(m + 2)**3/3
Determine x, given that 0 + 0*x + 2/15*x**4 - 2/15*x**3 - 4/15*x**2 = 0.
-1, 0, 2
Let k(o) be the second derivative of o**5/30 + o**4/3 + 4*o**3/3 + 3*o**2/2 + 2*o. Let x(z) be the first derivative of k(z). Suppose x(a) = 0. What is a?
-2
Let u(s) be the third derivative of -s**10/15120 + s**8/3360 - 5*s**4/24 - 2*s**2. Let w(c) be the second derivative of u(c). Suppose w(l) = 0. What is l?
-1, 0, 1
Suppose 9 = 2*t - u, 5 = 5*u + 10. Let f(j) = 6*j**3 - 2*j**2 + 2*j - 1. Let h be f(1). Suppose -a**5 + 2*a - t*a**3 + 2*a**h + a**5 = 0. Calculate a.
-1, 0, 1
Suppose 2*j - 264 = 214. Let u = -2149/9 + j. Factor 0 - u*o**4 + 2/3*o**3 - 2/3*o**2 + 2/9*o.
-2*o*(o - 1)**3/9
Let s(o) = 2*o**2 - 28*o. Let t be s(14). Let z(d) be the first derivative of 0*d - 2/27*d**3 + t*d**2 + 2. Factor z(q).
-2*q**2/9
Suppose 5*b = 1 + 19. What is w in -2 + 7*w + 0*w**2 + 5*w + b + 18*w**2 = 0?
-1/3
Let f(i) be the first derivative of 0*i**2 + 0*i + 0*i**4 - 1 + 1/6*i**3 - 1/10*i**5. Let f(d) = 0. What is d?
-1, 0, 1
Let g(d) be the second derivative of d**4/54 + d**3/27 - 4*d. Let g(x) = 0. Calculate x.
-1, 0
Suppose -4*q + q = -30. Determine s so that -18*s - 2*s**3 + 3*s**2 - 18 - 7*s**2 - 12*s - q*s**2 = 0.
-3, -1
Let -93*p + 114*p**2 - 224*p**3 + 64*p**4 + 8 + 114*p**2 + 17*p = 0. Calculate p.
1/4, 1, 2
Let a(p) be the second derivative of -p + 0 + 5/6*p**3 - 1/20*p**5 + 1/30*p**6 - p**2 - 1/4*p**4. Let a(h) = 0. Calculate h.
-2, 1
Let n(y) be the second derivative of y**6/105 + y**5/35 - 2*y**4/21 - 2*y**3/21 + 3*y**2/7 + 11*y. Factor n(c).
2*(c - 1)**2*(c + 1)*(c + 3)/7
Solve 2 + 10/3*i + 2/9*i**3 + 14/9*i**2 = 0.
-3, -1
Suppose -i + 0 + 3 = 0. Suppose i*y = -3*a - 3, -a + 2*a - 3*y = 11. Factor -2*j**2 - 2*j + a*j**3 + 2*j.
2*j**2*(j - 1)
Let v = 92/255 - -2/51. Let d(g) be the first derivative of 0*g**2 + 1/3*g**6 + 0*g**3 + v*g**5 + 0*g + 0*g**4 - 1. Solve d(c) = 0.
-1, 0
Let v(j) be the first derivative of -2*j**3/21 - 4*j**2/7 - 6*j/7 + 20. Let v(b) = 0. Calculate b.
-3, -1
Let v(y) = -2*y. Let l be v(2). Let r be l/(-14)*(-35)/(-20). Determine g, given that -r*g - 1/2 + g**2 = 0.
-1/2, 1
Let u(l) be the second derivative of -l**7/105 - l**6/20 - l**5/15 + 7*l**2/2 - 3*l. Let n(z) be the first derivative of u(z). Factor n(m).
-2*m**2*(m + 1)*(m + 2)
Let g = 94 - 468/5. Factor -2/5*k**2 - g + 4/5*k.
-2*(k - 1)**2/5
Let k(a) be the second derivative of -2*a - 1/720*a**6 + 0*a**2 + 0*a**4 + 0 + 0*a**5 + 1/3*a**3. Let j(y) be the second derivative of k(y). Factor j(z).
-z**2/2
Let o(c) = c**2 - c - 27. Let z be o(-5). Let k(p) = -p**2 + 6*p - 3. Let f be k(5). Find n such that f*n + 3*n + 4*n**2 + 0*n**2 - z*n = 0.
-1/2, 0
Suppose 2*f + 2*f = 16. Suppose 0 = 4*h - 20 - f. Let c(q) = -2*q**2 + 11*q - 2. Let n(d) = -d**2 + 5*d - 1. Let i(z) = h*c(z) - 14*n(z). Factor i(l).
