5
Let h(u) be the first derivative of -u**6/40 - u**5/20 + u**4/8 + u**3/2 - u**2 + 4. Let v(l) be the second derivative of h(l). Factor v(c).
-3*(c - 1)*(c + 1)**2
Let r(w) be the third derivative of w**6/90 - w**5/45 - 4*w**4/9 + 8*w**3/3 + 2*w**2 - 3*w. Solve r(d) = 0.
-3, 2
Let g(b) be the first derivative of b**6/105 - b**5/35 + 2*b**3/21 - b**2/7 - 7*b - 7. Let q(h) be the first derivative of g(h). Find m, given that q(m) = 0.
-1, 1
Let z(f) be the second derivative of f**4/4 - 2*f**3 + 6*f**2 - 9*f. Determine n, given that z(n) = 0.
2
Let o(b) be the second derivative of b**4/12 + 4*b**3/3 + 7*b**2/2 - 2*b + 23. Find q, given that o(q) = 0.
-7, -1
Let u(p) = -7*p**5 - 3*p**4 - p**3 + 3*p**2 - 4*p. Let j(o) = -15*o**5 - 6*o**4 - 3*o**3 + 6*o**2 - 9*o. Let y(a) = -4*j(a) + 9*u(a). What is k in y(k) = 0?
-1, 0, 1
Let i be (-10)/14*((-12)/(-10))/(-3). Determine s so that i*s**2 - 2/7*s**3 + 2/7*s - 2/7 = 0.
-1, 1
Let c(b) = 3*b - 1. Let x be c(1). Suppose 0 = 2*s + u - 12, s - x*u - 1 + 5 = 0. Determine a so that -a - a**3 - 4*a**s + 5*a**4 + 3*a**2 - 2*a**3 = 0.
0, 1
Suppose -3*n + p + 9 = 4*p, -n + 9 = 3*p. Let o(g) be the second derivative of 1/48*g**4 + n*g**2 - 2*g - 1/12*g**3 + 0 + 1/80*g**5. Let o(v) = 0. Calculate v.
-2, 0, 1
Let d(a) be the second derivative of 1/4*a**4 + 0*a**3 + 0*a**2 + a + 0. Let d(h) = 0. Calculate h.
0
Let f(h) = 4*h + 3. Let q be f(-2). Let r be -4*1/5*q. Factor 0*m**2 - r + m**2 + 3.
(m - 1)*(m + 1)
Let z be (7 - 3)*2 - 24/4. What is d in -8/3*d - 16/3 - 1/3*d**z = 0?
-4
Suppose 0 = -7*b + 32 - 11. Determine c, given that 9*c**2 + 2*c - 14*c + 6*c**2 + 9*c**b - 12 = 0.
-2, -2/3, 1
What is y in -4*y - 14*y**2 + 15*y**2 - y = 0?
0, 5
Let m = 12489/56 + -223. Let z(h) be the third derivative of -1/140*h**5 - m*h**6 + 0*h**4 + 0*h**3 + 0*h - 2/245*h**7 + h**2 + 0. Factor z(b).
-3*b**2*(b + 1)*(4*b + 1)/7
Let s = -45 - -47. Factor 1/3*a + a**s + 0.
a*(3*a + 1)/3
Let p(a) be the third derivative of -a**7/840 - 7*a**6/480 - 3*a**5/40 - 5*a**4/24 - a**3/3 + 33*a**2. Factor p(g).
-(g + 1)*(g + 2)**3/4
Let h = -4 + 7. Let p(x) be the first derivative of -x**2 - 2/9*x**h - 4/3*x + 1. Factor p(z).
-2*(z + 1)*(z + 2)/3
Suppose -37 = -3*u + u + 3*o, 3*u - 63 = -3*o. Let s = u + -17. Factor -2/3*a**4 - 1/3*a + 2/3*a**2 + 1/3*a**5 + 0*a**s + 0.
a*(a - 1)**3*(a + 1)/3
Let x = 19/84 + 1/42. Determine h, given that 2*h**2 - x + 1/2*h**3 - h**5 - 7/4*h**4 + 1/2*h = 0.
-1, 1/4, 1
Let a(o) be the second derivative of -o**8/840 + o**7/420 + o**6/40 + o**5/30 - o**4/12 + o. Let h(n) be the third derivative of a(n). What is m in h(m) = 0?
-1, -1/4, 2
Let s(p) be the first derivative of p**5/5 - p**3 - p**2 + 2. What is y in s(y) = 0?
-1, 0, 2
Let v(j) be the third derivative of -j**7/420 + j**6/720 + j**5/120 - j**4/144 - 4*j**2. Suppose v(c) = 0. What is c?
