e the third derivative of 0 + 0*b + 1/2*b**3 + 8*b**2 - 1/10*b**6 + f*b**7 + 3/10*b**5 - 1/2*b**4. Let s(p) = 0. What is p?
1
Let q(s) be the third derivative of -s**7/525 - 7*s**6/600 + s**5/75 - 14*s**2 - s. Solve q(o) = 0 for o.
-4, 0, 1/2
Let t be 301/735 + 1/(-7). Let m(p) be the first derivative of -2/9*p**3 - t*p**5 - 1/2*p**4 + 6 + 0*p + 0*p**2. Factor m(h).
-2*h**2*(h + 1)*(2*h + 1)/3
Let g(y) be the second derivative of -y**5/45 + y**4/9 + 16*y**3/9 - 4*y**2 - 18*y. Let m(z) be the first derivative of g(z). Factor m(u).
-4*(u - 4)*(u + 2)/3
Let y(t) be the second derivative of 15*t**7/14 + 19*t**6/2 + 5*t**5/2 - 65*t**4/3 - 20*t**3 - 7*t + 3. Let y(i) = 0. What is i?
-6, -2/3, 0, 1
Let k(t) be the first derivative of -t**5/20 - t**4/16 + t**3/12 + t**2/8 - 129. Suppose k(a) = 0. Calculate a.
-1, 0, 1
Let g(x) be the third derivative of x**6/120 - 7*x**5/60 + x**4/24 - x**3 + 2*x**2 - 23. Let m be g(7). Solve 15/2*i - m - 14*i**2 = 0.
1/4, 2/7
Let n(f) = -4*f**4 + 17*f**3 + 31*f**2 + 14*f - 2. Let h(v) = v**4 + v**3 - v**2 + v - 1. Let c(i) = 2*h(i) - n(i). What is y in c(y) = 0?
-1, -1/2, 0, 4
Let s(j) = -2*j**3 + 45*j**2 + 43*j + 11. Let x(t) = t**3 - 15*t**2 - 14*t - 4. Let f(w) = 4*s(w) + 11*x(w). Let f(l) = 0. What is l?
-3, -2, 0
Suppose -s - 5*s = 20*s. Solve 1/3*b**2 - 1/3*b**3 + s + 0*b = 0 for b.
0, 1
Let h be 12/(-3) + 5 - -2. Solve -40*a - 5*a**4 + 9*a**3 + 20*a**2 + 2*a**3 - a**h = 0.
-2, 0, 2
Solve -25/2 + 5/2*b**3 - 5/2*b + 25/2*b**2 = 0.
-5, -1, 1
Let b(o) be the third derivative of o**6/36 - o**5/24 - 5*o**4/4 + 2*o**3/3 + 16*o**2. Let k(x) be the first derivative of b(x). Factor k(l).
5*(l - 2)*(2*l + 3)
Let d(b) = 10*b**3 - 38*b**2 + 202*b - 317. Let q(z) = 3*z**3 - 13*z**2 + 68*z - 106. Let c(s) = -4*d(s) + 14*q(s). Factor c(y).
2*(y - 6)**2*(y - 3)
Let m(b) be the first derivative of -b**7/840 + b**5/40 + b**4/12 + 22*b**3/3 - 21. Let o(n) be the third derivative of m(n). Find t, given that o(t) = 0.
-1, 2
Let d(n) be the second derivative of -n**5/70 + n**4/6 + n + 1. Factor d(w).
-2*w**2*(w - 7)/7
Let q(x) be the first derivative of -19 + 0*x**2 + 0*x - 1/6*x**3. Factor q(z).
-z**2/2
Let t = 25 - 22. Factor 3*w**3 - 12*w - 10*w**2 + 18*w**2 + 12*w**2 + 5*w**t.
4*w*(w + 3)*(2*w - 1)
Let j(w) be the first derivative of w**4/8 + w**3/6 - w**2/4 - w/2 + 5. Let j(p) = 0. What is p?
-1, 1
Let l be 676/5 - 8/40. Suppose 6*g = -2*p + 3*g + 54, l = 5*p + 5*g. Factor -p*m**3 + 0*m**5 - 2*m - 3*m**5 - 15*m**4 - 4*m - 21*m**2.
-3*m*(m + 1)**3*(m + 2)
Let i be 30/9 + -3 + 7/(-30)*-2. Factor 3/5*b + i*b**2 - 7/5.
(b - 1)*(4*b + 7)/5
Let y(q) = q**3 - 78*q**2 + 229*q - 298. Let r be y(75). Factor 2/5*z**2 + 0 - 8/5*z**3 + 0*z + r*z**4 - 4/5*z**5.
