*5 - 4*b**5 - k*b**3 + b**4 + 2*b = 0.
-1, 0, 1/2
Let b = -8006 - -8006. Factor 0*z + b + 2/7*z**4 - 10/7*z**3 + 8/7*z**2.
2*z**2*(z - 4)*(z - 1)/7
Factor 80*r + 60 + 72*r - 35*r**2 + 5*r**3 - 132*r.
5*(r - 6)*(r - 2)*(r + 1)
Let z = -9 - -11. Determine o so that -10*o**z + 7 - 8*o + 49*o**3 + 1 - 43*o**3 = 0.
-1, 2/3, 2
Let i(o) = 5*o**2 - 303*o - 10924. Let u(y) = -4*y**2 + 302*y + 10928. Let k(v) = 6*i(v) + 7*u(v). Find f, given that k(f) = 0.
-74
Let q(r) be the first derivative of 0 + 2*r**4 + 0*r**4 + 4*r - 12 + 0*r - 9*r**2 + 2*r**3. Factor q(o).
2*(o - 1)*(o + 2)*(4*o - 1)
Let w(h) = 18*h**2 + 6*h - 2. Let r(p) = 21*p**2 + 6*p - 3. Let q(o) = 5*r(o) - 6*w(o). Determine n so that q(n) = 0.
-1
Let o(a) be the first derivative of -4*a**6/3 - 268*a**5/5 + 831*a**4/8 - 105*a**3/2 + 887. Factor o(k).
-k**2*(k + 35)*(4*k - 3)**2/2
Let y(k) be the third derivative of 0*k - 1/120*k**4 - 1/100*k**5 - 9*k**2 + 0 + 1/15*k**3. Factor y(z).
-(z + 1)*(3*z - 2)/5
Let n be ((-2)/4)/(4/176). Let y be n/(-18) - 2/6. What is c in 4/9*c**4 - 2/9*c + 0 + y*c**3 - 2/3*c**5 - 4/9*c**2 = 0?
-1, -1/3, 0, 1
Let i be 55/20*-2*4/(-11). Let m(s) = s**2 - 7*s + 4. Let w be m(7). Factor 0 + 0*q**3 + 0*q**i - 2/7*q**w + 0*q.
-2*q**4/7
Let w = -553/24 - -569/24. Find k such that -32/3*k - 128/3 - w*k**2 = 0.
-8
Let z(k) = 9*k**4 - 140*k**3 + 269*k**2 - 182*k - 11. Let s(d) = -2*d**4 + 28*d**3 - 54*d**2 + 36*d + 2. Let j(l) = -11*s(l) - 2*z(l). Factor j(w).
4*w*(w - 4)*(w - 2)*(w - 1)
Let f(c) be the second derivative of c**6/180 - c**5/90 - c**4/18 + 13*c**2/2 + 37*c. Let i(y) be the first derivative of f(y). Factor i(g).
2*g*(g - 2)*(g + 1)/3
Suppose 24*g = 8 + 64. Let c(p) be the second derivative of 1/21*p**4 + 0*p**2 + 0 + 1/21*p**g + 4*p + 1/70*p**5. What is h in c(h) = 0?
-1, 0
Let l = -9/85 + 367/255. Let c(v) be the first derivative of 2/15*v**5 - 9 - 2/3*v**3 - 1/3*v**4 + 8/3*v + l*v**2. Factor c(j).
2*(j - 2)**2*(j + 1)**2/3
Factor 2*l**3 - 5*l**4 - 30*l**2 + 8*l**3 - 20*l + 22*l**3 + 13 + 27 - 7*l**3.
-5*(l - 2)**3*(l + 1)
Suppose 0 = 6*b - 2*b - 8. Determine v, given that v**4 + 3*v**2 - 2*v**b - 2 + 0*v**4 - 3*v + 3*v**3 = 0.
-2, -1, 1
Let i(t) = -t**4 + 2*t**3 + 3*t**2 - 2*t + 2. Let x(g) = -9*g + 7 + 2 + 12*g**2 + 4*g**3 + 3*g**3 - 5*g**4. Let b(p) = 9*i(p) - 2*x(p). Let b(j) = 0. What is j?
-3, -1, 0
Let u = 6/781 + 178813/4686. Let t = -75/2 + u. Determine h, given that 0*h - 8/3 + 2*h**2 - t*h**3 = 0.
-1, 2
Factor 0 + 0*b + 2*b**3 + 3/2*b**2 + 1/2*b**4.
b**2*(b + 1)*(b + 3)/2
Let c = -3314/63 - -1184/21. Let -2/3 - 8/3*g**3 - 28/9*g**2 - 8/9*g**5 + c*g**4 + 32/9*g = 0. What is g?
-1, 1/4, 1, 3
Suppose -3*u = 4*w - 105, 46*w = 44*w - 2*u + 52. Solve 4/3 + 139/3*k**3 + w*k**5 - 5*k**2 + 69*k**4 - 8*k = 0 for k.
