e the third derivative of 0*j**5 + 0*j + 0 + 1/300*j**6 + 0*j**3 + 0*j**4 + 2*j**2 - 1/525*j**7. Find a, given that p(a) = 0.
0, 1
Factor 112/9*h**4 + 0*h + 62/9*h**3 + 0 - 32/9*h**5 + 8/9*h**2.
-2*h**2*(h - 4)*(4*h + 1)**2/9
Let y = 19 - 17. Factor 2/3*q - 1/3*q**y - 1/3.
-(q - 1)**2/3
Let s(p) be the third derivative of -p**6/720 + p**5/360 + p**4/72 + p**2. Determine b, given that s(b) = 0.
-1, 0, 2
Let d = 21 + -19. Let g(y) be the third derivative of 0*y**4 + 0*y + 0 + 1/360*y**6 - 1/360*y**5 + 0*y**3 - d*y**2 - 1/1260*y**7. Factor g(k).
-k**2*(k - 1)**2/6
Suppose 2*v = 6, -2*j + 3 = -2*v + 7. Suppose -3*s - 2*s - 5*m + 30 = 0, -4*s + 5*m = 3. Determine k, given that 2 - s*k**3 + j - 3 - 3*k**4 = 0.
-1, 0
Let d(n) be the first derivative of -2*n**3/21 + 6*n**2/7 - 18*n/7 - 1. Factor d(q).
-2*(q - 3)**2/7
Let x = -1/60 - -13/180. Let h(g) be the third derivative of -1/90*g**5 + 0 + 0*g**3 + 0*g + x*g**4 - g**2. Factor h(c).
-2*c*(c - 2)/3
Let p(i) = -2*i**4 - 2*i**3 + 12*i**2 - 2*i - 10. Let j(o) = 6*o**4 + 7*o**3 - 37*o**2 + 7*o + 31. Let q(k) = -4*j(k) - 14*p(k). Let q(b) = 0. What is b?
-2, -1, 1, 2
Let m(l) be the first derivative of -3*l**5/5 + 3*l**3 + 3*l**2 - 2. Factor m(i).
-3*i*(i - 2)*(i + 1)**2
Let m(i) be the second derivative of -i**8/120 - i**7/105 + i**6/150 - 2*i**2 + 5*i. Let b(s) be the first derivative of m(s). Factor b(t).
-2*t**3*(t + 1)*(7*t - 2)/5
Let u = 1867/3 + -622. Determine p so that 0*p + 2/3*p**2 + u*p**3 + 0 = 0.
-2, 0
Suppose 2*n = 5*f - 10, -2*f = 3*f + 2*n - 10. Suppose -4*g = -9*g, m - f*g = 2. Suppose 4*w + 2*w**m - w + w + 0*w = 0. Calculate w.
-2, 0
Suppose 4*i - 2*r = 8, 3*i + 3*r - 6 + 0 = 0. Let m be (2 - 3)*(-3)/9. Solve m*s**i + 1/3 - 2/3*s = 0.
1
Let p(r) be the second derivative of 0 + 2*r + 1/3*r**3 + 1/10*r**5 - 1/3*r**4 + 0*r**2. Determine g, given that p(g) = 0.
0, 1
Let l(p) = p + 1. Let y(g) = 4*g - 2. Let d(w) = -3*l(w) + y(w). Let z be d(5). Let -2/9*o**4 - 2/9*o**2 + z*o + 0 + 4/9*o**3 = 0. What is o?
0, 1
Suppose -3*l + 4*l + 3*f = 16, -4*l + 5*f - 4 = 0. Factor -27*w**3 - 5*w - 1/2 - 27/2*w**l - 18*w**2.
-(w + 1)*(3*w + 1)**3/2
Let h be 2/8 - 20/(-560). Determine m, given that 0 + 2/7*m**2 + h*m = 0.
-1, 0
Let v be (21/81)/(3/(-27414)). Let g = v + 2374. Factor 2 + 16/3*h + 16/9*h**3 + g*h**2 + 2/9*h**4.
2*(h + 1)**2*(h + 3)**2/9
Let v(o) be the first derivative of 4*o**3/3 + 2*o - 1. Let r(u) be the first derivative of -17*u**3/3 - 9*u + 1. Let q(k) = 6*r(k) + 26*v(k). Factor q(c).
2*(c - 1)*(c + 1)
Suppose -x = c, -4*c - x + 4 = 2*x. Let b(s) be the first derivative of 1/16*s**4 - 1/8*s**2 - c + 0*s + 0*s**3. Factor b(p).
p*(p - 1)*(p + 1)/4
Solve -3/4*r - 3/4*r**5 - 3/8*r**4 - 3/8*r**2 + 0 + 9/4*r**3 = 0.
