0*b**3 - 1/120*b**5 + 9*b**2. Factor p(t).
-t*(t - 4)/2
Let m(c) be the first derivative of -2*c**2 - 8*c - 12. Let x be m(-3). Find v, given that 3*v + 3/5*v**5 + 6*v**2 + 3/5 + 3*v**x + 6*v**3 = 0.
-1
Solve -162*z**3 + 180*z**2 + 9 - 27 - 81*z**5 - 33*z + 220*z**5 - 112*z**5 + 6*z**4 = 0 for z.
-3, -2/9, 1
Determine c, given that 0 + 2/9*c + 16/9*c**3 + 32/9*c**4 - 14/9*c**2 = 0.
-1, 0, 1/4
Factor 114/11*j**2 - 420/11*j - 8/11*j**3 + 98/11.
-2*(j - 7)**2*(4*j - 1)/11
Let c(r) be the second derivative of 5*r**7/42 + r**6/6 - r**5/2 - 18*r - 1. Suppose c(a) = 0. Calculate a.
-2, 0, 1
Let n(r) = 9*r**2 + 6*r + 4. Let b(q) = -125*q**2 - 85*q - 55. Let w = 122 + -67. Let x(t) = w*n(t) + 4*b(t). Factor x(l).
-5*l*(l + 2)
Let g be 0 - 9/(0 + -3). Determine x, given that 237*x**3 + 2*x**2 + 3 - 3*x - 234*x**g - 5*x**2 = 0.
-1, 1
Factor 33 + 343*j + 136*j**2 - 145*j + 4*j**3 - 65*j.
(j + 33)*(2*j + 1)**2
Let o(y) be the second derivative of 0 + 1/20*y**5 + 0*y**2 - 1/3*y**3 + 1/12*y**4 + 4*y. What is x in o(x) = 0?
-2, 0, 1
Suppose -25 + 145 = 5*s. Let y be 38/9 - s/108. Factor -1/3*z**y - 4/3*z - 5/3*z**3 + 0 - 8/3*z**2.
-z*(z + 1)*(z + 2)**2/3
Let p = 622259/6 + -104018. Let i = p - -309. Factor -5*b - i*b**2 - 15/2.
-5*(b + 3)**2/6
Suppose 0 + 1/9*f**4 + 16/9*f + 0*f**3 - 4/3*f**2 = 0. What is f?
-4, 0, 2
Factor -17/5*i**2 + 0 + 17/5*i**4 - 2/5*i**3 + 2/5*i.
i*(i - 1)*(i + 1)*(17*i - 2)/5
Let f(v) = -187*v - 23 - 20 - 65*v**3 + 330*v**2 - 2 - 33*v. Let x(p) = 3*p**3 - 15*p**2 + 10*p + 2. Let g(j) = -2*f(j) - 45*x(j). Suppose g(d) = 0. What is d?
0, 1, 2
Let r(u) be the second derivative of -u**5/12 - 5*u**4/24 + 10*u**2 + 23*u. Let b(d) be the first derivative of r(d). Let b(p) = 0. Calculate p.
-1, 0
Let i(x) be the third derivative of -x**5/480 + x**4/16 - 3*x**3/4 - 23*x**2 - x. Factor i(n).
-(n - 6)**2/8
Find n, given that 6/7*n**3 - 3/7*n + 12/7 - 24/7*n**2 + 12/7*n**4 - 3/7*n**5 = 0.
-1, 1, 4
Factor 6/5 + 2/5*q**2 - 8/5*q.
2*(q - 3)*(q - 1)/5
Factor 0*h - 6*h**3 - 10/3*h**2 - 2*h**4 + 0 + 2/3*h**5.
2*h**2*(h - 5)*(h + 1)**2/3
Find b such that -25/2 + 5/4*b**2 - 45/4*b = 0.
-1, 10
Let h be 0 + -10 + (-9805)/(-925). Factor -1/5*u - 1/5*u**4 - 2/5 + h*u**2 + 1/5*u**3.
-(u - 2)*(u - 1)*(u + 1)**2/5
Let m be 1/(-3) + 5*(-618)/(-9000). Let s = m + 39/100. Factor -s*j**2 + 0 + 2/5*j.
-2*j*(j - 1)/5
Solve -7/3*a - 1/3*a**2 - 10/3 = 0.
-5, -2
Let x = -19 + 8. Let a(n) be the first derivative of -3*n**4/4 + n**3 + 2*n**2 - 54. Let f(p) = 8*p**3 - 8*p**2 - 11*p. Let g(h) = x*a(h) - 4*f(h). Factor g(l).
l**2*(l - 1)
Let w be (((-663)/(-189))/(-1) - (-2)/9) + 5. Find h, given that -w + 9/7*h + 3/7*h**2 = 0.
-4, 1
Let c be ((-10)/15)/((-25)/10 - -2). Factor q**2 - c + 4/3*q - 4/3*q**3 + 1/3*q**4.
