*a. Let b be j(12). Let g be (-2)/(-9) + 6/b. Find k, given that g*k - 1/4*k**2 + 1/4 - 1/4*k**3 = 0.
-1, 1
Suppose 4*n**2 + 139*n - 2*n**2 - 135*n = 0. What is n?
-2, 0
Let w(m) = -m + 5. Let z be w(5). Suppose z = -5*c + c + 20. What is f in f**4 - f**2 + f**3 + 3*f**4 - f**c - 3*f**4 = 0?
-1, 0, 1
Let 2*z**4 + 0*z**4 + 2*z**4 - 2*z**3 - 2*z**4 = 0. What is z?
0, 1
Let l be 77/147 - (-6)/42. Factor -6*p**3 + 4*p**2 + 8/3*p**4 + 0 - l*p.
2*p*(p - 1)**2*(4*p - 1)/3
Suppose -3/4*g**3 - 36*g + 48 + 9*g**2 = 0. Calculate g.
4
Suppose -p - 27 = 25. Let w = 94 + p. Determine g, given that -59*g**2 - 342*g**3 - w*g + 4 + 47*g**2 + 184*g**2 + 328*g**4 - 120*g**5 = 0.
1/3, 2/5, 1/2, 1
Suppose 5*u - 26 = -1. Let n(r) be the second derivative of 0 + 1/6*r**4 - 1/15*r**6 + 0*r**2 + 3*r - 1/3*r**3 + 1/10*r**u. Determine h so that n(h) = 0.
-1, 0, 1
Let s(i) = 2*i**3 - 21*i**2 - 14*i + 36. Let w be s(11). Let c(m) be the first derivative of 0*m + 2 - 3/2*m**2 - m**w. Solve c(h) = 0 for h.
-1, 0
Suppose 15 = 2*j + 7. Suppose -j = -v - 2. Factor 2/3 + 2/3*w**3 - 2/3*w**v - 2/3*w.
2*(w - 1)**2*(w + 1)/3
Let s be (-6)/(-9)*12/2. Suppose -q = -s*q. Factor 3*w**3 + 2*w - w + q*w**2 + w**4 + 3*w**2.
w*(w + 1)**3
Let l be 1/2 - (-15)/10. Let x be (-6)/(-3)*1 + -1. Factor -6 + 5*c + 3*c - 3 + x - l*c**2.
-2*(c - 2)**2
Let f(b) be the second derivative of -b**5/80 + b**4/3 - 8*b**3/3 + 22*b. Determine j, given that f(j) = 0.
0, 8
Let o(h) = h**3 - 3*h**2 - 5*h - 1. Let l(c) = -c - 1. Suppose -p = 3*b + 2*b - 35, 0 = p - 5*b + 15. Let t(m) = p*l(m) - 2*o(m). Suppose t(q) = 0. Calculate q.
-1, 2
Let g(b) be the first derivative of 2*b**3/33 - 2*b/11 + 11. Find p such that g(p) = 0.
-1, 1
Let w = -34/9 + 310/63. Find j such that -2/7*j**4 - w*j - 8/7 + 4/7*j**3 + 6/7*j**2 = 0.
-1, 2
Let y(m) = 31*m**3 - 72*m**2 + 39*m - 13. Let a(b) = b**3 + b + 1. Suppose 0 = -4*k + 6 - 2. Let q(o) = k*y(o) + 5*a(o). Suppose q(c) = 0. What is c?
1/3, 2/3, 1
Let r(p) be the third derivative of -2*p**6/15 + 9*p**5/5 - 9*p**4 + 18*p**3 - 15*p**2. Find x, given that r(x) = 0.
3/4, 3
Factor -5*h**2 + 5*h - 2*h**4 - 49*h**3 + 44*h**3 + 5*h**4 + 2*h**4.
5*h*(h - 1)**2*(h + 1)
Suppose 6*f + 10 = 4*f. Let h(d) = d**3 + 4*d**2 - 6*d. Let q be h(f). What is m in -2*m**2 + 3*m - 8 + 0*m**2 + q*m = 0?
2
Factor 4/3*c + 7/3*c**4 + 5*c**3 + 13/3*c**2 + 1/3*c**5 + 0.
c*(c + 1)**3*(c + 4)/3
Suppose 2 = -b - 27. Let z be b/(-9) + (1 - 4). Factor -8/9*y - 8/9 - z*y**2.
-2*(y + 2)**2/9
Let w(y) be the first derivative of 10*y**3/9 + 7*y**2/3 + 4*y/3 - 5. Let w(r) = 0. What is r?
-1, -2/5
Find h such that h**2 - 2*h**2 + 2*h**2 + h**2 = 0.
0
Find n such that 18/5*n**2 - 4/5 - 14/5*n**4 + 2*n - 2*n**3 = 0.