-2, -1/2, 0, 1
Let u = -6 + 9. Find z, given that 3*z**u - 3*z**2 - 5*z**2 + 2*z**2 + 0*z**3 = 0.
0, 2
Let k(d) be the second derivative of -d**6/900 + d**5/100 - d**4/30 - d**3/2 - 3*d. Let f(c) be the second derivative of k(c). Factor f(s).
-2*(s - 2)*(s - 1)/5
Let f = -5 + 8. Find m, given that -6*m + 2*m**2 + 2*m**2 - 6*m**4 + 6*m**5 + 2 - m**3 - 4*m**5 + 5*m**f = 0.
-1, 1
Let h = 156/1099 - -1/1099. Factor -h*u**3 + 0*u**2 + 0 + 1/7*u.
-u*(u - 1)*(u + 1)/7
Let s be (-159)/(-106)*6/7. Let 0 + s*t**4 + 3/7*t + 3/7*t**2 - 15/7*t**3 = 0. Calculate t.
-1/3, 0, 1
Let w(f) be the second derivative of 0*f**2 + 5*f - 1/6*f**4 + 1/5*f**6 + 2/3*f**3 + 0 - 2/5*f**5. Factor w(p).
2*p*(p - 1)**2*(3*p + 2)
Let d(v) = 3*v**2 - 2*v. Let q(m) = 4*m**2 - 3*m. Let i(y) = -3*d(y) + 2*q(y). Solve i(t) = 0.
0
Suppose 6*b = 244 - 226. Solve -1/2*m**2 - 1/6*m**b - 1/6 - 1/2*m = 0 for m.
-1
Let i(l) = -11*l**2 + 43*l + 71. Let p(r) = -4*r**2 + 14*r + 24. Let y(z) = 3*i(z) - 8*p(z). Let c be y(18). Solve 3/2*d**2 + 9/2*d + c = 0 for d.
-2, -1
Let z(p) = -p**3 - 5*p**2 - 7*p - 5. Let v be z(-4). Let b(f) = 9*f**5 + 7. Let q = -14 + 8. Let x(g) = 8*g**5 + 6. Let i(r) = q*b(r) + v*x(r). Factor i(w).
2*w**5
Let n(b) be the second derivative of -b**6/60 + b**5/15 - b**4/12 + b**2/2 - 3*b. Let x(q) be the first derivative of n(q). Determine y so that x(y) = 0.
0, 1
Let w(v) be the first derivative of 2*v**3/3 - 20*v**2 + 38*v - 57. Find z such that w(z) = 0.
1, 19
Let n = 4363/180 + -218/9. Let a(u) be the third derivative of 0*u**6 + 0*u**3 + 0*u + 0 + 0*u**4 + 1/210*u**7 - n*u**5 - 5*u**2. Suppose a(f) = 0. Calculate f.
-1, 0, 1
Let g = -7 - -19. Factor -9*d**2 + d + g*d + 12 - d.
-3*(d - 2)*(3*d + 2)
Let h(k) be the third derivative of -k**6/120 - k**5/20 - k**4/12 + 10*k**2. Factor h(b).
-b*(b + 1)*(b + 2)
Let v(a) be the first derivative of 0*a**2 + 0*a**4 - a + 2/3*a**3 - 1/5*a**5 + 5. Determine f so that v(f) = 0.
-1, 1
Suppose 0 = -4*i + 4*s + 16, 2*i + i - 5*s - 14 = 0. Let d(v) be the second derivative of -2*v + 1/3*v**i + 0 + 1/12*v**4 + 1/2*v**2. Factor d(h).
(h + 1)**2
Let s(u) = u**3 + 3*u**2 - 6*u - 6. Let d be s(-4). Solve 0*n**3 + 0*n**d + n**3 + 2*n**2 - n + 2*n = 0 for n.
-1, 0
Suppose 7/2*q**3 + 0 - 3/2*q**2 - 5/2*q**5 + 3/2*q**4 - q = 0. Calculate q.
-1, -2/5, 0, 1
Factor -2/17*k**2 + 0 + 8/17*k.
-2*k*(k - 4)/17
Let u(s) be the second derivative of s**7/840 - s**6/240 + s**5/240 - 2*s**2 - 3*s. Let b(h) be the first derivative of u(h). Let b(k) = 0. What is k?
0, 1
Let a(d) be the second derivative of 0*d**2 + 1/20*d**5 + 3*d + 0 - 1/6*d**3 + 1/12*d**4 - 1/30*d**6. Factor a(i).
-i*(i - 1)**2*(i + 1)
Suppose 2*k - 35 = 3*r + 2*r, 0 = 3*k - 5*r - 40. Factor 4/11*j**4 + 0*j**3 + 2/11*j**k + 0 - 4/11*j**2 - 2/11*j.
