/15
Let b(z) be the second derivative of 0 + 0*z**2 + 0*z**4 - 1/30*z**5 - z + 0*z**3 - 1/45*z**6. Let b(q) = 0. Calculate q.
-1, 0
Let a(q) be the third derivative of -q**6/1440 + q**4/96 + 2*q**3/3 - 2*q**2. Let u(l) be the first derivative of a(l). Factor u(i).
-(i - 1)*(i + 1)/4
Let c(o) be the third derivative of o**7/1260 - o**6/120 + o**5/30 - o**4/24 + 5*o**2. Let m(l) be the second derivative of c(l). Let m(i) = 0. What is i?
1, 2
Let l(p) be the first derivative of -2 + 3/5*p**2 + 1/15*p**6 + 0*p**5 + 4/15*p**3 - 2/5*p**4 - 4/5*p. Suppose l(a) = 0. What is a?
-2, -1, 1
Let i(a) be the first derivative of 2*a**5/5 + 7*a**4/2 + 16*a**3/3 - 16*a**2 - 27. Factor i(l).
2*l*(l - 1)*(l + 4)**2
Suppose -4*n + 6 = -n. Factor -2*z + 3*z**3 + z - n*z**3.
z*(z - 1)*(z + 1)
Determine x, given that -24/7*x - 48/7 - 3/7*x**2 = 0.
-4
Suppose -8 = -6*d - 8. Let p(a) be the first derivative of -4/3*a**3 - 1 - 1/3*a**6 + d*a**4 + a**2 + 0*a + 4/5*a**5. Factor p(b).
-2*b*(b - 1)**3*(b + 1)
Find g such that 18/5 + 2/5*g**2 - 12/5*g = 0.
3
Let m(x) be the first derivative of -5*x**4/24 + 35*x**3/18 - 55*x**2/12 + 25*x/6 + 36. Factor m(p).
-5*(p - 5)*(p - 1)**2/6
Let m(f) be the first derivative of -7*f**6/54 + 16*f**5/45 - f**4/9 - 14*f**3/27 + 11*f**2/18 - 2*f/9 + 15. Solve m(i) = 0 for i.
-1, 2/7, 1
Let l = 126 + -123. Determine f so that 0 + 4/9*f**4 - 4/9*f**2 + 0*f**l - 2/9*f + 2/9*f**5 = 0.
-1, 0, 1
Suppose 0 = -3*h + h + 2. Let m be (h - 0/(-1))*2. Factor 2*c**5 - 2/3*c**4 + 0*c - 2/9*c**m - 10/9*c**3 + 0.
2*c**2*(c - 1)*(3*c + 1)**2/9
Let p(w) = 1. Let g(i) = -i**2 + i + 7. Let u(o) = 2*g(o) - 10*p(o). Factor u(h).
-2*(h - 2)*(h + 1)
Determine x so that 3/5*x**3 + 3/5*x**2 - 3/5*x**5 + 0 + 0*x - 3/5*x**4 = 0.
-1, 0, 1
Let f(i) be the second derivative of i**6/3 - 5*i**5/4 + 5*i**4/12 + 5*i**3/3 - 57*i. Suppose f(l) = 0. What is l?
-1/2, 0, 1, 2
Let d(k) = 1. Let q(x) be the second derivative of -x**4/12 - x**3/6 + 3*x**2 + x. Let f(m) = -6*d(m) + q(m). Factor f(h).
-h*(h + 1)
Let d be -1 + (4 - -2)/2. Factor 5*n + 2*n**d + 4 - n + 2*n.
2*(n + 1)*(n + 2)
Let k(m) be the second derivative of m**7/126 + 8*m**6/45 + 8*m**5/5 + 64*m**4/9 + 128*m**3/9 + 9*m. Solve k(q) = 0 for q.
-4, 0
Let q = -53 + 57. Factor 2*n - 1/2*n**q + 0 - 3/2*n**3 + 0*n**2.
-n*(n - 1)*(n + 2)**2/2
Let l be (-2)/(-10) + (-22)/10. Let h be l/(-1 - 1/(-2)). Factor -3*o**3 + 3*o**3 - h*o**2 - 5*o**3 + 3*o**3.
-2*o**2*(o + 2)
Let -2/7*z**2 - 4/7*z - 2/7 = 0. What is z?
-1
Let b(o) be the third derivative of o**7/42 - 7*o**5/12 - 5*o**4/4 - 37*o**2. Suppose b(u) = 0. Calculate u.
-2, -1, 0, 3
Let o be (-1)/(-4) + 22/8. Let p(l) be the third derivative of -1/90*l**5 - 1/18*l**4 + 0*l**o + 1/180*l**6 + 0 + 0*l + 2*l**2. Factor p(y).
2*y*(y - 2)*(y + 1)/3
Let i = 1 + 2. Suppose -i*k - 2*m - 4 = -0*k, 0 = k + 5*m + 23. Factor -w**4 + w**k - 1/2*w**5 + 0*w**3 + 1/2*w + 0.
