Factor 6*u - 2*u + x*u - 2*u - 2*u**3.
-2*u*(u - 1)*(u + 1)
Suppose 12*v = 3*v + 27. Let s(h) be the second derivative of 2*h + 1/120*h**6 + 1/48*h**4 + 0 + 1/40*h**5 + 0*h**v + 0*h**2. Let s(n) = 0. Calculate n.
-1, 0
Let d = -1 + -3. Let v = 10 + d. Factor 3*z + 5*z**3 + 0*z**3 - v*z**2 - 2*z**3 + 0*z.
3*z*(z - 1)**2
Let q(k) be the third derivative of k**6/30 + k**5/15 - k**4/6 - 2*k**3/3 - 19*k**2. Factor q(t).
4*(t - 1)*(t + 1)**2
Let i(o) be the third derivative of 0*o**3 - o**2 - 2/3*o**5 - 5/12*o**6 + 0 + 0*o - 1/3*o**4. Let i(g) = 0. What is g?
-2/5, 0
Let v = 145/14 + -69/7. Factor -b**2 - v*b**3 + 1/2*b + 1.
-(b - 1)*(b + 1)*(b + 2)/2
Let u = 5 + -1. Let j(g) = g**u - 4*g**2 - 3*g**2 + 0*g**4 + 8*g**2. Let d(m) = m**4 - 4*m**3 - 3*m**2 + 2*m. Let z(c) = 3*d(c) + 6*j(c). Solve z(n) = 0.
-2/3, 0, 1
Let d be (0 - 8)*(-5)/10. Suppose d*l = -0*l. Factor -1/4*t - 1/4*t**2 + 1/4*t**4 + l + 1/4*t**3.
t*(t - 1)*(t + 1)**2/4
Let d(q) be the second derivative of 0*q**2 + q + 0 - 2/21*q**3 - 1/42*q**4. Find t such that d(t) = 0.
-2, 0
Let q = -1133/2 + 567. Suppose -q + 1/4*a + 1/4*a**2 = 0. Calculate a.
-2, 1
Let g be -1*(-3 + 0 - -1). Factor -3*r**g - 2 - r**3 - r**2 + 0 - 5*r.
-(r + 1)**2*(r + 2)
Factor -2 - 7*o**3 - 2*o**4 + 4 + 0 + 0*o**4 - 6*o**2 + o.
-(o + 1)**2*(o + 2)*(2*o - 1)
Let y = 1297 + -165. Let o = 12460/11 - y. Suppose -6*m**2 + o - 34/11*m**3 - 8/11*m + 42/11*m**5 + 58/11*m**4 = 0. What is m?
-1, -2/3, 2/7, 1
Let u = -2 - -8. Let v(m) = -5*m**2 + 7*m - 8. Let x(w) = -4*w**2 + 6*w - 7. Let b(f) = u*x(f) - 5*v(f). Factor b(d).
(d - 1)*(d + 2)
Let a(v) be the third derivative of 3/40*v**6 + 0*v + 0*v**3 + 1/20*v**5 + v**2 - 1/4*v**4 + 0. Find x, given that a(x) = 0.
-1, 0, 2/3
Let a = -4 + 10. Factor -a*w**3 + 3*w**5 + 6*w**2 - 3*w**3 + 0*w**5.
3*w**2*(w - 1)**2*(w + 2)
Let r be ((16 - 6)/80)/(2/8). Solve -1/2*h**3 - 1/2 + 1/2*h**2 + r*h = 0 for h.
-1, 1
Factor -8/5*b**4 + 0 - 12/5*b**2 - 2/5*b - 18/5*b**3.
-2*b*(b + 1)**2*(4*b + 1)/5
Let q(w) = 3*w**5 - 7*w**4 + 6*w**3 + 10*w**2 + 9*w. Let t(p) = p**5 - 3*p**4 + 3*p**3 + 5*p**2 + 4*p. Let u(x) = -2*q(x) + 5*t(x). Factor u(z).
-z*(z - 2)*(z + 1)**3
Suppose 7*f = 3*f + 4. Suppose 5*c - 16 = -3*t, 4*c - 7 = t - f. Factor 1/2*o**c + 0 + o - 3/2*o**3.
-o*(o - 1)*(3*o + 2)/2
Factor -722/5*k + 13718/15 - 2/15*k**3 + 38/5*k**2.
-2*(k - 19)**3/15
Let f(w) be the first derivative of -w**3/9 - w**2/6 + 2*w/3 + 18. Determine r, given that f(r) = 0.
-2, 1
Factor 6/7*z**3 + 0*z - 3/7*z**4 - 3/7*z**2 + 0.
-3*z**2*(z - 1)**2/7
Let y(t) = -19*t**3 - 21*t**2 + 19*t + 39. Let n(h) = 9*h**3 + 11*h**2 - 9*h - 19. Let i(a) = 9*n(a) + 4*y(a). What is f in i(f) = 0?