2*j*(j - 1)*(j + 1)**3/11
Let a(m) be the third derivative of m**6/160 - m**5/120 - 16*m**2. Factor a(y).
y**2*(3*y - 2)/4
Suppose -14 - 1 = -5*g. Factor -2*r - 7*r**2 + 0*r + 2 - 1 - 2*r**3 - 2*r**g.
-(r + 1)**2*(4*r - 1)
Let j(p) be the second derivative of p**6/10 + 21*p**5/20 + 9*p**4/2 + 10*p**3 + 12*p**2 + 3*p. Let j(g) = 0. What is g?
-2, -1
Let j be 4/6*(3 + 0). Suppose -3*v + 2*f + j*f + 25 = 0, -2*v - 3*f = 6. Determine b so that 1/3 + 1/3*b**4 - 1/3*b - 1/3*b**5 + 2/3*b**v - 2/3*b**2 = 0.
-1, 1
Let z(g) be the first derivative of g**6/6 + g**5 + 7*g**4/4 - g**3/3 - 4*g**2 - 4*g + 14. Factor z(n).
(n - 1)*(n + 1)**2*(n + 2)**2
Let h = 1 - -9. Let f be (h/(-25))/(12/(-20)). Find a such that 1/3*a**3 + f*a**2 + 0 + 1/3*a = 0.
-1, 0
Suppose 4*w = -3*a + 19 - 1, 3*a - w - 3 = 0. Suppose 14 - a = 4*h. Factor -4 - 5*r**2 + h - 3*r + 3.
-(r + 1)*(5*r - 2)
Let y = 20 + -14. Factor -2*s**2 + 2*s**4 + 1 - 1 + 4*s - y*s**3 + 0*s**2 + 2*s**5.
2*s*(s - 1)**2*(s + 1)*(s + 2)
Let q be (-2 - -2)*10/(-30). Factor -1/4*o**2 + 1/2*o + q.
-o*(o - 2)/4
Suppose -10/7*i + 22/7*i**4 + 6/7*i**3 + 4/7*i**5 - 22/7*i**2 + 0 = 0. What is i?
-5, -1, -1/2, 0, 1
Solve 10*l + 2*l**2 - l**3 - 10*l = 0.
0, 2
Let i = 1/147 + 16/49. Factor 0*x + 0 - 1/3*x**2 - i*x**3.
-x**2*(x + 1)/3
Let c(s) = 51*s**3 + 51*s**2 - 30*s - 51. Let m(r) = -5*r**3 - 5*r**2 + 3*r + 5. Let w(a) = 2*c(a) + 21*m(a). Let w(y) = 0. What is y?
-1, 1
Let h be 57/(-120) - 18/(-30). Let n(a) be the first derivative of -1/12*a**3 + h*a**6 + 1/16*a**4 + 0*a**2 + 1/4*a**5 + 2 + 0*a. Find l such that n(l) = 0.
-1, 0, 1/3
Let t = -61/22 - -36/11. Determine a so that -a + 1 - 7/4*a**2 - t*a**3 = 0.
-2, 1/2
Let q(x) be the third derivative of x**5/60 - x**4/12 + x**3/6 - 5*x**2. Factor q(u).
(u - 1)**2
Let s(i) be the second derivative of 0*i**4 + 0 - 3*i + 0*i**3 + 0*i**2 + 1/90*i**5. Factor s(k).
2*k**3/9
Let d be (-56)/20*((-25)/(-15))/(-1). Solve 8/3 + d*u**2 + 44/3*u - 49*u**3 = 0.
-2/7, 2/3
Let t(l) be the second derivative of -l**6/30 - l**5/16 - l**4/48 - 3*l. Let t(c) = 0. What is c?
-1, -1/4, 0
Let a(f) be the first derivative of 0*f + 0*f**2 + 3/4*f**4 + f**3 + 7. Factor a(i).
3*i**2*(i + 1)
Determine t so that 2/9*t**2 + 2/9*t**3 + 0*t + 0 = 0.
-1, 0
Let w(z) = -99*z**2 - 6*z. Let f(b) be the first derivative of 20*b**3/3 + b**2/2 - 4. Let n(i) = 24*f(i) + 5*w(i). Factor n(m).
-3*m*(5*m + 2)
Factor -2/15*d**2 + 0 - 2/15*d**3 + 0*d + 2/15*d**4 + 2/15*d**5.
2*d**2*(d - 1)*(d + 1)**2/15
Suppose -5*b + 4*t + 4 = -2, 0 = -2*b + 5*t - 1. Factor 3 - 3 + 22*x**b - 2*x - 15*x**2.
x*(7*x - 2)
Determine h so that -6*h**2 + 27*h**2 - 11*h**2 - 12*h**2 + 2*h**4 = 0.
-1, 0, 1
Let u(k) be the second derivative of -k**5/110 + 5*k**4/66 - 4*k