-w*(w - 1)*(w + 1)**3/2
Let v(t) be the third derivative of t**6/180 + t**3/2 - 5*t**2. Let n(m) be the first derivative of v(m). Factor n(p).
2*p**2
Suppose 0 = 4*d + 2 - 18. Let h(a) = 2*a**4 - 5*a**3 - 5*a - 4. Let j(l) = -3*l**4 + 10*l**3 + l**2 + 9*l + 7. Let w(v) = d*j(v) + 7*h(v). Factor w(o).
o*(o + 1)**2*(2*o + 1)
Let s(i) = 2*i + 2. Let y be s(0). Let o(u) = 3*u**2 + u + 1. Let h be o(-1). Factor -y*z**2 - 2/3*z**h - 2/3 - 2*z.
-2*(z + 1)**3/3
Let t = -265 - -1327/5. Suppose t*v**3 + 0 + 0*v + 2/5*v**2 = 0. Calculate v.
-1, 0
Let o(d) be the first derivative of 3*d**5/10 + 9*d**4/4 + 13*d**3/2 + 9*d**2 + 6*d - 2. Factor o(m).
3*(m + 1)**2*(m + 2)**2/2
Let l = 19/13 - 272/195. Let a(t) be the first derivative of 0*t**2 + 0*t**3 + 0*t**4 + 0*t + 1 - 2/25*t**5 + l*t**6. Factor a(u).
2*u**4*(u - 1)/5
Let i = -3/8 - -7/8. Factor i*m + 0 + 1/2*m**4 + 3/2*m**3 + 3/2*m**2.
m*(m + 1)**3/2
Let o(l) be the third derivative of l**5/30 + l**4/4 - 4*l**3/3 - 34*l**2. Factor o(y).
2*(y - 1)*(y + 4)
Let g = -14698/25 - -588. Let a(f) be the first derivative of g*f**5 + 2/5*f - 1 - 4/15*f**3 + 1/15*f**6 - 1/5*f**4 + 1/5*f**2. What is t in a(t) = 0?
-1, 1
Suppose 4*i = 5*j - 13, j = 4*i - 3*j + 8. Suppose -4*s + 2*r = 0, -r = i*s + 2*s - 14. What is w in -1 - w - 3*w**3 + w**s + 2*w**3 + 2*w**3 = 0?
-1, 1
Let v(a) = -60*a - 300. Let c be v(-5). Factor -4/7*j**2 + c*j**4 + 0 + 2/7*j**5 - 6/7*j**3 + 0*j.
2*j**2*(j - 2)*(j + 1)**2/7
What is o in -2/7*o**2 + 4/7*o - 2/7*o**3 + 0 = 0?
-2, 0, 1
Let o(n) be the third derivative of -1/48*n**4 - 1/12*n**3 + 1/160*n**5 - 1/1680*n**7 - 5*n**2 + 1/480*n**6 + 0 + 0*n. Factor o(c).
-(c - 2)**2*(c + 1)**2/8
Let n(v) = v**4 + v**3 - v**2 + v - 1. Let i(a) = -3*a**5 + a**4 + 4*a**3 - 4*a**2 - 5*a + 5. Let f(z) = i(z) + 2*n(z). Factor f(p).
-3*(p - 1)**3*(p + 1)**2
Determine b, given that 2/13*b + 0 + 2/13*b**3 + 4/13*b**2 = 0.
-1, 0
Let s(x) be the first derivative of x**2 - 1/36*x**4 + 0*x**3 + 0*x + 2 + 1/90*x**5. Let d(n) be the second derivative of s(n). Suppose d(o) = 0. What is o?
0, 1
Factor 0 + 0*l - 2/9*l**4 - 2/9*l**2 - 4/9*l**3.
-2*l**2*(l + 1)**2/9
Let u be (((-6)/10)/(-3))/((-4)/(-10)). Let z(w) be the first derivative of -5/3*w**3 - u*w**5 - 4 + 5/4*w**2 + 5/4*w**4 + 1/12*w**6 - 1/2*w. Factor z(d).
(d - 1)**5/2
Let r(x) be the second derivative of 2/21*x**3 - 3*x + 0 + 0*x**2 - 1/42*x**4. Factor r(o).
-2*o*(o - 2)/7
Let z = 124/3 - 41. Suppose 3*c - 8 + 2 = 0. Let -2/3*l + z*l**c + 0 = 0. What is l?
0, 2
Let b = 21 - 11. Let u be b/((-1)/(-1 - 0)). Factor 2 - o + 2*o - 6 + u*o**2 + 5*o.
2*(o + 1)*(5*o - 2)
Let k(l) = 23*l**3 - 17. Let h(z) = 4*z**3 - 3. Let a(g) = -34*h(g) + 6*k(g). What is o in a(o) = 0?