-2*z**2*(z - 1)**2*(2*z - 1)/5
Let x be -8*2*(-2)/36. Let k = -8350 + 75158/9. Factor -x*m + k + 2/9*m**2.
2*(m - 2)**2/9
Let m = -43 - -45. Factor 3*z**m + z**5 + 6*z**3 - 4*z**5 + 6*z**4 + 5*z**5 - z**2.
2*z**2*(z + 1)**3
Let o = -1209 + 1215. Let r(t) be the first derivative of 2 + 12/5*t**5 - 2*t**4 - 2/3*t**o - 8/3*t**3 - 4*t + 6*t**2. Factor r(h).
-4*(h - 1)**4*(h + 1)
Let f(t) = -99*t + 12. Let s be f(-3). Let y = s - 2162/7. Determine c, given that -y*c**5 + 3/7*c**4 - 3/7*c**3 + 0 + 0*c + 1/7*c**2 = 0.
0, 1
Let v(n) be the second derivative of n**6/720 + n**5/80 + 3*n**3/2 - 24*n. Let l(b) be the second derivative of v(b). Find a such that l(a) = 0.
-3, 0
Let q(r) be the first derivative of r**3/6 + 15*r**2/2 + 225*r/2 - 34. Factor q(j).
(j + 15)**2/2
Let c(k) be the second derivative of -k**6/10 + 21*k**5/20 - 15*k**4/4 + 9*k**3/2 - 463*k - 1. Factor c(d).
-3*d*(d - 3)**2*(d - 1)
Factor 3*g**5 + 297*g**3 - 53*g**4 - 72*g**3 - 7403*g**2 + 7484*g**2.
g**2*(g - 9)**2*(3*g + 1)
Let f(p) = -14*p**3 + 6*p**2 - 2*p + 50. Let l(y) = -5*y**3 + 2*y**2 - y + 19. Let t(o) = -3*f(o) + 8*l(o). Factor t(i).
2*(i - 1)**2*(i + 1)
Let u = 39/14 - 149/56. Let d(c) be the second derivative of u*c**3 + 0 + 1/4*c**2 + 4*c + 1/48*c**4. Factor d(f).
(f + 1)*(f + 2)/4
Let j = -16 - 11. Let q be 8/(-12)*j/6. Factor q + 9*v - 5*v**3 + 3*v**3 - v**3 - 3*v**2 - 6*v**3.
-3*(v - 1)*(v + 1)*(3*v + 1)
Determine z so that 3*z**2 + 9*z**3 + 291*z - 291*z = 0.
-1/3, 0
Suppose 10/11*c**2 + 0 + 2/11*c**3 - 12/11*c = 0. Calculate c.
-6, 0, 1
Let f be 12 - 15 - (-2 - 6). Let c(h) be the first derivative of -12/5*h**2 - 22/5*h**3 - 2/5*h**6 - 21/5*h**4 - 51/25*h**f - 3/5*h - 3. Factor c(i).
-3*(i + 1)**4*(4*i + 1)/5
Let f(r) be the third derivative of 7*r**6/360 - 173*r**5/180 - 25*r**4/36 + 23*r**2 - 8*r. Solve f(z) = 0 for z.
-2/7, 0, 25
Let w(t) be the second derivative of -t**7/42 - 14*t**6/45 - 52*t**5/45 - 44*t**4/27 - 8*t**3/9 - 94*t. Suppose w(h) = 0. Calculate h.
-6, -2, -2/3, 0
Let i(h) be the third derivative of h**9/40320 - h**8/8960 + h**7/6720 - 7*h**4/8 - 9*h**2. Let t(o) be the second derivative of i(o). Solve t(w) = 0.
0, 1
Determine l so that 32/3 - 112/3*l - 86/3*l**3 - 2/3*l**5 + 22/3*l**4 + 146/3*l**2 = 0.
1, 4
Let j(h) = 5*h**3 - 66*h**2 + 152*h + 640. Let k(d) = -d**2 + 2*d. Let t(y) = -j(y) - 4*k(y). Factor t(b).
-5*(b - 8)**2*(b + 2)
Let o(n) be the third derivative of n**6/720 + n**5/90 + n**4/144 - n**3/6 - n**2 - 14. Solve o(h) = 0 for h.
-3, -2, 1
Suppose -83*p = 24 - 24. Factor -2/9*h + p + 2/9*h**2.
2*h*(h - 1)/9
Let r(i) be the first derivative of -3/2*i**2 - 5 - 2/7*i**3 - 9/7*i + 3/7*i**5 + 1/14*i**6 + 9/14*i**4. Factor r(a).
3*(a - 1)*(a + 1)**3*(a + 3)/7
Let a(z) be the second derivative of -z**7/22680 - z**6/3240 - z**4/12 + 4*z. Let w(f) be the third derivative of a(f). Suppose w(d) = 0. Calculate d.