-3, -1, 1
Suppose -2*y + 8*r - 3*r = 1, -y - 3 = -3*r. Let o be -1*-2*3/y. Suppose 0*b + o*b**3 - 1/2*b**4 + 0*b**2 + 0 = 0. What is b?
0, 1
Suppose -6/17*x**2 + 4/17*x + 0 + 2/17*x**3 = 0. Calculate x.
0, 1, 2
Suppose -1 + 9 = 4*l. Suppose -l*b = b - 24. Factor 2*o**3 - 4*o**2 - o**3 - b - 2*o**2 + 12*o.
(o - 2)**3
Find m, given that 8/7*m**2 - 2/7*m**3 - 8/7*m + 0 = 0.
0, 2
Suppose 0 = 3*h + 7 + 5. Let o be (2/h)/((-2)/8). Factor -1/2*r**o + r - 1/2.
-(r - 1)**2/2
Let m = -72 - -72. Determine z, given that 1/4 + 1/2*z**3 - 1/2*z + m*z**2 - 1/4*z**4 = 0.
-1, 1
Let r(w) be the third derivative of -w**8/168 - w**7/42 + w**6/24 + w**5/12 - w**4/8 - 17*w**2. Determine x, given that r(x) = 0.
-3, -1, 0, 1/2, 1
Let k(t) be the first derivative of t**6/6 - t**5/5 - 5*t**4/4 + t**3/3 + 4*t**2 + 4*t + 4. Factor k(v).
(v - 2)**2*(v + 1)**3
Factor 4*n - 25*n - 6*n**3 + 2*n**3 - 24*n**2 - 23*n - 24.
-4*(n + 1)*(n + 2)*(n + 3)
Find k, given that -14/3*k**2 - 88/9*k - 8/9 = 0.
-2, -2/21
Determine x, given that 6*x**2 + 2*x**3 - 10*x + 10*x - 4*x**2 = 0.
-1, 0
Factor -55*t - 44*t**4 - 99*t**3 + 14*t**4 + 7*t - 120*t**2 - 3*t**5.
-3*t*(t + 1)**2*(t + 4)**2
Let t(o) be the second derivative of -o**3/6 + 13*o**2/2 + 4*o. Let r be t(6). Find v such that 2*v**2 + v**3 + r*v**5 - 6*v**3 - 12*v**4 + 8*v**3 = 0.
-2/7, 0, 1
Let r be ((-3)/(-4))/((-9)/(-36)). Let p(y) be the first derivative of 7/6*y**r + 3 - 2*y - 1/4*y**4 - y**2. Factor p(s).
-(s - 2)**2*(2*s + 1)/2
Suppose -10 = -0*g - 5*g. Factor -4*l + 3*l**g - 2*l**4 + 2*l + 2*l**3 - l**2 + 0*l.
-2*l*(l - 1)**2*(l + 1)
Factor 0*i - 32/7*i**3 + 4/7*i**4 + 64/7*i**2 + 0.
4*i**2*(i - 4)**2/7
Let v(d) = -13*d**5 - 13*d**4 + 35*d**3 - 24*d**2 + 5*d - 5. Let k(z) = -7*z**5 - 7*z**4 + 17*z**3 - 12*z**2 + 3*z - 3. Let y(s) = 5*k(s) - 3*v(s). Factor y(o).
4*o**2*(o - 1)**2*(o + 3)
Factor 2/5 + 4/5*x**3 - 4/5*x - 2/5*x**4 + 0*x**2.
-2*(x - 1)**3*(x + 1)/5
Let o(i) be the second derivative of -i**7/63 + 2*i**6/15 - 13*i**5/30 + 2*i**4/3 - 4*i**3/9 - 12*i. Factor o(z).
-2*z*(z - 2)**2*(z - 1)**2/3
Let b(c) = c**3 - 2*c**2 + 2*c. Let w be b(2). Find q such that -6/5*q**3 + 0*q + 0 - 3/5*q**w - 3/5*q**2 = 0.
-1, 0
Factor 2/5*o**3 + 54/5 + 18/5*o**2 + 54/5*o.
2*(o + 3)**3/5
Let l(b) be the second derivative of 4*b**7/21 + 2*b**6/5 - 31*b**5/40 - 11*b**4/12 + 5*b**3/4 - b**2/2 + 4*b. Find c, given that l(c) = 0.
-2, -1, 1/4, 1
Let r(n) = 2*n**2 - 8*n - 6. Let z(k) = k**2 - 8*k - 6. Let b(y) = 3*r(y) - 4*z(y). Factor b(i).
