erivative of q**4/6 + 4*q**3/3 + 4*q**2 - 4*q. Let a(n) = 0. Calculate n.
-2
Let j(t) = t. Let i be j(4). Let h(c) = -c**3 + 7*c**2 + 2*c - 14. Let p be h(7). Solve -1/2*u**i - 1/2 + u**2 + 0*u + p*u**3 = 0 for u.
-1, 1
Suppose -p = 3*p. Let z(f) be the third derivative of -1/45*f**5 + 1/12*f**4 + p - 1/9*f**3 - 1/90*f**6 - f**2 + 1/105*f**7 - 1/504*f**8 + 0*f. Factor z(n).
-2*(n - 1)**4*(n + 1)/3
Let h = -15 + 15. Let m be h - 50/18 - -3. Find d, given that -2/9*d**3 + 0 + 0*d**2 + m*d = 0.
-1, 0, 1
Suppose 0 = 3*j - 4*j. Factor -1/3 + j*l + 1/3*l**2.
(l - 1)*(l + 1)/3
Let -13*y + 7/4*y**3 - 3 - 33/4*y**2 = 0. Calculate y.
-1, -2/7, 6
Let i(b) be the third derivative of 2*b**2 - 1/9*b**3 + 0*b + 1/90*b**5 + 1/72*b**4 - 1/360*b**6 + 0. Solve i(k) = 0.
-1, 1, 2
Let h(k) be the second derivative of k**6/225 - 2*k**5/75 + 2*k**4/45 - 4*k. Factor h(q).
2*q**2*(q - 2)**2/15
Suppose -3*z + 7*z = 12. Find k, given that 8*k + 44 - k**3 - 7*k**z - 40 - 4*k**4 = 0.
-1, 1
Let i(u) be the third derivative of -3*u**8/896 + u**7/112 - u**6/160 + 4*u**2. Factor i(r).
-3*r**3*(r - 1)*(3*r - 2)/8
Solve -2*p**3 + 8*p**3 - 4*p**2 - 5*p**2 + 3*p = 0.
0, 1/2, 1
Let m(k) = -7*k**3 + 9*k**2 - 7*k - 5. Let h(t) = -6*t**3 + 8*t**2 - 6*t - 4. Let x be 6/3 + -1 - 6. Let p(d) = x*h(d) + 4*m(d). Factor p(n).
2*n*(n - 1)**2
Suppose -k = 2*k. Suppose 5*t + k*c + c - 16 = 0, 0 = -2*t + c + 5. Factor -2*w + 2 + w**3 + 3*w - 3 - t*w**2 + 2*w.
(w - 1)**3
Suppose -9 = -6*j + 3. Let f = 0 - -2. Factor j*c**f + 0 + 2/3*c.
2*c*(3*c + 1)/3
Factor 0*x**4 + 0*x**2 - 2/11*x**5 - 2/11*x + 0 + 4/11*x**3.
-2*x*(x - 1)**2*(x + 1)**2/11
Let j = 19/66 + 1/22. Let b be (-8)/12 + 2/3. Factor -j*c + b + 1/3*c**2.
c*(c - 1)/3
Let m(z) be the third derivative of z**7/165 - 4*z**6/165 + z**5/30 - z**4/66 - z**2. Solve m(o) = 0.
0, 2/7, 1
Let v = -40 - -441/11. Let s(w) be the first derivative of -v*w**2 - 1/33*w**6 - 2/11*w - 2/55*w**5 + 1/11*w**4 + 4/33*w**3 + 2. Solve s(i) = 0.
-1, 1
Let o(t) be the third derivative of -t**7/1365 - t**2. Let o(v) = 0. Calculate v.
0
Let q(p) be the first derivative of 3/4*p**4 + 0*p**2 - 2*p**3 + 0*p - 1. Let q(k) = 0. Calculate k.
0, 2
Suppose h = 3*f - 11, 0*h - 2*f + 6 = -h. Factor 0*o**5 + 2*o**4 - 5*o**h - o**5 + 2*o**4.
-o**4*(o + 1)
Let b(q) be the second derivative of q**6/75 + q**5/25 - 2*q. Solve b(p) = 0 for p.
-2, 0
Factor 0*y**5 + 2*y**5 - 4*y**2 - 4*y**5 + 6*y**3 + 0*y**5.
-2*y**2*(y - 1)**2*(y + 2)
Let g(t) be the third derivative of t**5/20 + t**4/4 - 5*t**2. Let g(k) = 0. Calculate k.
-2, 0
Suppose -3*f + 2*x + 2*x = -2, -3*x + 11 = 4*f. Suppose 2*y**2 - y**2 + 0*y**f - 1 + 0 = 0. What is y?
-1, 1
Let g = -70/9 - -709/90. Let u(s) be the second derivative of 0*s**3 - 1/30*s**6 + 2*s + 0*s**2 - g*s**5 - 1/12*s**4 + 0. Factor u(a).