-1, 2/7, 1
Let u be 10/6 - 1/(-3). Let -4*p**u + 0 + 2*p**2 + 3 - 1 = 0. What is p?
-1, 1
Let x = -267 + 803/3. Factor 7/3*s + x + 5/3*s**2.
(s + 1)*(5*s + 2)/3
Let z(j) = -4*j**4 - 2*j**3 - j**2. Let h(r) = r - 3. Let u be h(-3). Let x(g) = -7*g**4 - 4*g**3 - 2*g**2. Let o(t) = u*x(t) + 10*z(t). Solve o(p) = 0 for p.
-1, 0
Let x(g) = -g**3 + 4*g**2 + 8*g - 3. Let b be x(5). Suppose -2*h + 5*h = b, -3*h + 12 = -3*q. Factor -2 + 1 + q*k + 2*k - k**2.
-(k - 1)**2
Suppose 2*g = 5*a - 91, 2*a - 5*a = 4*g - 39. Let f(j) = -38*j**2 + 65*j - 12. Let h(n) = 13*n**2 - 22*n + 4. Let b(w) = a*h(w) + 6*f(w). Factor b(d).
-(d - 2)*(7*d - 2)
Let q(z) be the second derivative of -z**8/26880 + z**7/10080 + z**4/12 - 2*z. Let a(c) be the third derivative of q(c). Find g, given that a(g) = 0.
0, 1
Suppose -6/11*x**4 + 0*x - 2/11*x**5 + 0*x**2 - 4/11*x**3 + 0 = 0. What is x?
-2, -1, 0
Let o(y) = -y**2 - 2*y + 50. Let x be o(6). Factor 4/7*k**x + 2/7*k - 4/7*k**4 + 0 + 0*k**3 - 2/7*k**5.
-2*k*(k - 1)*(k + 1)**3/7
Factor -1/7*o**2 - 6/7 - o.
-(o + 1)*(o + 6)/7
Let d be (-6)/8 + 14/8. Suppose x - d = 2. Factor -x*p**2 - 3*p**4 + 4*p**4 - 4*p + 2 + 3*p + p**3.
(p - 1)**2*(p + 1)*(p + 2)
Let m(c) be the second derivative of -c**7/147 + c**5/70 + 9*c. Suppose m(o) = 0. Calculate o.
-1, 0, 1
Factor -2*d + 9*d**2 + 3*d - 10*d - 3*d**3 + 3.
-3*(d - 1)**3
Let i(j) = -j**4 + 36*j**3 - 25*j**2 + 23*j - 11. Let m(r) = 12*r**3 - 8*r**2 + 8*r - 4. Let s(x) = 4*i(x) - 11*m(x). Find k, given that s(k) = 0.
0, 1
Let h(k) = 2*k - 2. Let n = 9 - 7. Let r be h(n). Solve 10 - 6 - 6*m**2 + 4*m**4 - r*m**4 + 2*m - 2*m**3 = 0 for m.
-1, 1, 2
Let q be 2*((-35)/(-3000))/7. Let b(t) be the third derivative of q*t**5 + t**2 + 0 + 2/15*t**3 + 0*t - 1/30*t**4. Determine a so that b(a) = 0.
2
Let z(n) be the third derivative of -n**9/1512 - n**8/280 - n**7/140 - n**6/180 + 5*n**3/6 + 5*n**2. Let w(u) be the first derivative of z(u). Factor w(i).
-2*i**2*(i + 1)**3
Suppose 7 = 3*n - 2. Let j be (2/(-3))/(n/(-39)). Factor 2/3 + 92/3*m**2 - 20/3*m**3 - 350/3*m**4 + j*m + 250/3*m**5.
2*(m - 1)**2*(5*m + 1)**3/3
Let d(g) be the first derivative of 2/21*g**3 - 2 + 1/14*g**4 + 0*g + 0*g**2 - 2/35*g**5 - 1/21*g**6. Solve d(t) = 0.
-1, 0, 1
Let t(i) be the third derivative of -i**6/24 - 7*i**5/12 - 25*i**4/8 - 15*i**3/2 + 3*i**2. Let t(z) = 0. What is z?
-3, -1
Let r be 10 - (6 + (-2 - 0)). Let x(q) = 4*q - 21. Let z be x(r). Factor 0*k + 2/5*k**z + 0 + 2/5*k**2.
2*k**2*(k + 1)/5
Let q(y) be the first derivative of 2*y**5/25 - y**4/2 + 6*y**3/5 - 7*y**2/5 + 4*y/5 - 13. Determine u, given that q(u) = 0.
1, 2
Factor -1/2*j**3 - 4*j**2 - 13/2*j - 3.
-(j + 1)**2*(j + 6)/2
Determine n so that -2/7*n**2 - 2/7*n**3 + 2/7 + 2/7*n = 0.
