*b + 80/3*b**2 + 1/3*b**5 + 40/3*b**3 = 0.
-2
Let w(y) be the third derivative of y**6/80 + 56*y**2. What is k in w(k) = 0?
0
Let c(v) be the first derivative of v**2 + 10/21*v**3 + 6/7*v - 10 + 1/14*v**4. Factor c(g).
2*(g + 1)**2*(g + 3)/7
Suppose -4*l + 58 = 5*y, -2*y + 3 = 3*l - 23. Suppose y*i = 9*i + 3. Factor 8*s**4 + 1 - 4*s + 11*s**4 + 4*s**i - 22*s**4 + 2*s**2.
-(s - 1)**2*(s + 1)*(3*s - 1)
Suppose 4*r = 3*w + 4, -5*r = -r - 16. Suppose w*x = 3*x. Suppose x + 1/5*a**2 + 2/5*a - 1/5*a**3 = 0. Calculate a.
-1, 0, 2
Let m be (3 - 6/(-4))*(-9 - -13). Let n(j) be the first derivative of m*j**2 + 8/3*j**3 - 3 + 16*j. Factor n(w).
4*(w + 4)*(2*w + 1)
Suppose 12 = 3*f, -4*f - 4 = 3*h - 7*h. Let p(a) be the second derivative of 6*a - 1/4*a**4 + 3/80*a**h + 0*a**2 + 0 + 1/2*a**3. Let p(c) = 0. What is c?
0, 2
Let r(z) be the second derivative of z**4/12 - 5*z**3/6 - 15*z. Factor r(t).
t*(t - 5)
Let m(s) be the second derivative of s**6/50 + 9*s**5/50 - 6*s**4/5 + 13*s**3/5 - 27*s**2/10 + 23*s. Find x, given that m(x) = 0.
-9, 1
Suppose 4/9*t**2 - 12*t + 104/9 = 0. Calculate t.
1, 26
Let l(x) be the second derivative of 0*x**3 - 1/120*x**6 + 0*x**2 - 1/16*x**4 - 1/168*x**7 + 0 + 1/16*x**5 - 17*x. Factor l(a).
-a**2*(a - 1)**2*(a + 3)/4
Find j, given that 52/5*j**3 + 64/5 + 28/5*j**5 + 352/5*j + 172/5*j**4 - 668/5*j**2 = 0.
-4, -1/7, 1
Suppose 0*c = 4*n + 2*c - 4, 2*c = 2*n - 14. Suppose b - 2*b + 3 = n*m, 0 = 3*b + m - 9. Factor -b*a**4 + 12*a**3 - 11*a**2 + 0*a**4 + 7*a**2 - 8*a**2.
-3*a**2*(a - 2)**2
Let h(p) be the third derivative of p**7/70 + p**6/60 - 2*p**3/3 + 20*p**2. Let r(a) = -5*a**4 - 4*a**3 + 7. Let g(c) = 7*h(c) + 4*r(c). Factor g(v).
v**3*(v - 2)
Suppose -15 = q - 6*q. Let n(d) = 5*d**2 + 7*d + 1. Let x(o) = -5*o**2 - 4*o**2 + 8*o**2. Let m(i) = q*x(i) - 3*n(i). Factor m(w).
-3*(w + 1)*(6*w + 1)
Suppose -6771*c + 90 = -6726*c. Suppose -28/9*u**c + 64/9*u - 16/9 = 0. Calculate u.
2/7, 2
Let z(v) be the third derivative of -1/12*v**4 + 1/60*v**6 + 0*v + 9*v**2 + 2/3*v**3 + 0 - 1/15*v**5. Find j such that z(j) = 0.
-1, 1, 2
Let d(g) be the third derivative of g**8/1344 + 11*g**7/840 + 43*g**6/480 + 73*g**5/240 + 7*g**4/12 + 2*g**3/3 + 174*g**2. Let d(b) = 0. Calculate b.
-4, -1
Let c = 196/9 - 64/3. Suppose -32*h + 36*h = 0. Factor h - 2/9*x - 2/9*x**3 + c*x**2.
-2*x*(x - 1)**2/9
Let r(g) be the first derivative of -g**7/210 + g**5/20 + g**4/12 - 8*g**2 - 2. Let v(c) be the second derivative of r(c). What is j in v(j) = 0?
-1, 0, 2
Suppose 5*f = 20 + 10. Let z be f/(-70) - 14/(-49). Factor 0 + 0*h + 0*h**3 - 1/5*h**2 + z*h**4.
h**2*(h - 1)*(h + 1)/5
Let o = -5 - -9. Factor 36*m**3 + 8*m**2 - 4 + 27*m**5 + 53*m**o + 4 + m**4.
m**2*(3*m + 2)**3
Factor -13/3*y - 10/3 + y**2.
