6*n**2 - 3*n**3 = 0. What is n?
-1, 0, 1/3
Let x be (-22 - -18) + 12/((-3)/(-1)). Factor -4/13*a**2 + 2/13*a**4 + 2/13 + 0*a + x*a**3.
2*(a - 1)**2*(a + 1)**2/13
Factor 39/4*j**3 + 27*j + 36*j**2 + 0 + 3/4*j**4.
3*j*(j + 1)*(j + 6)**2/4
Let n = -52 + 32. Let j = -17 - n. Factor -2 + 0*z + 1/2*z**j + 3/2*z**2.
(z - 1)*(z + 2)**2/2
Suppose 2*j - 1 = v, j - 3*v + 9 = 2. Let m(u) = u**2. Let x be m(-2). Factor -j*r**4 + x*r**3 + r**4 - 5*r**3.
-r**3*(r + 1)
Let m(a) be the third derivative of a**8/26880 + a**7/3360 - a**6/320 + a**5/30 - 5*a**2. Let i(z) be the third derivative of m(z). Find r, given that i(r) = 0.
-3, 1
Let z = 1/92 + 83/828. Let m(k) be the second derivative of -2*k + z*k**3 - 1/54*k**4 + 0 - 2/9*k**2. Factor m(p).
-2*(p - 2)*(p - 1)/9
Let n(h) = -h**3 - 13*h**2 + 11*h - 12. Let t be n(-14). Factor -t*l**2 - 5*l**3 - 7*l**3 + 3*l**3 + 1 - 7 - 27*l.
-3*(l + 1)*(l + 2)*(3*l + 1)
Suppose 8 = 3*j + 2. Let n be ((-3)/j)/((-12)/16). What is r in 2 + 2*r**n - 2*r + 2*r - 4*r = 0?
1
Suppose 3*b = -0*b - 9. Let a(u) = 25*u**4 - 44*u**3 + 8*u**2 + 4*u. Let y(i) = 24*i**4 - 45*i**3 + 9*i**2 + 3*i. Let o(p) = b*a(p) + 4*y(p). Factor o(q).
3*q**2*(q - 2)*(7*q - 2)
Let m(s) = 9*s**4 - 2*s**3 - 7*s**2 - 10*s + 10. Let f(d) = d**4 - d**3 - d + 1. Let t(b) = -6*f(b) + m(b). Suppose t(n) = 0. Calculate n.
-2, -1, 2/3, 1
Let d = 33/7 + -191/42. Let a(v) be the first derivative of -d*v**3 + 0*v - 1/4*v**2 - 3. Suppose a(q) = 0. Calculate q.
-1, 0
Let u(i) be the second derivative of -64*i**7/105 - 112*i**6/75 - 4*i**5/5 + 2*i**4/3 + 14*i**3/15 + 2*i**2/5 + 4*i. Determine o so that u(o) = 0.
-1, -1/2, -1/4, 1/2
Let x(t) be the second derivative of -1/24*t**3 - 1/48*t**4 + 0*t**2 + 1/120*t**6 + 1/80*t**5 + 3*t + 0. Factor x(z).
z*(z - 1)*(z + 1)**2/4
Let z(f) be the second derivative of f**4/8 + f**3/2 + 3*f**2/4 - 7*f. Factor z(m).
3*(m + 1)**2/2
Let p(b) = -b - 1. Let d be p(-3). Let u = 4 - d. Determine f so that 2 + f - f - 2*f**u = 0.
-1, 1
Suppose -4*t = t + 35. Let g(v) = -v - 1. Let y be g(t). Let b(k) = k**2 + 4*k. Let p(m) = m**2 + 5*m. Let q(c) = y*b(c) - 5*p(c). Factor q(f).
f*(f - 1)
Let a = 1161 + -1159. Solve 3/4*h**4 - 3/4*h**a + 0 - 1/2*h + 1/2*h**3 = 0 for h.
-1, -2/3, 0, 1
Suppose 0 = -5*l - 6 + 26, -2*l = -2*y - 2. Factor 0*c**2 + c**3 + c**3 - 4*c**y + 4*c**2.
-2*c**2*(c - 2)
Suppose -4*g + 4*h + 20 = 0, 5*g - 1 = 2*g - 4*h. Factor -4*z**3 + 6*z**2 + 5*z**g + 2*z**3 - 3*z**2.
3*z**2*(z + 1)
Let v(z) be the third derivative of 0 + 5*z**2 + 1/315*z**7 - 1/36*z**4 - 1/60*z**6 + 0*z**3 + 0*z + 1/30*z**5. Factor v(d).
2*d*(d - 1)**3/3
Let b(y) = -12*y**2 + 6*y. Let r(d) = 11*d**2 - 5*d. Let m(a) = -6*b(a) - 7*r(a). Let c(v) = -14*v**2 - 3*v. Let s(i) = -4*c(i) + 11*m(i). Factor s(g).
g*(g + 1)
Let z be (-10)/(-4) - (-1)/(-2). Factor 55*u - 25*u - 4*u**2 - z*u**3 - 32*u.