2*(l - 1)**2
Let p(i) be the third derivative of 6*i**2 + 0 + 1/14*i**4 + 1/105*i**5 + 0*i + 4/21*i**3. Factor p(l).
4*(l + 1)*(l + 2)/7
Let z be 5 + ((-2)/(-3))/(16/(-24)). Suppose 2/3*s - 19/3*s**z - 1/3*s**2 - 5*s**3 + 0 - 7/3*s**5 = 0. What is s?
-1, 0, 2/7
Let p(g) be the third derivative of g**6/60 - g**5/30 + 3*g**2. Factor p(v).
2*v**2*(v - 1)
Suppose -r = 4*r - 10. Factor 5*h**3 + 4*h**3 - r*h**4 - 9*h**3 + 2*h**3.
-2*h**3*(h - 1)
Suppose 20 = 3*a - 5*r, -1 - 7 = 2*r. Factor 0*f**4 + a*f - 1/3*f**5 + 1/3*f**3 + 0*f**2 + 0.
-f**3*(f - 1)*(f + 1)/3
Let p(c) be the first derivative of 0*c + 1/20*c**4 + 1/6*c**6 + 4 - 2/15*c**3 + 8/25*c**5 + 0*c**2. Suppose p(l) = 0. What is l?
-1, 0, 2/5
Let p(i) be the first derivative of 7*i**5/60 + 3*i**4/8 + i**3/3 + 5*i**2/2 - 2. Let c(j) be the second derivative of p(j). Factor c(t).
(t + 1)*(7*t + 2)
Let v(c) be the second derivative of -c**4/36 + c**2/6 - c. Factor v(t).
-(t - 1)*(t + 1)/3
Let t(c) be the third derivative of -c**7/105 - 29*c**6/540 - 4*c**5/45 - c**4/27 + 15*c**2. What is z in t(z) = 0?
-2, -1, -2/9, 0
Let z(p) be the third derivative of p**9/75600 + p**8/25200 - p**7/25200 - p**6/3600 - p**5/10 + p**2. Let j(m) be the third derivative of z(m). Factor j(b).
(b + 1)*(2*b - 1)*(2*b + 1)/5
Suppose -2*z = -10, 28 = -4*d + 5*d + 5*z. Let t(w) be the first derivative of 0*w - 3 - 2/13*w**2 + 2/39*w**d. What is c in t(c) = 0?
0, 2
Let v(g) be the second derivative of -g**5/130 - 2*g**4/39 - g**3/13 + 9*g. What is k in v(k) = 0?
-3, -1, 0
Factor -1/2*h + 0 - 1/2*h**5 - 2*h**4 - 3*h**3 - 2*h**2.
-h*(h + 1)**4/2
Factor -2/3*u**2 + 0*u - 2/3*u**3 + 0.
-2*u**2*(u + 1)/3
Let t(l) be the first derivative of 0*l + 1/6*l**3 - 5 - 3/4*l**2. Suppose t(p) = 0. What is p?
0, 3
Let j be 50/60 + 23/(-42). Let i be (-2)/1 + (-54)/(-21). Factor -4/7*h + 2/7*h**4 + 0*h**2 + i*h**3 - j.
2*(h - 1)*(h + 1)**3/7
Find z, given that -279*z**2 - 1155/4*z**3 - 12 - 225/4*z**4 - 99*z = 0.
-4, -2/5, -1/3
Let s(w) = -12*w**2 + 1. Let y(j) = -4*j**2. Let h(z) = -4*s(z) + 11*y(z). Factor h(x).
4*(x - 1)*(x + 1)
Let j(x) be the second derivative of x**5/5 - 7*x**4/12 + x**3/3 + x**2/2 + 12*x. Solve j(f) = 0.
-1/4, 1
Suppose 0*q + 4*q = 16. Find w such that 15*w**2 - 18*w**q + 6 - 18*w**4 - 27*w + 27*w**3 + 15*w**4 = 0.
-1, 2/7, 1
Let k(m) be the third derivative of 0*m + 0 + 0*m**3 + 0*m**4 - 1/20*m**6 - 8*m**2 - 1/20*m**5 - 1/70*m**7. Solve k(x) = 0.
-1, 0
Factor 0 + 2*m**4 + 2*m**2 - 1/2*m - 3*m**3 - 1/2*m**5.
-m*(m - 1)**4/2
Let g = -1407 - -4292/3. Let q = g - 23. Factor 0*k**2 + q*k - 2/9*k**3 - 4/9.
-2*(k - 1)**2*(k + 2)/9
Let l(t) be the first derivative of t**3 - 6*t**2 + 9*t - 2. Factor l(i).