(q - 2)**2*(q - 1)*(q + 1)/3
Suppose -9*d + 5*d + 88 = 0. Suppose 22 = j + 4*c, -7*c + 2*c + d = j. Solve -56/3*t**2 + 0 + 32/3*t**5 + 8/3*t + j*t**3 + 112/3*t**4 = 0 for t.
-2, 0, 1/4
Let j(p) be the first derivative of 2*p**5/35 - 2*p**4/7 - 18*p**3/7 - 38*p**2/7 - 32*p/7 - 780. Factor j(x).
2*(x - 8)*(x + 1)**2*(x + 2)/7
Let 2*n**5 - 265598*n + 2260*n**3 - 137842 + 3656*n**3 - 117916*n**2 - 242*n**4 + 3680*n**3 = 0. What is n?
-1, 41
Let o(u) be the second derivative of 5*u**7/168 - 11*u**6/24 - 25*u**5/16 - 65*u**4/48 - 387*u. Suppose o(m) = 0. What is m?
-1, 0, 13
Let i(o) = -7*o - 5. Let r be i(-1). Let h be 0/(42/(-28) + (-1)/r). Factor -1/6*q**3 + h*q**2 + 0 + 0*q.
-q**3/6
Let o = 2656 - 79661/30. Let i = o - -1/30. Factor -j**2 - i*j + 0.
-j*(3*j + 2)/3
Let q = 689 + -687. Let r(h) be the second derivative of 4/15*h**3 - 2/25*h**5 + 0*h**4 - 2/5*h**q + h + 2/75*h**6 + 0. Factor r(x).
4*(x - 1)**3*(x + 1)/5
Let v(p) be the third derivative of 1/78*p**5 + 0*p**3 - 51*p**2 - 1/1365*p**7 + 0*p + 0 - 1/780*p**6 - 1/52*p**4. Suppose v(h) = 0. What is h?
-3, 0, 1
Let k = -2/2027 + 6091/10135. Suppose 0*s + 0 - k*s**3 + 3/5*s**2 = 0. Calculate s.
0, 1
Factor -179*z - 51*z + 245*z**2 - 564*z**3 + 559*z**3 - 480.
-5*(z - 48)*(z - 2)*(z + 1)
Suppose 1 + 1 = -2*o. Let k be (6 - 2)*(o + 2). Solve 0*m**4 + 5*m**k - 2*m**4 + 12*m**3 + 4*m + 12*m**2 + m**4 = 0 for m.
-1, 0
Factor 175*v - 21*v**3 + 5*v**3 + v + 48 + 13*v**3 - 33*v**3 - 188*v**2.
-4*(v - 1)*(v + 6)*(9*v + 2)
Let x(h) be the third derivative of h**6/24 + 4*h**5/3 - 85*h**4/24 - 2*h**2. Factor x(z).
5*z*(z - 1)*(z + 17)
Factor 10/13*w**2 - 220/13 + 42*w.
2*(w + 55)*(5*w - 2)/13
What is d in -16/3 - 2/3*d**2 + 6*d = 0?
1, 8
Let m(o) be the second derivative of -3/4*o**2 - 1/180*o**6 + 1/30*o**5 + 5*o - 1/3*o**3 + 0 + 1/36*o**4. Factor m(t).
-(t - 3)**2*(t + 1)**2/6
Let f(r) be the third derivative of -1/30*r**5 - 1/20*r**4 + 1/100*r**6 + 0 + 4/15*r**3 + 1/525*r**7 - 6*r**2 + 0*r. Find q, given that f(q) = 0.
-4, -1, 1
Suppose 0 = -r + 3, -19 = -7*u + 2*u - 3*r. Determine p, given that 15/2*p + 10*p**4 - 75/2*p**3 + 0 + 20*p**u = 0.
-1/4, 0, 1, 3
Suppose 29*h - 210 + 94 = 0. Factor 0*k**h + 4/3*k**5 - 8/3*k**3 + 0 + 0*k**2 + 4/3*k.
4*k*(k - 1)**2*(k + 1)**2/3
Let u(k) = 18*k**4 - 16*k**3 + 40*k**2 - 22*k. Let b(x) = -3*x**4 - x**3 + x**2 - x. Let l(i) = -5*b(i) - u(i). Determine a so that l(a) = 0.
0, 1, 3
Suppose -3*w + 2*o - 82 = -6*w, 0 = w - 3*o - 20. Let i = w - 23. Determine a, given that -a**4 + 2 + 3*a + 2*a**2 + i*a**3 - 6*a**3 - 6*a**2 + 3*a**2 = 0.
-2, -1, 1
Find y, given that -5*y - 3*y - 16*y**2 + 9*y + 10*y + 33*y = 0.