0
Let f = -26 - -4. Let w = -22 - f. Factor -1/3*d**5 + w*d**4 + 0 - 1/3*d + 0*d**2 + 2/3*d**3.
-d*(d - 1)**2*(d + 1)**2/3
Let 1/2*c + 0 - 1/4*c**4 + 1/4*c**5 - 3/4*c**3 + 1/4*c**2 = 0. What is c?
-1, 0, 1, 2
Suppose 0 = -26*j + 31*j - 15. Factor 7/2*p**j + 3/2*p**4 + 1/2*p + 5/2*p**2 + 0.
p*(p + 1)**2*(3*p + 1)/2
Let p be 10/(-55) + 136/22. Let a = -3 + p. Let 0 - 2*d**4 + 6/7*d**a + 6/7*d**5 + 6/7*d**2 - 4/7*d = 0. Calculate d.
-2/3, 0, 1
Suppose -5*n + 2*n = -2*c - 7, 0 = 4*c - n - 11. Determine r, given that 2/3*r + 0 - 2/3*r**3 - 2/3*r**2 + 2/3*r**c = 0.
-1, 0, 1
Factor -15 - 20*j - 47*j**2 + 17*j**2 + 25*j**2.
-5*(j + 1)*(j + 3)
Suppose -f + 4/9*f**4 - 2/9*f**2 + f**3 - 2/9 = 0. Calculate f.
-2, -1, -1/4, 1
Let w be 6*(18/15 - 1). Factor w*u - 2/5*u**2 - 4/5.
-2*(u - 2)*(u - 1)/5
Let s(x) = 8*x**3 - x**2 + 9*x - 9. Let v(c) = c**3 + c - 1. Let n(u) = 0*u + 2*u + u + 3. Let b be n(5). Let o(a) = b*v(a) - 2*s(a). Factor o(h).
2*h**2*(h + 1)
Let j(t) = -t**3 + 5*t**2 - 5. Let o(u) be the second derivative of u**5/20 - u**4/2 + 3*u**2 + 2*u. Let y(k) = 6*j(k) + 5*o(k). Let y(w) = 0. Calculate w.
0
Let g(w) = 3*w + 27. Let x be g(-9). Factor -4/5*y**2 - 4/5*y**4 + 1/5*y + 6/5*y**3 + 1/5*y**5 + x.
y*(y - 1)**4/5
Suppose -2*x = 2 + 2. Let i(p) = -3*p**3 + 4*p**2 - 7*p. Let s(m) = -4*m**3 + 4*m**2 - 8*m - 1. Let a(t) = x*s(t) + 3*i(t). Solve a(r) = 0.
1, 2
Let v(l) = l + 10. Let x(w) = w**3 + 5*w**2 + w - 2. Let n be x(-5). Let g be v(n). Find y such that 1 + 3 + 6*y**2 - 6 + 4*y**g = 0.
-1, 1/2
Suppose -3*v + 1 = 2*q, 4*v + 23 = 5*q + 9. What is c in c**4 + c**2 + 2*c**q + 9*c - 3*c**3 - 10*c = 0?
0, 1
Factor 0 + 1/3*n - 1/3*n**2.
-n*(n - 1)/3
Suppose 2*k - 3 = 5. Let 5 + 0*b**3 - k - b**3 + b - b**2 = 0. Calculate b.
-1, 1
Let a(w) be the first derivative of 0*w**3 + 1/2*w**4 - 7/6*w**6 + 0*w + w**5 + 5 + 0*w**2. Factor a(r).
-r**3*(r - 1)*(7*r + 2)
Let q(s) be the third derivative of -2*s**2 - 1/18*s**4 + 1/3*s**3 + 1/270*s**5 + 0*s + 0. Suppose q(k) = 0. Calculate k.
3
Suppose 4*s = -4*l - 36, 2*s - 3*l = 11 - 44. Let i be -2*(s/(-3) + -5). Solve -4/3 - 2/3*y**i + 2*y = 0.
1, 2
Suppose -2 = -2*z + z. Determine d, given that 3*d**z - 4*d**2 + 0*d**2 = 0.
0
Let c(m) be the first derivative of m**3 - 3*m - 7. Factor c(o).
3*(o - 1)*(o + 1)
Let y(u) be the first derivative of 3*u**5/20 + 9*u**4/16 - 5*u**3/4 - 9*u**2/8 + 3*u + 3. Factor y(h).
3*(h - 1)**2*(h + 1)*(h + 4)/4
Suppose -7 = -4*v + 3*m + 5, 5*v = -m - 4. Suppose 1/2*n**5 + 0 + 1/2*n + v*n**2 + 0*n**4 - n**3 = 0. What is n?
-1, 0, 1
Suppose 2*b + 2 = h + 5, 3*h = 4*b - 11. Let q be (-1 - -2) + 2 + b. Factor -m**q - 2*