-2*u*(u + 1)**2
Let a(g) = -11*g**2 - 26*g - 21. Let w(b) = 10*b**2 + 25*b + 20. Let f(k) = 5*a(k) + 6*w(k). Determine n, given that f(n) = 0.
-3, -1
Let z = 8/37 + 636/481. Factor z*c**2 + 2/13 + 10/13*c**4 + 10/13*c + 2/13*c**5 + 20/13*c**3.
2*(c + 1)**5/13
Let d(l) be the first derivative of 5*l**3/3 + 45*l**2/2 + 70*l + 23. Factor d(x).
5*(x + 2)*(x + 7)
Let q(g) = -g**4 - g**2 - g - 1. Let l(r) = 6*r**4 + 12*r**2 + 8*r + 6. Let n(v) = l(v) + 8*q(v). Factor n(o).
-2*(o - 1)**2*(o + 1)**2
Let o(f) be the first derivative of f**6/21 - 44*f**5/105 + 26*f**4/21 - 4*f**3/3 + 3*f**2/7 - 7. Suppose o(i) = 0. Calculate i.
0, 1/3, 1, 3
Let p(f) = 3*f**3 + f**2 - 3*f + 3. Let w(q) = -q**3 - q. Let r(a) = -p(a) - 2*w(a). Determine i, given that r(i) = 0.
-3, 1
Let l be (-5)/(-40) - (-66)/(-16). Let c = l + 4. Factor -2/7*t**2 + c - 2/7*t.
-2*t*(t + 1)/7
Let l(m) be the second derivative of 0*m**4 + 0 - 1/10*m**5 + 0*m**2 + 1/3*m**3 - 2*m. Factor l(d).
-2*d*(d - 1)*(d + 1)
Let z(x) be the third derivative of 2*x**7/105 - 2*x**6/15 + x**5/5 + 2*x**4/3 - 8*x**3/3 + 17*x**2. Factor z(p).
4*(p - 2)**2*(p - 1)*(p + 1)
Let m(r) be the first derivative of 6 - 1/3*r**3 + 2*r + 1/2*r**2. Factor m(u).
-(u - 2)*(u + 1)
Let u(j) = 21*j**4 + 84*j**3 + 153*j**2 + 84*j - 6. Let x(s) = 3*s**4 + 12*s**3 + 22*s**2 + 12*s - 1. Let m(o) = 4*u(o) - 27*x(o). Factor m(t).
3*(t + 1)**4
Let u(y) be the second derivative of y**7/231 + 2*y**6/165 - y**5/55 - 4*y**4/33 - 7*y**3/33 - 2*y**2/11 + 18*y. Let u(d) = 0. Calculate d.
-1, 2
Suppose -4*o = -l - 21, -2*o - 2*o + 41 = -5*l. Factor 0 - 2/7*k**2 - 10/7*k**5 - 18/7*k**3 + 4/7*k + 26/7*k**o.
-2*k*(k - 1)**3*(5*k + 2)/7
Let v(s) = s**3 - 16*s**2 + 15*s + 4. Let i be v(15). Let f(k) be the second derivative of 3*k + 0 + 0*k**2 - 1/12*k**i + 1/6*k**3. Find g such that f(g) = 0.
0, 1
Let d be 35/(-7)*8/(-10). Let s be (-4)/6*(-3)/d. Factor s - 1/4*u - 1/4*u**2.
-(u - 1)*(u + 2)/4
Find u such that -2/3 + 4/3*u**2 - 4/3*u**5 - 4/3*u - 2/3*u**4 + 8/3*u**3 = 0.
-1, -1/2, 1
Let b = 22 + -12. Find w, given that -174*w**5 + 188*w**5 - w**3 - 3*w**3 - b*w**4 = 0.
-2/7, 0, 1
Let w(b) be the second derivative of b**4/6 + 2*b**3/3 + b**2 - 8*b. Determine r, given that w(r) = 0.
-1
Let r be ((-24)/20)/(2/(-15)). Suppose 0 = 2*l - n - 6 - 1, -n - r = -3*l. Find k such that 2/7*k**5 + 0*k**l + 0*k**3 + 0*k**4 + 0*k + 0 = 0.
0
Let m be 0 + -1 - (-84)/21. Let 0 + 4/5*f**2 + 0*f + 2/5*f**m = 0. What is f?
-2, 0
Let q(r) = r**3 - 2*r + r + 1 + 2*r**4 - 3*r**4 + r**2. Let k(s) = s**3 - s + 1. Let w(u) = -k(u) + q(u). Factor w(v).