-a**2*(a + 1)**2
Let f(q) be the third derivative of -q**9/60480 - q**8/20160 - q**5/20 + q**2. Let j(p) be the third derivative of f(p). Solve j(x) = 0 for x.
-1, 0
Let r = -5 + 15. Suppose -3*n = 2*n - r. Suppose n*x**2 - 6*x - 2*x + 0*x + 8 = 0. What is x?
2
Let i(b) be the third derivative of b**6/600 - b**5/300 - b**4/120 + b**3/30 + 10*b**2. Factor i(v).
(v - 1)**2*(v + 1)/5
Let y = 162941/7 + -23350. Let m = y - -73. Factor -2/7*f**2 + m*f + 0.
-2*f*(f - 1)/7
Let q be 16/(-96) - (-1)/2. Determine z so that 8/3 + 2*z**2 - 4*z - q*z**3 = 0.
2
Factor 2*h**2 + 3*h**5 - 17*h**4 + 4*h - 4*h**3 - 9*h**4 - 14*h**3 - 13*h**5.
-2*h*(h + 1)**3*(5*h - 2)
Let w be (4 - 17 - -5)/(-10). Factor -4/5*x**2 - w*x**3 + 1/5*x + 1/5.
-(x + 1)*(2*x - 1)*(2*x + 1)/5
Let b(u) be the first derivative of -u**4/5 - 4*u**3/5 - 5. What is y in b(y) = 0?
-3, 0
Let x(p) be the first derivative of 2/15*p**3 + 0*p**2 + 0*p + 2/15*p**6 - 1/5*p**4 + 2 - 2/25*p**5. Find s such that x(s) = 0.
-1, 0, 1/2, 1
Suppose 0 = -g - g + 8. Suppose -h - 20 = -4*j, 5*h - 8 = -g*j + 3*h. Factor -2*v**4 - j*v**4 + 4*v**4 + 2*v**3.
-2*v**3*(v - 1)
Determine b, given that 8*b**2 + 5*b - 3*b**2 - 36 - 6*b**3 + b**3 + 31 = 0.
-1, 1
Let a(j) = 5*j**3 - j**2 - j + 3. Let r(f) = -f**2 + 7*f - 3. Let p be r(7). Let d(w) = -26*w**3 + 4*w**2 + 6*w - 16. Let l(k) = p*d(k) - 16*a(k). Factor l(b).
-2*b*(b - 1)**2
Let r(j) be the second derivative of -j**6/120 + j**5/80 + j**4/48 - j**3/24 + 4*j. Factor r(z).
-z*(z - 1)**2*(z + 1)/4
Let u(t) = -6*t**3 + 10*t**2 + 2*t - 14. Let y(o) = -7*o**3 + 11*o**2 + 3*o - 15. Let s(i) = -6*u(i) + 5*y(i). Factor s(k).
(k - 3)**2*(k + 1)
Let q(r) be the second derivative of 3*r + 1/12*r**4 + 0 + 0*r**2 - 1/6*r**3. Let q(w) = 0. Calculate w.
0, 1
Suppose -4*v - 4*g + 8 = 0, 0 = 5*g - 10*g. Let p = v + 0. Factor -3*m**p + 3*m - 1 - m + 2*m**2.
-(m - 1)**2
Let w be (-19409)/35 + 4/10. Let b = w - -555. Suppose -6/7*j + b*j**4 + 2/7*j**5 + 4/7*j**3 - 2/7 - 4/7*j**2 = 0. What is j?
-1, 1
Factor -4/21*a + 0 - 2/21*a**2.
-2*a*(a + 2)/21
Factor 90 + 4*w**2 + 345*w + 35*w**4 + 53*w**2 - 211*w**3 - 2*w**2 + 46*w**3.
5*(w - 3)**2*(w + 1)*(7*w + 2)
Let p(f) = 23*f**2 - 65*f - 43. Let x(l) = -11*l**2 + 32*l + 22. Let r(n) = -2*p(n) - 5*x(n). Find h such that r(h) = 0.
-2/3, 4
Let m = 214 - 214. Solve -1/2*d**2 + 1/2*d**3 + m + 0*d = 0 for d.
0, 1
Let z(t) be the third derivative of -1/15*t**6 + 1/12*t**3 + 7/60*t**5 - 2*t**2 - 1/336*t**8 + 0*t + 0 + 3/140*t**7 - 1/8*t**4. Let z(j) = 0. Calculate j.
1/2, 1
Let u(v) be the first derivative of 0*v**3 + 0*v**4 + 1 + 0*v**2 + 1/10*v**6 - 3/25*v**5 + 0*v. Find g such that u(g) = 0.
0, 1
Let n(v) be the second derivative of -v**6/45 + v**4/18 - 7*v. Factor n(i).
-2*i**2*(i - 1)*(i + 1)/3
Suppose 5*d - 3 = -8. Let c be (-110)/(-45) + -1 + d. What is g in 0 + c*g - 2/9*g**2 = 0?