3*(i - 3)*(i - 1)
Let t(n) = -n**3 - n. Let u be ((-1)/(-3))/(3/9). Let j(v) = 14*v**3 + 4*v**2 + 4*v. Let a(f) = u*j(f) + 4*t(f). Solve a(r) = 0 for r.
-2/5, 0
Let r(t) be the second derivative of t**7/42 - 2*t**6/15 + t**5/5 - 4*t. Factor r(o).
o**3*(o - 2)**2
Let k = 42 + -29. What is p in -7*p + 28*p**4 - k*p**3 + 43*p - 23*p**3 - 20*p**2 - 8 = 0?
-1, 2/7, 1
Suppose -3*w = -9, 2*o - 4*o - 9 = -w. Let b be -5 + 5 - o/2. Determine x, given that 0 + 3/2*x**5 - b*x**3 + 1/2*x**4 + 0*x - 1/2*x**2 = 0.
-1, -1/3, 0, 1
Let w(q) be the third derivative of 0*q**3 + 1/300*q**5 + 0*q**4 + 0*q + 0 - 1/600*q**6 + 1/1680*q**8 - 1/1050*q**7 - q**2. Let w(b) = 0. What is b?
-1, 0, 1
Let i(u) = -u. Suppose 5*s + 6 + 9 = 0, -g - 2*s = 10. Let h(q) = -3*q**2 - 6*q + 1. Let f(z) = g*i(z) + h(z). Factor f(l).
-(l + 1)*(3*l - 1)
Let c(i) be the third derivative of 1/540*i**6 - 1/1512*i**8 + 0*i**5 + 0*i + 0 + 0*i**4 + 0*i**7 + 0*i**3 + 6*i**2. Suppose c(s) = 0. What is s?
-1, 0, 1
Let y(o) be the third derivative of 0*o - 1/4*o**4 + 0*o**3 + 0 - 1/8*o**6 + 3*o**2 + 7/20*o**5. Factor y(b).
-3*b*(b - 1)*(5*b - 2)
Factor 0 + 2/9*d**4 - 2/9*d - 2/9*d**2 + 2/9*d**3.
2*d*(d - 1)*(d + 1)**2/9
Let y be 5*2 + (12 - 18). Solve 21/2*z**y - 15/2*z**5 + 0 - 3*z**3 + 0*z**2 + 0*z = 0 for z.
0, 2/5, 1
Let j(b) be the third derivative of b**8/60480 - b**7/15120 - b**5/15 - 4*b**2. Let i(x) be the third derivative of j(x). Find o such that i(o) = 0.
0, 1
Let r(s) be the second derivative of 1/10*s**3 - 3/5*s**2 + 1/20*s**4 - 11*s + 0. Find j, given that r(j) = 0.
-2, 1
Let s be (7 - 8)/(1/(-8)). Factor -6*t**2 + 2*t + 10*t - 4*t + s.
-2*(t - 2)*(3*t + 2)
Let a be 120/(-252) + -4 + 16/3. Factor a*n + 0 - 3/7*n**2.
-3*n*(n - 2)/7
Let z be (3/6)/(2/188). Let d = 142/3 - z. Factor 0 - 4/3*r**2 + d*r**3 + 4/3*r.
r*(r - 2)**2/3
Let q(x) be the second derivative of -1/5*x**2 + 0 + 1/30*x**3 + 2*x + 1/20*x**4. Factor q(z).
(z + 1)*(3*z - 2)/5
Let w be ((-12)/(-135))/((-36)/(-162)). Determine p, given that w*p**3 - 8/5 - 2*p**2 + 16/5*p = 0.
1, 2
Let t(q) be the third derivative of q**6/24 - 5*q**5/2 + 125*q**4/2 - 2500*q**3/3 - 27*q**2. Suppose t(n) = 0. What is n?
10
Suppose 3/5 + 1/5*n**2 + 4/5*n = 0. Calculate n.
-3, -1
Let z = -18 - -21. Factor 2*v**z + 2*v**3 + 3*v**3 - 3*v**3 - 4*v.
4*v*(v - 1)*(v + 1)
Factor -10/7*k**2 - 4/7*k + 0 - 2/7*k**4 - 8/7*k**3.
-2*k*(k + 1)**2*(k + 2)/7
Factor -w**3 - 5*w**2 - 4*w - 32*w + 5*w**3 - 7*w**2 - 20.
4*(w - 5)*(w + 1)**2
Let h(l) = l**2 - 3*l + 3. Let p be h(2). Let i(b) = -b + 1. Let q(j) = j**2 + 6*j - 6. Let m(t) = p*q(t) + 6*i(t). Factor m(a).
a**2
Let b(q) be the second derivative of -q**8/2520 + q**7/1260 + q**3/2 - q. Let w(h) be the second der