + i**4 + 2*i**3/3 - 6*i. Factor v(p).
4*p*(p + 1)**3
Suppose -2*v + 0 = 4. Let p = v - -5. Factor 4*s**3 + 2*s**2 - s**p - s**3.
2*s**2*(s + 1)
Let m be 2/(-6)*(-5 - (-1 + -4)). Factor 1/5*a**5 + 2/5*a**3 - 3/5*a**4 + 0 + 0*a + m*a**2.
a**3*(a - 2)*(a - 1)/5
Let y(m) = -54*m**3 - 19*m**2 + 26*m - 9. Let u(l) = 54*l**3 + 18*l**2 - 26*l + 10. Let g(k) = 5*u(k) + 6*y(k). Let g(s) = 0. Calculate s.
-1, 2/9, 1/3
Let y = 0 + 3. Suppose 2 = -4*l - 6, 4*i + 5*l = -10. Factor -m**3 + i*m**5 - 2*m**4 + 2*m**2 + 3*m**y - 2*m**5.
-2*m**2*(m - 1)*(m + 1)**2
Let i = 8 + -11. Let a be 4*i/(-6)*1. Factor -2*f + 3*f**3 - a*f**3 - 2*f**3 - 3*f**2.
-f*(f + 1)*(f + 2)
Let v(l) = 1 + 0*l**3 - 9*l + 6*l**3 + 11*l + 10*l**2. Let a(q) = 6*q**3 + 10*q**2 + 2*q. Let o(h) = -3*a(h) + 2*v(h). Factor o(k).
-2*(k + 1)**2*(3*k - 1)
Let i(l) = 26*l**2 - l + 26. Let r(a) = -9 + 11*a**2 + 0 - 20*a**2. Let b(z) = -6*i(z) - 17*r(z). Factor b(v).
-3*(v - 1)**2
Let m(b) be the first derivative of 4*b**5/5 + 2*b**4 - 4*b**3/3 - 4*b**2 + 15. Factor m(w).
4*w*(w - 1)*(w + 1)*(w + 2)
Let r = 221533/34965 - 1742/189. Let w = -3/37 - r. What is o in 0 - 16/5*o**3 - w*o**2 - 6/5*o**4 - 4/5*o = 0?
-1, -2/3, 0
Suppose -30*n = -31*n + 2. Find w, given that 12/7*w**n + 24/7*w + 2/7*w**3 + 16/7 = 0.
-2
Let m(f) = 6 + 0*f**3 + 2*f**2 - 5*f**2 + 4*f**3 - 4*f + 9*f. Let k(x) = -12*x**3 + 9*x**2 - 14*x - 17. Let o(b) = 6*k(b) + 17*m(b). Solve o(g) = 0.
-1/4, 0, 1
Let n be (6/21)/((-2)/(-14)). Factor 1/2*r**n + 0*r - 1/2.
(r - 1)*(r + 1)/2
Factor -4/5 - 6/5*a**2 + 2/5*a**4 + 2*a - 2/5*a**3.
2*(a - 1)**3*(a + 2)/5
What is r in -3*r**4 + 30*r**2 + 6*r - 10*r**2 + 4*r**3 - r**4 + 6*r = 0?
-1, 0, 3
Solve -8/9*x**4 + 0 + 14/9*x**3 + 0*x + 4/9*x**2 = 0.
-1/4, 0, 2
Let t be (171/(-570))/(-2*(-6)/(-8)). Solve 0*l**3 + t - 2/5*l**2 + 0*l + 1/5*l**4 = 0 for l.
-1, 1
Suppose 4*f - 4*k - 9 = 19, -2*k - 4 = 0. Determine t, given that 3 - t - 5*t - 2*t**2 + f*t**2 = 0.
1
Let q(z) be the third derivative of -z**8/2800 + 3*z**7/1400 - z**6/200 + z**5/200 - z**4/6 + 2*z**2. Let c(f) be the second derivative of q(f). Factor c(s).
-3*(s - 1)**2*(4*s - 1)/5
Solve -2*f**2 + f + 3/4*f**3 + 0 - 1/4*f**5 + 1/2*f**4 = 0 for f.
-2, 0, 1, 2
Suppose 3*n - n + 20 = 4*u, 0 = -2*u + 10. Suppose -2*z + z + 3 = 0. What is k in -1/4*k**5 + 0*k**z + 0*k + 0*k**2 + n - 1/4*k**4 = 0?
-1, 0
Let k(t) = 3*t**4 - 2*t**3 + 2*t**2 + 2*t - 3. Let b(q) = -4*q**4 + 2*q**3 - 3*q**2 - 2*q + 4. Let x(m) = -2*b(m) - 3*k(m). Determine n, given that x(n) = 0.
-1, 1
Suppose 8*a - 13*a + 10 = 0. Factor 2/7 - 2/7*r**a + 2/7*r - 2/7*r**3.
-2*(r - 1)*(r + 1)**2/7
What is c in -12*c - 3*c**4 - 3*c**2 - 9*c**2 - 12*c**2 - 15*c**3 = 0?
-2, -1, 0
Let g(v) = v**3 - 6*v**2 + 5*v + 2. Let u be g(5). Let w be (-1*(u + -2))/(-3). Find x such that 2/5*x**4 + 2*x**2 + w + 4/5*x + 8/5*x**3 = 0.
-2, -1, 0
Let p = -34 - -36. Let g(m) be the third derivative of p*m**2 + 1/70*m**7 + 0*m + 1/336*m**8 + 0 + 0*m**4 + 0*m**3 + 1/40*m**6 + 1/60*m**5. Factor g(h).
h**2*(h + 1)**3
Solve -3*j**5 - 3*j + 6*j**4 - 12*j**2 + 6*j**3 - 10 + 0*j**2 + 16 = 0.
-1, 1, 2
Let z(n) be the first derivative of 2*n**5/15 - 2*n**3/9 + 9. Factor z(w).
2*w**2*(w - 1)*(w + 1)/3
Let z be ((-36)/2)/9 + 7 + -1. Factor 0*d**3 + 4/3*d**2 + 0 + 2/3*d - 2/3*d**5 - 4/3*d**z.
-2*d*(d - 1)*(d + 1)**3/3
Let x(p) = -56*p**3 + 112*p**2 + 6*p - 6. Let l(n) = 280*n**3 - 561*n**2 - 29*n + 29. Let h(y) = 2*l(y) + 11*x(y). Factor h(w).
-2*(w - 2)*(4*w - 1)*(7*w + 2)
Let p(l) be the first derivative of 9/2*l**2 - 9/4*l**4 + 7/5*l**5 - 2*l - 5/3*l**3 - 1. Find i such that p(i) = 0.
-1, 2/7, 1
Let l = 0 - -2. Suppose 3*a = f - 8, f - 4*a = 11 - 1. Factor j**l - 2*j**2 - j**f - j + j**2.
-j*(j + 1)
Factor 5*v + 10*v**3 - 5/2*v**4 + 0 - 25/2*v**2.
-5*v*(v - 2)*(v - 1)**2/2
Factor 