-1, 1
Let b(w) = w**2 + 4*w + 7. Let l be b(-5). Suppose -3*t + 9 = 2*q, -t - 3*t = 4*q - l. Determine h, given that -2*h**t - 4*h - 2*h**3 + 2 + 8*h**3 - 2*h**4 = 0.
-1, 1
Factor 2*u**4 + 19*u**3 - 7*u**3 + 2*u**4.
4*u**3*(u + 3)
Let m be (-2)/(-10)*(0 + 4). Let q = 1146/5 - 228. Factor 2/5*b**2 + m - q*b.
2*(b - 2)*(b - 1)/5
Let n = -157/20 + 33/4. Find w, given that n*w**2 - 4/5 - 2/5*w = 0.
-1, 2
Suppose -4*z + 2*q = 9 + 1, -4*z - 14 = 2*q. Let h be (-9)/21 - 3/z. Find w such that 4/7*w**4 - h*w**2 + 0 + 2/7*w - 2/7*w**3 = 0.
-1, 0, 1/2, 1
Find c such that 0*c**3 + 0 + 1/2*c**2 - 1/2*c**4 + 0*c = 0.
-1, 0, 1
Let d = -10 + 4. Let a be 4/3*d/(-28). Factor 2/7 - a*b**2 + 0*b.
-2*(b - 1)*(b + 1)/7
Factor w**4 + 10*w**4 - 5*w**2 + 5*w**5 + 10*w - 15*w**3 - 6*w**4.
5*w*(w - 1)**2*(w + 1)*(w + 2)
Suppose 5 - 25 = -4*d. Let l(g) be the second derivative of -5/9*g**3 + 0 + 2/3*g**2 - 1/30*g**d + 2/9*g**4 + g. Let l(p) = 0. Calculate p.
1, 2
Let d = 94 - 93. What is l in d - 1/2*l - 1/2*l**2 = 0?
-2, 1
Let u(s) be the second derivative of -s**5/4 + s**4/6 + 10*s**3/3 - 4*s**2 + 13*s. Factor u(b).
-(b - 2)*(b + 2)*(5*b - 2)
Suppose -5*t + 25 = 3*j, j + 0*j = -5*t + 15. Let q(g) be the third derivative of 0*g**3 - 2*g**2 + 0*g + 0 - 1/132*g**4 - 2/165*g**j. Factor q(n).
-2*n*(4*n + 1)/11
Let w(r) be the first derivative of -8*r**5/25 + 13*r**4/10 - 2*r**3 + 7*r**2/5 - 2*r/5 + 29. Factor w(k).
-2*(k - 1)**3*(4*k - 1)/5
Find k such that 2*k**2 - 304*k + 290*k + 0*k**2 = 0.
0, 7
Let o(g) be the first derivative of -g**4 + g**3 + 2*g**2 + 7*g - 2. Let i(a) = -a**3 + a**2 + a + 1. Let f(p) = -10*i(p) + 2*o(p). Factor f(s).
2*(s - 2)*(s - 1)*(s + 1)
Let z = -795/4 - -4047/20. What is j in 12/5*j + z + 2/5*j**2 = 0?
-3
Let m(o) be the third derivative of -o**9/7560 + o**7/1050 - o**5/300 - o**3/2 + 3*o**2. Let q(n) be the first derivative of m(n). Let q(x) = 0. Calculate x.
-1, 0, 1
Let f = 0 + 4. Let z(b) be the second derivative of -2*b - 1/6*b**f + 0 + 0*b**3 - 3/10*b**5 - 1/5*b**6 - 1/21*b**7 + 0*b**2. Factor z(m).
-2*m**2*(m + 1)**3
Suppose -8*z = -z. Solve z - 2/9*t**2 + 2/9*t = 0 for t.
0, 1
Suppose -1 = -2*c + 7. Find v such that -2*v**3 + 8*v - c*v**2 - 4*v**3 + 2*v**3 + 0*v**2 = 0.
-2, 0, 1
Let a(q) be the first derivative of -q**4/54 - 4*q**3/27 - 4*q**2/9 - q - 1. Let i(p) be the first derivative of a(p). Suppose i(y) = 0. Calculate y.
-2
Let o(r) be the second derivative of 1/2*r**3 + 3/20*r**5 + 0 - r - 1/2*r**4 + 0*r**2. Determine j, given that o(j) = 0.
0, 1
Let f(g) be the second derivative of -3*g**5/20 + g**3/2 + 40*g. Let f(n) = 0. Calculate n.
-1, 0, 1
Let n(m) be the first derivative of -1/30*m**5 + m**2 + 0*m + 1 + 1/3*m**3 + 0*m**4. Let k(i) be the second derivative of n(i). Factor k(c).
-2*(c - 1)*(c + 1)
Let d = 702 + -4910/7