0, 11/4
Let j(d) be the second derivative of 0*d**2 + 0*d**3 - 9/40*d**5 + 1/12*d**4 - 13*d + 7/60*d**6 + 0. Factor j(x).
x**2*(x - 1)*(7*x - 2)/2
Let n be (0 - -1) + (12 - 9). Determine j, given that 6*j**3 - 10*j**4 - 3*j**2 - 9*j**4 - 6*j**n + 22*j**4 = 0.
0, 1
Suppose 0 = s - 32*x + 27*x - 25, -4*s = 5*x. Suppose 0 + 8/9*q - 2/3*q**3 - 2/3*q**s - 8/3*q**2 + 20/9*q**4 = 0. What is q?
-1, 0, 1/3, 2
Let n(a) = -a**2 - a. Suppose 3 = u - p, -3*u + 2 = 7*p - 3*p. Let b(h) = -25*h - h**2 + 29*h - 9 - u*h**2. Let x(f) = b(f) - 2*n(f). Solve x(z) = 0.
3
Let r(j) be the third derivative of 0 - 4/3*j**3 + 5*j**2 + 1/90*j**5 + 1/1080*j**6 + 1/18*j**4 + 0*j. Let b(t) be the first derivative of r(t). Factor b(g).
(g + 2)**2/3
Let i be (-10)/5 - (-2 + 1). Let w(b) = -2*b**4 + 4*b**3 + 14*b**2 + 14*b. Let q(m) = m**3 + m**2 + m. Let a(t) = i*w(t) + 6*q(t). Factor a(z).
2*z*(z - 2)*(z + 1)*(z + 2)
Let h = 42/191 + 1784/573. Factor 2/3*q + 4/3 - 16/3*q**2 + h*q**3.
2*(q - 1)**2*(5*q + 2)/3
Factor -64*a - 2/5*a**2 - 2560.
-2*(a + 80)**2/5
Let m = -3695/24 - -154. Let o(x) be the third derivative of 1/840*x**7 + 0*x**5 - 6*x**2 + 0 - m*x**3 + 1/48*x**4 - 1/240*x**6 + 0*x. Factor o(v).
(v - 1)**3*(v + 1)/4
Let k(x) be the third derivative of -x**6/60 + x**5/6 + 2*x**4/3 - 4*x**3 + x**2 + 110. Solve k(p) = 0 for p.
-2, 1, 6
Find u such that -6/5*u**3 + 1/5*u**4 + 12/5*u**2 + 0 - 8/5*u = 0.
0, 2
Let c(q) = 6*q**4 - 23*q**3 + 120*q**2 + 144*q. Let h(s) = 5*s**4 - 23*s**3 + 120*s**2 + 144*s. Let k(a) = 4*c(a) - 5*h(a). Factor k(u).
-u*(u - 12)**2*(u + 1)
Let c(l) be the first derivative of l**8/4200 + 2*l**7/2625 - l**5/375 - l**4/300 - 13*l**2 + 13. Let j(d) be the second derivative of c(d). Factor j(g).
2*g*(g - 1)*(g + 1)**3/25
Let n be ((-9)/(-6))/((-5)/(-10)). Let m(u) be the first derivative of -n*u**4 + 0*u + 8*u**2 - 3 + 16/3*u**3. Suppose m(r) = 0. Calculate r.
-2/3, 0, 2
Let p(l) be the third derivative of 0*l**3 - 1/180*l**6 + 1/36*l**4 + 0 - 1/90*l**5 + 9*l**2 + 0*l + 1/315*l**7. Find i, given that p(i) = 0.
-1, 0, 1
Let i = 29 + -10. What is u in -2*u**3 - 2*u**3 - 10*u - 5*u + i*u = 0?
-1, 0, 1
Let i = 1957 - 1954. Let o(z) be the first derivative of 5 + 8/21*z**i - 6/7*z - 11/7*z**2. Factor o(q).
2*(q - 3)*(4*q + 1)/7
Let g = -104 + 104. Let o(y) be the second derivative of 0*y**2 - 2*y - 3/2*y**3 - 1/4*y**4 + g. Factor o(a).
-3*a*(a + 3)
Suppose g = -4*g + 130. Let p = 37 - g. Factor 26*h**2 + 4*h + 46*h**4 + 53*h**3 + p*h**3 + h**3 - 11*h**3 + 14*h**5.
2*h*(h + 1)**3*(7*h + 2)
Let c(u) be the third derivative of -4/195*u**5 + 0 + 1/39*u**3 + 0*u - 7/156*u**4 - 20*u**2. Factor c(g).
-2*(g + 1)*(8*g - 1)/13
Let z(o) = -o**5 - 2*o**4 - 17*o**3 + 14*o**2 + 6*o - 6. Let i(r) = -2*r**5 - 5*r**4 - 32*r**3 + 28*r**2 + 11*r - 11. Let w(k) = 6*i(k) - 11*z(k). Factor w(d).
-d**2*(d - 1)*(d