-1, 0, 1/3, 1
Suppose 20 = 4*v + 4*s, -4*s = 2 - 10. Suppose 5*z = v*z. Suppose -2*h**4 + z*h + 5/4*h**5 + 0 + 1/2*h**2 + 1/4*h**3 = 0. What is h?
-2/5, 0, 1
Let t(u) be the third derivative of u**4/8 - 5*u**3/3 + 2*u**2. Let q be t(4). Suppose 0 - 2/3*c**q + 0*c + 7/3*c**4 + 5/3*c**3 = 0. Calculate c.
-1, 0, 2/7
Let f(t) be the second derivative of t**8/336 - t**7/210 - t**6/120 + t**5/60 + 2*t**2 - 4*t. Let y(n) be the first derivative of f(n). Factor y(l).
l**2*(l - 1)**2*(l + 1)
Let b = 4 + -14. Let t be 8/b*(-15)/6. Solve 3 + 8*r**2 + r**t - r - 8*r - 3*r**3 + 0 = 0 for r.
1
Factor 0*c - 4 + 4*c**3 - 6*c + 6*c**2 + 2*c - 2*c**2.
4*(c - 1)*(c + 1)**2
Factor 4/3*o**2 + 16/3*o + 16/3.
4*(o + 2)**2/3
Let t = -2/155 - -33/155. Let d(g) be the first derivative of -3 - 3/5*g**2 + t*g**3 + 3/5*g. Factor d(m).
3*(m - 1)**2/5
Let k(d) be the third derivative of 2*d**6/15 + d**5/3 + d**4/6 + 8*d**2. Factor k(t).
4*t*(t + 1)*(4*t + 1)
Factor -2/3*t**3 - 2/3*t**2 + 2/3*t + 2/3.
-2*(t - 1)*(t + 1)**2/3
Suppose 4*d = -4*t + 112, 3*t + 13 = d + 1. Determine l, given that -l**2 - 24 + d = 0.
0
Let i(c) be the first derivative of c**5/70 + c**4/42 - c**3/21 - c**2/7 + 6*c + 6. Let h(f) be the first derivative of i(f). Suppose h(b) = 0. Calculate b.
-1, 1
Let c(r) = -5*r**4 - 50*r**3 - 124*r**2 - 120*r - 43. Let k(h) = 36*h**4 + 351*h**3 + 867*h**2 + 840*h + 303. Let z(t) = -15*c(t) - 2*k(t). Solve z(a) = 0.
-13, -1
Let a = -10 + 18. Let u = -5 + a. Factor -2*t**3 + 2*t - 2*t**3 + 2*t**u.
-2*t*(t - 1)*(t + 1)
Suppose -276 = -4*q - 5*j, -3*j + 316 = 5*q - 4*j. Let h be (-22)/63 - q/(-112). Solve 0*f**3 + 0*f + h*f**2 - 2/9*f**4 + 0 = 0.
-1, 0, 1
Let y be (-8)/(-324)*3*6. Suppose -y + 2*x**3 - 40/9*x**2 + 26/9*x = 0. Calculate x.
2/9, 1
Solve -5*m + 0*m**3 + 2*m**3 + m**3 + 2*m = 0 for m.
-1, 0, 1
Let a(o) be the first derivative of -o**5/270 + o**4/54 - 3*o**2/2 - 3. Let g(h) be the second derivative of a(h). Factor g(t).
-2*t*(t - 2)/9
Let g(a) = a**2 - 6*a - 3. Let o be g(3). Let v be 8/o*(-1 - 0). Suppose -2/3*m**2 + v + 0*m = 0. Calculate m.
-1, 1
Suppose 3*w + 43 = 2*d, 5*d = -4*w + 2*d - 29. Let o be 1*3*w/(-132). Factor -o*f**2 + 1/4 + 1/4*f**3 - 1/4*f.
(f - 1)**2*(f + 1)/4
Solve -1/3*y + 0 - 1/3*y**3 + 2/3*y**2 = 0 for y.
0, 1
Let o(u) be the first derivative of 2*u**3 + u**2 - 1. Solve o(x) = 0.
-1/3, 0
Suppose q - 12 - 5 = -3*z, -z - 13 = 5*q. Let c(r) = -2*r**2 + 0*r - r**2 + z*r. Let x(y) = 2*y**2 - 6*y. Let h(t) = -4*c(t) - 5*x(t). Factor h(m).
2*m*(m + 1)
Factor -192*n - 16*n**2 + 60*n**2 + 24 + 52*n.
4*(n - 3)*(11*n - 2)
Let t(b) = b**2 + b - 1. Let s(d) = -d**3 - d**2 - 6*d + 7. Let y(f) = -s(f) - 5*t(f). Let x be y(4). Let 6 + 2/3*l**x + 4*l = 0. Calculate l.