-v**2*(v - 1)*(v + 1)
Factor 216/7*v**3 + 0*v**2 + 4/7 - 324/7*v**4 - 24/7*v.
-4*(3*v - 1)**3*(3*v + 1)/7
Let s(i) = 11*i**5 + 4*i**4 - 4*i**2 - 11*i. Let c(p) = 10*p**5 + 5*p**4 - 5*p**2 - 10*p. Let w(r) = -6*c(r) + 5*s(r). Factor w(o).
-5*o*(o - 1)*(o + 1)**3
Let j(z) be the first derivative of z**4/4 + 2*z**3/3 + z**2 + z - 2. Let f be j(-1). Factor 2/5*d**2 + 4/5*d + f.
2*d*(d + 2)/5
Solve 4*x**3 + 10*x**3 - 14*x - 10*x**2 - 12*x - 8 - 6*x = 0 for x.
-1, -2/7, 2
Let o(i) be the third derivative of i**8/6720 - i**7/1680 - i**5/60 - 3*i**2. Let v(z) be the third derivative of o(z). Determine b so that v(b) = 0.
0, 1
Let r(g) be the second derivative of g**6/15 + 17*g**5/40 + g**4 + 13*g**3/12 + g**2/2 - 10*g. Solve r(n) = 0 for n.
-2, -1, -1/4
Let t(m) = -m. Let x(o) = -3*o**2 - 12*o. Let a = -50 + 32. Let p(g) = a*t(g) + x(g). Determine l, given that p(l) = 0.
0, 2
Let p(z) = 5*z**2 - 5. Let q(v) = -4*v**2 - 1 + 1 + 2 + 2. Let a(k) = -5*p(k) - 6*q(k). What is b in a(b) = 0?
-1, 1
Let s(i) = -3*i - 3. Let f be s(4). Let a = f + 18. Solve 0*y**2 + 2/5*y - 1/5*y**4 - 2/5*y**a + 1/5 = 0.
-1, 1
Let t be (2/90)/(8/6). Let f(i) be the third derivative of 0*i**3 - t*i**6 + 0 + 1/12*i**4 - 2*i**2 + 0*i + 0*i**5. Factor f(m).
-2*m*(m - 1)*(m + 1)
Let z(o) be the first derivative of -3*o**5/5 + 7*o**4/4 + o**3/3 - 7*o**2/2 + 2*o + 8. Determine u, given that z(u) = 0.
-1, 1/3, 1, 2
Let i(z) be the third derivative of z**8/252 + 4*z**7/315 - z**6/30 - 23*z**2. Factor i(x).
4*x**3*(x - 1)*(x + 3)/3
Let y be -2 - ((-4)/(-2) + -2). Let o be (-6)/y*12/18. Factor -22*x**4 - 9*x**5 - 4*x - 20*x**o - 8*x**4 + 0*x**4 - 37*x**3.
-x*(x + 1)**2*(3*x + 2)**2
Let q = 40 - 23. Suppose -4*d + 2*d = -w + 11, 4*w + d = q. Factor l**2 - 4*l + 3 - 5*l + w*l**2.
3*(l - 1)*(2*l - 1)
Let a(h) = -h**2 + 5*h - 3. Let b be a(3). Let i be 0 - (1 + -3 - b). What is f in -10*f**3 - f**5 - 4*f**3 + 4*f**2 - 5*f**i + 16*f**4 = 0?
0, 2/3, 1
Let h(u) be the third derivative of u**7/840 + u**6/96 + u**5/60 + 6*u**2. Solve h(j) = 0.
-4, -1, 0
Let x(z) be the third derivative of -z**8/504 - z**7/315 + z**6/45 + 2*z**5/45 - 20*z**2. What is p in x(p) = 0?
-2, -1, 0, 2
Let h = 69921/80 + -874. Let c(t) be the third derivative of -1/840*t**7 + 1/24*t**4 + 2*t**2 - 1/240*t**6 - 1/6*t**3 + 0*t + h*t**5 + 0. Solve c(f) = 0 for f.
-2, 1
Let -4/3*d + 4/3 + 1/3*d**2 = 0. What is d?
2
Let o(g) be the third derivative of g**6/60 + g**5/30 - g**4/12 - g**3/3 - 6*g**2. Factor o(b).
2*(b - 1)*(b + 1)**2
Let 21/5*f**2 - 3/5*f - 12/5*f**5 - 9*f**3 + 39/5*f**4 + 0 = 0. Calculate f.
0, 1/4, 1
Let n(k) = -3*k**3 + 3*k**2 + 6*k - 5. Let o(d) = d**3 - 2*d**2 - 3*d + 2. Let c(q) = 4*n(q) + 10*o(q). Factor c(g).
-2*g*(g + 1)*(g + 3)
Let u(b) = 2*b**4 + 9*b**3 + 7*b**2 - 6*b - 6. Suppose 4*q - 35 = -q. Let d(c) 