-1, 2/9
Suppose -21*d + 81 = -3. Suppose -12*x + d*x = x. Factor x*m**2 + 0*m + 9/5*m**5 + 0 + 0*m**3 + 6/5*m**4.
3*m**4*(3*m + 2)/5
Let w = -8324 + 8326. Factor w*h**2 + 0*h - 343/4*h**5 + 0 - 21*h**3 + 147/2*h**4.
-h**2*(7*h - 2)**3/4
Let y(r) be the first derivative of -2*r**3/21 - 39*r**2/7 - 76*r/7 + 22. Solve y(h) = 0 for h.
-38, -1
Let o = 1627/10829 - -3/833. Factor 0*n - o*n**2 + 0 + 2/13*n**4 + 0*n**3.
2*n**2*(n - 1)*(n + 1)/13
Let y(c) = 4*c**2 + 1. Let w be y(1). Let -36*z - 4 + 25*z**w - 44*z**2 + 4 + 80*z**4 - z**3 + 48*z = 0. What is z?
-3, -1, 0, 2/5
Let c(z) be the first derivative of -z**4/16 + 7*z**3/12 - 3*z**2/2 - 30. Factor c(p).
-p*(p - 4)*(p - 3)/4
Suppose w = -2 + 5. Suppose 3*l - 2 - 10 = -w*z, -5*z - 4 = -l. Factor z + 10*v + 282*v**2 + 0 - 277*v**2.
5*v*(v + 2)
Let t(w) = w**2 - w. Let c be t(2). Suppose c*m = 4*n + 10, -3*m + 0*n + 7 = 2*n. Find u such that 15*u**2 + 33 - 36 - 3*u - 6*u**m - 3*u**3 = 0.
-1/3, 1
Let x be 0 + (-2)/(8/(-140)). What is r in r**2 + 21 - 2*r + 15 - x + 4*r = 0?
-1
Let c(f) be the third derivative of f**5/450 - f**4/10 - 19*f**3/45 + 8*f**2 - 25*f. Let c(m) = 0. Calculate m.
-1, 19
Let n = 5805 + -17413/3. Factor -1/3*q**2 + 0 + 1/3*q**4 - 2/3*q + n*q**3.
q*(q - 1)*(q + 1)*(q + 2)/3
Factor 33/2*p - 5/2*p**2 - 1/2*p**3 - 27/2.
-(p - 3)*(p - 1)*(p + 9)/2
Let j(q) = 4*q**3 + 20*q**2 - 28*q + 4. Let z(x) = 3*x**3 + 19*x**2 - 27*x + 5. Let b(k) = -5*j(k) + 6*z(k). Solve b(d) = 0 for d.
1, 5
Let r(w) be the first derivative of -w**3/3 - 196*w**2 - 38416*w - 455. Factor r(k).
-(k + 196)**2
Let m(a) = -3*a**2 - 5*a + 10. Suppose 0 = -2*f, -4*w + f - 88 = -0*f. Let h(n) = 16*n**2 + 26*n - 50. Let y(l) = w*m(l) - 4*h(l). Factor y(q).
2*(q - 2)*(q + 5)
Let l = 2127 + -2123. Let i(p) be the second derivative of -2*p - 1/11*p**3 + 0 + 0*p**2 + 1/66*p**l. Factor i(s).
2*s*(s - 3)/11
Let a = 3 - 4. Let x(s) = s**3 + s + 1. Let w be x(a). Let y(o) = o**3 + 3*o**2 + 2*o + 4. Let c(p) = -p**3 - p**2 - 1. Let q(d) = w*y(d) - 4*c(d). Factor q(j).
j*(j + 1)*(3*j - 2)
Let s(k) = 4*k**3. Let w(c) be the first derivative of c**4/4 - c**3/3 - 2. Let l(r) = -s(r) + 2*w(r). Determine u, given that l(u) = 0.
-1, 0
Determine a, given that -6*a + 0 - 21/5*a**2 - 3/5*a**3 = 0.
-5, -2, 0
Find b, given that -3/7*b**2 - 240/7 + 9*b = 0.
5, 16
Suppose -4*o + 3*y + 11 = 0, -3*o - 5*y = -2 - 28. Factor 10*a**2 + 5*a - 1 - 1 - o*a**3 + 0 - 8.
-5*(a - 2)*(a - 1)*(a + 1)
Let g(h) be the third derivative of 11/210*h**5 + 1/21*h**4 + 1/60*h**6 + 0*h**3 + 0 + 19*h**2 + 0*h. Let g(m) = 0. What is m?
-1, -4/7, 0
Let j(b) be the second derivative of -1/22*b**4 + 0 - 6*b + 0*b**2 - 1/165*b**6 - 2/55*b**5 + 0*b**3. Factor j(k).