-2, 0
Suppose 4*y - a = 4, -9*a - 2 = 3*y - 11*a. Factor x**y + 1/3*x**5 - x**4 + 1/3*x**3 - 2/3*x + 0.
x*(x - 2)*(x - 1)**2*(x + 1)/3
Let a = -1146 + 14906/13. Let p = -3/806 + 127/806. Solve -p*j**2 - a*j - 6/13 = 0.
-3, -1
Let c be -4 + (17 - (-1)/(-1)). Let q be (-7)/((-224)/c)*12. Factor -3*w + q + 1/2*w**2.
(w - 3)**2/2
Factor -z - 1/6*z**3 + 5/6*z**2 + 0.
-z*(z - 3)*(z - 2)/6
Solve -5/2*p**2 - 11*p + 15/2 = 0 for p.
-5, 3/5
Suppose -3 = -15*x + 14*x. Let o(q) be the second derivative of 0*q**2 + 3/50*q**5 + 1/75*q**6 + 0 - q + 0*q**x + 1/15*q**4. Factor o(g).
2*g**2*(g + 1)*(g + 2)/5
Let u(g) be the first derivative of -g**4/20 + 2*g**3/15 + g**2/2 - 6*g/5 - 20. Suppose u(r) = 0. What is r?
-2, 1, 3
Let k(a) be the third derivative of -a**7/840 + 7*a**5/240 + a**4/16 + a**2 - 29. Factor k(t).
-t*(t - 3)*(t + 1)*(t + 2)/4
Let w(g) = -g**3 + 4*g**2 + 4*g + 7. Let p be -2*((-44)/8 - -3). Let h be w(p). Find y such that 6*y**4 - 1 - 3*y**4 - 6*y**h + 4 = 0.
-1, 1
Let h(x) = x + 3. Let v be h(0). Let w = -164 - -169. Solve -2*o**5 - o**3 + 3*o**5 + 2*o**4 - 3*o**w - 2*o**2 + 3*o**v = 0 for o.
-1, 0, 1
Let v be 4/8 + 3/2. Let x be 3 - 2/4*v. Determine u, given that -x*u**4 + u**4 - 3*u**3 + u**3 = 0.
-2, 0
Suppose -30*s**3 - 299*s - 173*s + 253*s**2 + 52*s - 211*s**4 + 196 + 212*s**4 = 0. What is s?
1, 14
Solve -4/5*i**3 - 3*i**4 - 4/5 + 4/5*i + 19/5*i**2 = 0.
-1, -2/3, 2/5, 1
Suppose -28 = -4*r - 12. Suppose -4*q - 22 = -2*u, 2*u + 28 = 6*u - r*q. Find g such that -184 + g**2 + u*g + 184 = 0.
-3, 0
Let k = -1/220 - -443/660. Let s(w) be the first derivative of -2/9*w**3 - k*w**2 - 2/3*w - 6. Suppose s(d) = 0. What is d?
-1
Solve 1/8*w**2 - 3/2 - 1/2*w = 0.
-2, 6
Let b(z) be the first derivative of z**4/2 + 2*z**3/3 - 4*z**2 - 8*z + 9. Factor b(y).
2*(y - 2)*(y + 1)*(y + 2)
Suppose -10 = -3*s - 2*s. Factor 7 + 2*t**2 + 3*t**2 - 8*t**s + 5.
-3*(t - 2)*(t + 2)
Solve -1/4*y**3 + 0*y**2 + 0*y**4 + 0 + 1/8*y + 1/8*y**5 = 0.
-1, 0, 1
Suppose -6*s**2 + 13*s**3 - 5*s**4 + 128 - 160*s + 21*s**2 + 6*s**4 + 0*s**4 + 3*s**2 = 0. Calculate s.
-8, 1, 2
Let n(y) be the second derivative of y**6/10 + y**5/20 - y**4/3 + 4*y + 145. Factor n(g).
g**2*(g - 1)*(3*g + 4)
Let d(k) be the first derivative of 1/9*k**3 + 4/3*k - 2/3*k**2 + 11. Determine j, given that d(j) = 0.
2
Let q(y) be the second derivative of -y**5/10 + 13*y**4/6 - 16*y**3 + 36*y**2 - 202*y. Factor q(g).
-2*(g - 6)**2*(g - 1)
Suppose 0 = -3*c, 12*c + 10 = 5*k + 14*c. Determine r so that 2/9*r**k + 0 + 0*r = 0.
0
Let n(z) be the first derivative of -z**5/45 - 2*z**4/9 - 8*z**3/9 + 11*z**2/2 + 7. Let y(u) be the second derivative 