-3
Let s(a) = 3*a**5 + 5*a**4 - 19*a**3 - 9*a**2 + 12*a. Let z(r) = r**4 - r**3 - r**2 - 1. Let b(o) = s(o) - 4*z(o). Solve b(x) = 0 for x.
-2, -1, -1/3, 1, 2
Let q be 4 + -2 + (-5)/(-4) - 3. Factor -1/4*o + q*o**2 - 1/2.
(o - 2)*(o + 1)/4
Let c be 3*4/3*1. Factor 0*v + 2/3*v**c + 0*v**2 + 2/3*v**3 + 0.
2*v**3*(v + 1)/3
Let l(p) be the third derivative of p**5/270 - p**4/108 - 2*p**3/27 + 2*p**2. Factor l(f).
2*(f - 2)*(f + 1)/9
Let z(y) be the first derivative of 1/6*y**6 - 3/5*y**5 + 6 + 1/4*y**4 + y**3 + 0*y - y**2. Factor z(p).
p*(p - 2)*(p - 1)**2*(p + 1)
Suppose -7 = -3*r + 2*r. Suppose r = 4*g - 1. Suppose -y**2 + 1 + 4*y - 2*y - g = 0. Calculate y.
1
Factor -k**3 - 12*k**3 + 7*k**2 + 15*k + 9 + 14*k**3.
(k + 1)*(k + 3)**2
Factor 1/2*y**4 + 1/2*y**2 + 0*y + 0 - y**3.
y**2*(y - 1)**2/2
Let k(o) = o + 14. Let z be k(-10). Factor 23*s**3 + s**4 + 4*s + 5*s**3 - 20*s**2 - 4*s**z - 9*s**4.
-4*s*(s - 1)**2*(3*s - 1)
Let s(x) be the third derivative of x**5/420 - 6*x**2. Factor s(m).
m**2/7
Let h(k) = 13 + 11*k - 3 + 5*k**3 - 6*k**3 - 9*k**2. Let v be h(-10). Determine y, given that -2/3*y**3 + v*y**2 - 2/3*y**5 + 0 + 0*y + 4/3*y**4 = 0.
0, 1
Let w(c) be the first derivative of -c**4 + 4*c**3/3 + 2*c**2 - 4*c + 3. Solve w(y) = 0 for y.
-1, 1
Let c(n) be the first derivative of 4*n**3/9 + 2*n**2 + 8*n/3 - 41. Factor c(o).
4*(o + 1)*(o + 2)/3
Let i = -22 + 46. Let q be (i/84)/(9/7). Factor -q*c**2 + 4/9*c - 2/9.
-2*(c - 1)**2/9
Let c(q) be the third derivative of q**5/40 + q**4/16 - q**3/2 + 4*q**2. Factor c(j).
3*(j - 1)*(j + 2)/2
Factor -5*b**4 - 10*b - 524*b**3 - 12*b**2 + 4*b**4 + 518*b**3 - 3.
-(b + 1)**3*(b + 3)
Let q(k) = -k**3 + 18*k**2 - 32*k. Let u be q(16). Find x, given that 0*x**2 + 0 - 1/3*x**3 + u*x - 1/3*x**4 = 0.
-1, 0
Let u(j) = j + j**3 - 6*j - 1 + 7*j. Let h be u(1). Factor -6*l**4 + l**5 - 3*l**5 + 4*l**3 - h*l**2 - 10*l**3.
-2*l**2*(l + 1)**3
Factor -5*o + 5/2 + 5/2*o**2.
5*(o - 1)**2/2
Let t(q) = q**2 - 11*q + 15. Let a be t(10). Let j(d) be the third derivative of 0*d**4 + 0*d + 0 + 1/120*d**a - 1/12*d**3 - d**2. Find o such that j(o) = 0.
-1, 1
Let v(s) = -3*s. Let w be v(2). Let q be (0 - w) + 4/(-2). What is u in -u**q - u**2 + 4*u**2 - 2*u**2 = 0?
-1, 0, 1
Let g(u) be the second derivative of 9*u**6/20 - 18*u**5/5 + 79*u**4/8 - 13*u**3 + 9*u**2 + 3*u. What is x in g(x) = 0?
2/3, 1, 3
Factor 27 - 12*u - 24*u**2 + 63*u**3 - 11 - 16.
3*u*(3*u - 2)*(7*u + 2)
Suppose 0 = -q + j + 24, q - j + 5*j = 24. Determine w so that -q*w**5 + 0 + 6*w**2 + 44*w**4 - 51/2*w**3 - 1/2*w = 0.
0, 1/4, 1/3, 1
Factor -8/7*a - 8/7 + 6/7*a**2 + 8/7*a**3 + 2/7*a**4.
2*(a - 1)*(a + 1)*(a + 2)**2/7
Let g = 321/4 - 78. F