-2*k**2*(k + 1)*(k + 3)/11
Suppose -541 + 537 = -w. Let h(l) be the third derivative of 1/14*l**w + 0 + l**2 + 0*l**3 + 2/35*l**5 - 1/56*l**6 + 0*l. Find d, given that h(d) = 0.
-2/5, 0, 2
Factor -2/9*k**2 + 2/9*k**3 - 2/3 - 10/9*k.
2*(k - 3)*(k + 1)**2/9
Let d be 1 + -2 + 0 + 2. Let i be -1*6/9*-6. Factor -18*x - 27*x**i + d + 2 + 0*x**3 + 24*x**2 + 12*x**5 + 6*x**3.
3*(x - 1)**3*(x + 1)*(4*x - 1)
Let t = -35 - -141/4. Let u = 4946 - 4943. Let 0*j**2 + 0*j + 0 + t*j**u + j**5 + 5/4*j**4 = 0. Calculate j.
-1, -1/4, 0
Let w = 15 + -12. Factor 32*l**3 - 40*l**2 + 13*l**2 - 29*l**3 + w*l**4 + 33*l - 12.
3*(l - 1)**3*(l + 4)
Let j be (12/(-33))/(2/33*-15). What is y in 0 + 3/5*y**2 + j*y + 1/5*y**3 = 0?
-2, -1, 0
Solve 34*x**5 - 52*x**3 + 0*x**4 + 27*x**2 + 33*x**2 - 30*x**5 + 8*x**4 - 20*x**2 = 0.
-5, 0, 1, 2
Suppose -1/3*c**2 + 4/3 + 1/6*c**3 - 2/3*c = 0. What is c?
-2, 2
Suppose 0 = -h + 3*f - 4 - 3, 2*h + 5 = 3*f. Let t(x) = -1. Let b(w) = w**3 - 3*w - 7. Let o(d) = h*b(d) - 10*t(d). Determine i so that o(i) = 0.
-1, 2
Let k = -35 - -43. Let a be (8 + (0 - 4))*1/k. Factor 1/2*b**3 + 1/2 - 1/2*b**2 - a*b.
(b - 1)**2*(b + 1)/2
Let s = 1 - -3. Suppose 4*a - 24 = -3*p, -2*p + 16 = -p + s*a. Solve -3*w**4 + w**2 + 4*w**4 + 0*w**p - 2*w**3 = 0.
0, 1
Suppose 17 + 13 = -5*a. Let o be (-57)/a - 4/8. Suppose -o*d**3 - 3*d**2 + 2*d + d**4 - 3*d**4 + 6 - d**4 + 7*d = 0. What is d?
-2, -1, 1
Factor -7*g**4 - 6*g**3 - 55*g**2 + 11*g**3 + 57*g**2.
-g**2*(g - 1)*(7*g + 2)
Suppose 2*o = 4*r - 14, -3*r = -0*r + 5*o - 4. Factor -5*z**2 + 13*z**3 - z**r - 7*z**3.
5*z**2*(z - 1)
Factor 19/4*u + u**2 + 3.
(u + 4)*(4*u + 3)/4
Factor -44 + 14*v - v**2 + 3 + 34 - 33.
-(v - 10)*(v - 4)
Suppose -1/2 - 1/2*k**3 - 13/6*k**2 - 13/6*k = 0. Calculate k.
-3, -1, -1/3
Let r(x) = x**2 - 16*x + 30. Let h(f) = -f**2 + f + 1. Let b(t) = -2*h(t) - r(t). Let l be b(-16). Solve -1/4*n**3 + n**4 + 0 + 0*n**2 + l*n = 0 for n.
0, 1/4
Suppose 2*c - 259 = -5*c. Factor c*n**2 - 490*n**3 + 5*n**5 + 430*n**3 + 43*n**2.
5*n**2*(n - 2)**2*(n + 4)
Let f(q) be the third derivative of -q**6/30 - 2*q**5/15 + q**4/6 + 4*q**3/3 + 17*q**2 + 2. Factor f(g).
-4*(g - 1)*(g + 1)*(g + 2)
Let l = -25 - -20. Let z be l - ((-10)/5 + -3). Let 0 + 3/5*r**5 + z*r + 0*r**2 + 12/5*r**4 + 12/5*r**3 = 0. Calculate r.
-2, 0
Let j(c) be the first derivative of -c**4 + 8*c**3 + 76. Find r, given that j(r) = 0.
0, 6
Determine c, given that -12*c + 4 + 527*c**2 - 523*c**2 + 4 = 0.
1, 2
Let r(b) be the second derivative of b**4/21 + 2*b**3/7 + 4*b**2/7 - 74*b - 2. Find z such that r(z) = 0.
-2, -1
Suppose 1 - 1 = 7*d. Let v(l) be the first derivative of d*l - 3*l**4 - 1/3*l**6 - 8/5*l**5 - 8/3*l**3 - l**2 + 6. Suppose v(y) = 0. Calculate y.
-1, 0
Suppose 4*j = 3*t - 23, -3*t + 3 = 4*j + 