(y - 5)*(3*y + 2)/3
Let c(r) be the first derivative of -2*r**3/15 + 2*r**2 + 48*r/5 - 728. Factor c(k).
-2*(k - 12)*(k + 2)/5
Let f = 68 + -66. Let d(c) = -c**3 - 7*c**2 + 9*c + 11. Let v be d(-8). Let -32*g**3 - 25*g**v + 22*g**3 - 56*g**2 - 4*g**f + 20*g = 0. What is g?
-2, 0, 2/7
Let l(d) be the first derivative of 28/9*d**3 + 2/3*d**2 - 5/3*d**4 - 4*d - 13. Factor l(b).
-4*(b - 1)**2*(5*b + 3)/3
Let x(w) be the third derivative of 7/60*w**6 - 31/30*w**5 + 0 - 34/21*w**4 - 3*w**2 - 20/21*w**3 + 0*w. Factor x(g).
2*(g - 5)*(7*g + 2)**2/7
Factor -17*b - 33*b + 250266*b**2 - 120 - 250271*b**2.
-5*(b + 4)*(b + 6)
Suppose 4*i + 2*t - 40 = -52, -4*i - 6*t = 36. Solve l**3 + 1/2*l**4 + 1/2*l**2 + 0 + i*l = 0 for l.
-1, 0
Suppose -3*z - 2*s + 8 = 0, 3*z - 14 = s - 0. Let t be (-91)/(-130) + (-2)/z. Find j, given that 3/5*j - t*j**2 - 2/5 = 0.
1, 2
Let o(x) be the third derivative of x**8/112 + x**7/35 - 7*x**6/40 - x**5 - 3*x**4/2 - x**2 - 33. Suppose o(z) = 0. What is z?
-2, -1, 0, 3
Let w(o) be the third derivative of -8*o**2 - 1/6*o**3 + 0 + 1/24*o**4 + 0*o. Let c(t) = -t**2 - 5. Let d(a) = c(a) - 3*w(a). Find b, given that d(b) = 0.
-2, -1
Factor 45*g**2 - 80*g + 3*g**2 - 18*g**3 + 40 + 18 + 54*g**2 - 258.
-2*(g + 1)*(3*g - 10)**2
Suppose 0 = -j + 5*g + 12, -4*g - 27 = -j - 17. Determine o, given that 0 - j*o**2 + 0*o - 2*o**4 + 20/3*o**3 = 0.
0, 1/3, 3
Suppose 17*d + 6 = 20*d. Let c be 6 - d/3*6. Let -2/3*n**3 + 4/3*n + 0 - 2/3*n**5 + 2*n**c - 2*n**4 = 0. What is n?
-2, -1, 0, 1
Factor -1/9*z**3 - 1/9*z**2 + 4/3 + 8/9*z.
-(z - 3)*(z + 2)**2/9
Let s(r) = 3*r**3 + 5*r**2 + 2*r - 4. Let k(q) = -15*q**3 - 24*q**2 - 9*q + 21. Let b(x) = -4*k(x) - 21*s(x). Factor b(z).
-3*z*(z + 1)*(z + 2)
Let t = -31 - -36. Let f(x) be the second derivative of -12*x + 1/28*x**7 + 1/4*x**3 + 0 + 0*x**2 + 0*x**6 - 3/20*x**t + 0*x**4. Factor f(w).
3*w*(w - 1)**2*(w + 1)**2/2
Let f(r) be the second derivative of -r**4/36 - 7*r**3/9 - 4*r**2 - 20*r. Let f(o) = 0. What is o?
-12, -2
Let u(r) be the first derivative of r**6/480 + r**5/120 + r**4/96 + 9*r**2 - 14. Let a(z) be the second derivative of u(z). Determine w so that a(w) = 0.
-1, 0
Let w(i) be the second derivative of -i**5/70 + 9*i**4/14 - 68*i**3/21 - 96*i**2/7 + 94*i - 2. Solve w(j) = 0 for j.
-1, 4, 24
Let q(c) be the first derivative of 0*c**2 + 2 + 2*c**3 + 21/20*c**5 - 4*c + 4*c**4. Let w(k) be the first derivative of q(k). Factor w(r).
3*r*(r + 2)*(7*r + 2)
Suppose -14 = -3*b - o, 0*o - 17 = -4*b - 3*o. Let -z**4 - 4*z**2 - z - 2*z**3 + 2*z**5 + b*z**4 + 0*z**3 + z**5 = 0. What is z?
-1, -1/3, 0, 1
Let u(h) be the third derivative of -1/30*h**6 - 1/30*h**5 + 0 + 2/105*h**7 + 5/24*h**4 + 0*h - 1/336*h**8 + h**2 - 1/3*h**3. Factor u(f).