0, 2
Suppose -2*a + 5*t + 16 = 0, 20 + 2 = 4*a - 5*t. Suppose -5*x + 23 = -0*w - w, 2*w + a*x = 19. Factor q**3 + 1/2*q + 3/2*q**w + 0.
q*(q + 1)*(2*q + 1)/2
Suppose p = f + 3*p - 10, 3*p = -5*f + 15. Factor f + 4*o**2 + 4*o**3 - 2*o**5 - 5*o**3 - 2*o**4 - 2*o - 2 + 5*o**3.
-2*(o - 1)**2*(o + 1)**3
Suppose 0 + 1/4*a**4 - a**3 + 3/4*a**2 + 0*a = 0. What is a?
0, 1, 3
Let l = -139 + 3754/27. Let h = 115/189 - l. Suppose 6/7*r - h*r**2 + 4/7 - 6/7*r**3 = 0. Calculate r.
-1, -2/3, 1
Suppose -3*s + 21 = 9. Factor 0 - 1/4*t**2 - 1/4*t**3 + 1/4*t**s + 1/4*t.
t*(t - 1)**2*(t + 1)/4
Let w be (-86)/14 - 4/(-28). Let u = 8 + w. Let -3*m**2 - 4*m + 4 + 0*m**u + 4*m**2 = 0. What is m?
2
Let c be (-3 - (-1 + -123))/(-3). Let d = c + 41. Find g, given that d*g**4 - g**3 + 0 + 0*g**2 + 1/3*g = 0.
-1/2, 0, 1
Let x(g) = -g**2 + 8*g - 5. Let q be x(7). Factor 3*n**4 + 3*n**2 - n**4 - q*n - 3*n**4.
-n*(n - 1)**2*(n + 2)
Let q be 285/2*(-72)/105. Let h = 98 + q. Find d such that -2/7*d**2 + 0 + 4/7*d**3 - h*d**4 + 0*d = 0.
0, 1
Let t(q) = q**3 + q**2 + q + 4. Let v be t(0). Let r(k) = -2*k + 14. Let c be r(6). Solve -26/3*g**3 + 2/3*g + 14/3*g**c - 2/3 + v*g**4 = 0 for g.
-1/3, 1/2, 1
Let w(j) be the third derivative of j**8/448 - j**7/280 - j**6/80 + j**5/40 + j**4/32 - j**3/8 - 3*j**2. Determine k so that w(k) = 0.
-1, 1
Let s = -127/2 + 67. Let -3/2*x**3 + 1 + 4*x**2 - s*x = 0. What is x?
2/3, 1
Let q be ((-39)/65)/((-9)/10). Factor 2/9*j - 2/9*j**4 + 0 - 2/3*j**2 + q*j**3.
-2*j*(j - 1)**3/9
Factor 4/5*z**4 - 8/5*z + 12/5 + 8/5*z**3 - 16/5*z**2.
4*(z - 1)**2*(z + 1)*(z + 3)/5
Let h(k) = 4*k**4 + 12*k**3 + 4*k**2 - 7*k - 8. Let z(m) = -3*m + 6*m**3 + 2*m**2 - 4 + 2*m**4 - 3*m**4 + 3*m**4. Let x(l) = 6*h(l) - 10*z(l). Factor x(j).
4*(j - 1)*(j + 1)**2*(j + 2)
Let w(m) = 29*m**4 + 200*m**3 + 270*m**2 - 81*m - 7. Let x(d) = -19*d**4 - 133*d**3 - 180*d**2 + 54*d + 5. Let r(g) = -5*w(g) - 7*x(g). Factor r(u).
-3*u*(u + 3)**2*(4*u - 1)
Let c = 6 - 8. Let r(q) = q + 2. Let s be r(c). Factor 3/2*d**5 + 3/2*d**4 - 3/2*d**3 + s*d + 0 - 3/2*d**2.
3*d**2*(d - 1)*(d + 1)**2/2
Let v(z) be the first derivative of 2*z**6/3 + 16*z**5/5 + 5*z**4 + 8*z**3/3 + 8. Find d, given that v(d) = 0.
-2, -1, 0
Let s(t) = t**2 - 1. Let j be s(-3). Factor j*i**3 + 5 + 8 - 14*i + 7*i**2 - 17*i**2 - 9.
2*(i - 2)*(i + 1)*(4*i - 1)
Determine p, given that -3/8*p**4 + 0 + 3/4*p + 3/2*p**3 - 15/8*p**2 = 0.
0, 1, 2
Let x = -2 - -5. Suppose -4*c + 2*l + x*l = -13, -5*c - 4*l = -6. Solve -2*u + c*u**2 + 0*u + 0*u**2 = 0.
0, 1
Suppose -3*j + 1 = 2*l, 6*j - 3*l - 8 = j. Suppose -j = 5*c - 11. F