-(f - 2)*(f - 1)**3*(f + 1)
Let p be (-9)/(-26) - ((-148)/(-52) - 3). Let k(t) be the second derivative of 0*t**3 + 1/12*t**4 + 0 - p*t**2 + t. Factor k(b).
(b - 1)*(b + 1)
Suppose 4*k - 3*w - 2 - 33 = 0, 3*w = k - 11. What is s in -32/3*s - 40/3*s**3 + 82*s**2 - k = 0?
-1/4, 2/5, 6
Let p(x) be the second derivative of -112*x**6/165 + 4*x**5/5 + x**4/2 - 7*x**3/33 - 2*x**2/11 - 34*x. Find o such that p(o) = 0.
-1/4, 2/7, 1
Let u(d) be the first derivative of 0*d**2 - 1/1620*d**6 - 2/3*d**3 - 1/540*d**5 + 0*d**4 + 0*d - 5. Let z(f) be the third derivative of u(f). Factor z(m).
-2*m*(m + 1)/9
Let a = 48 + -44. Solve -11*v**a - 5*v**4 - 4*v**5 + 52*v - 56*v - 16*v**2 - 24*v**3 = 0.
-1, 0
Let v(i) be the second derivative of i**4/60 - 94*i**3/15 + 4418*i**2/5 - 4*i - 8. Solve v(t) = 0.
94
Suppose 0 = 13*b - 6*b - 28. Let d(p) be the second derivative of 0 - 2/9*p**3 + 1/3*p**2 + p + 1/18*p**b. Let d(a) = 0. What is a?
1
Let d(y) be the second derivative of 0 + 3/2*y**4 - 4*y**2 + 4*y**3 - 7/10*y**5 - 18*y. Solve d(l) = 0 for l.
-1, 2/7, 2
Let r = 3/829 + 3277/10777. Determine b, given that -54/13*b**3 - r - 84/13*b**2 - 34/13*b = 0.
-1, -1/3, -2/9
Suppose 0 = -3*r + 5*i + 11, -4*i - 24 = -20. Factor 1/4*x**3 + 3/8*x**r - 1/4*x - 3/8*x**4 + 0.
-x*(x - 1)*(x + 1)*(3*x - 2)/8
Let x be ((-2)/72*-2)/(44/264). Factor x*i**3 - 1/3*i**2 - 1/3*i + 1/3.
(i - 1)**2*(i + 1)/3
Factor -111/2*c - 45 - 27/2*c**2.
-3*(c + 3)*(9*c + 10)/2
Let t = -67 - -98. Let u = -16 + t. Find y such that 16 + 56*y**5 - 15*y - 220*y**2 - 13*y + 439*y**3 - 282*y**4 + 4*y + u*y**3 = 0.
-1/4, 2/7, 1, 2
Let r(i) be the second derivative of 0*i**2 - 1/55*i**6 + 1/22*i**4 - 2/33*i**3 + 1/55*i**5 + 0 + 6*i. Solve r(x) = 0 for x.
-1, 0, 2/3, 1
Let i(x) = 6*x**3 - 2*x**2 + 2*x - 1. Let n be i(1). Suppose -n = -4*w + 3. Factor g**5 - 11*g**5 - w*g**5 - 3*g**4.
-3*g**4*(4*g + 1)
Let q(j) be the first derivative of 1/16*j**4 - 1/8*j**2 + 19 + 1/12*j**3 - 1/4*j. Factor q(g).
(g - 1)*(g + 1)**2/4
Let y = 1629 - 1622. Let o(s) be the third derivative of 13/210*s**5 - 8*s**2 + 1/70*s**6 + 0 + 0*s + 1/735*s**y + 4/21*s**3 + 1/7*s**4. Factor o(n).
2*(n + 1)**2*(n + 2)**2/7
Let n = -7/131 - -4227/655. Let x = 782/5 + -156. Let -x + n*d - 128/5*d**2 = 0. What is d?
1/8
Suppose 4*j + j = 0. Suppose c - 4 - 28 = j. Factor c*s**4 + 3 + 3*s**2 - s - 9*s - 8*s + 16*s**4 + 72*s**3.
3*(s + 1)**2*(4*s - 1)**2
Let k(j) be the third derivative of -5*j**8/336 + j**7/14 - j**6/12 - 259*j**2. Solve k(c) = 0.
0, 1, 2
Let p(l) be the first derivative of -5/11*l**2 - 7 - 4/11*l**3 + 0*l - 1/22*l**4. What is q in p(q) = 0?
-5, -1, 0
Suppose 16/7*c - 2/7*c**2 - 2 = 0. Calculate c.
1, 7
Let b(k) be the third derivative of k**6/30 - 13*k**5/15 + 23*k**4/6 - 22*k**3