2*(i + 1)*(i + 3)
Suppose 5*o + 9 = -16. Let m(j) = 8*j**2 + 9*j + 5. Let x(q) = -q**2 - 1. Let p(n) = o*x(n) - m(n). Factor p(d).
-3*d*(d + 3)
Let v = 59 - 56. Factor 3/4*p**5 + 27/4*p + 9/2*p**4 + 3/2 + 12*p**2 + 21/2*p**v.
3*(p + 1)**4*(p + 2)/4
Suppose 0 = 9*j - 5*j + k - 9, 5*k + 5 = 5*j. Factor 0*f + 0 - 3/2*f**4 + 3/4*f**3 + 3/4*f**j.
-3*f**2*(f - 1)*(2*f + 1)/4
Let b(k) be the third derivative of -k**8/13440 + k**6/1440 + k**4/24 + 3*k**2. Let r(c) be the second derivative of b(c). Factor r(y).
-y*(y - 1)*(y + 1)/2
Let g = 1/700 - -17/2100. Let o(n) be the third derivative of -3*n**2 - 1/60*n**5 + 0*n + 0*n**3 + g*n**7 + 0 + 0*n**4 + 1/120*n**6. Factor o(q).
q**2*(q + 1)*(2*q - 1)
Factor 0 - 4/3*a**4 - 2/3*a**2 - 1/3*a**5 - 5/3*a**3 + 0*a.
-a**2*(a + 1)**2*(a + 2)/3
Suppose -2*c + 9 = 3*j, 5*j = -2*c - 3 + 14. Let h(p) = 6*p**2. Let t be h(j). Let -r**5 - 2*r**4 - 5*r**5 + 6*r**4 - 4*r**2 + t*r**3 = 0. Calculate r.
-1, 0, 2/3, 1
Factor -16*c - 203 - 4*c**2 + 203.
-4*c*(c + 4)
Let c = -121/10 - -25/2. Solve -2/5 + c*w**2 + 2/5*w**3 - 2/5*w = 0.
-1, 1
Let f be 9 - 8 - (-4)/(-6). Suppose f - 1/3*d**2 + 0*d = 0. Calculate d.
-1, 1
Let h(x) = x**2 - 1. Let n(f) = -4*f**2 + 2*f + 2. Let v(m) = -5*h(m) - n(m). Factor v(c).
-(c - 1)*(c + 3)
Let w(l) = l - 2. Let o be w(2). Factor o + 8/7*i**2 + 12/7*i**3 + 2/7*i**5 + 8/7*i**4 + 2/7*i.
2*i*(i + 1)**4/7
Suppose -c = -2*d - 10 + 1, 0 = -5*c + d + 9. Let t be -3 + c/((-4)/(-19)). Factor 0 + 1/2*y**3 + 0*y - 5/4*y**4 + 0*y**2 - t*y**5.
-y**3*(y + 1)*(7*y - 2)/4
Let u(q) be the third derivative of -q**5/45 + q**4/12 - q**3/9 + 3*q**2. Factor u(o).
-2*(o - 1)*(2*o - 1)/3
Solve -18*l**2 - 9/2 - 21/4*l**5 - 33/2*l**3 + 45/2*l**4 + 87/4*l = 0.
-1, 2/7, 1, 3
Let c be (2 - (0 - -13))/1. Let s(g) = g**3 + 11*g**2 - g - 8. Let l be s(c). Determine z, given that -3*z**3 + l*z**4 + 2*z**4 + 5*z**3 - 3*z**4 = 0.
-1, 0
Let t = -1435/4 + 359. Factor -t*z**2 + 0*z + 0.
-z**2/4
Factor 6*m**2 + 8*m - 8/3 - 14/3*m**3.
-2*(m - 2)*(m + 1)*(7*m - 2)/3
Let c(s) be the first derivative of 0*s - s**3 + 3/5*s**5 - 1/2*s**6 + 6 + 0*s**2 + 3/4*s**4. Factor c(p).
-3*p**2*(p - 1)**2*(p + 1)
Find f such that -2*f**5 + 12*f**3 - 9*f**3 + 4*f**4 - 5*f**3 = 0.
0, 1
Factor -18/5*i - 2/5*i**5 + 32/5*i**2 + 4/5 + 12/5*i**4 - 28/5*i**3.
-2*(i - 2)*(i - 1)**4/5
Let d be 23/56 + (76/32)/(-19). Find r, given that d*r**2 + 4/7 - 4/7*r**3 + 10/7*r = 0.
-1, -1/2, 2
Let w be 2*((-9)/(-2) + 2). Let c = 16 - w. Factor 0 + j**2 + 1/3*j**4 - 1/3*j - j**c.
j*(j - 1)**3/3
Let i(p) be the first derivative of 5/2*p**2 - 3 + 2*p + 4/3*p**3 + 1/4*p**4. Factor i(f).
(f + 1)**2*(f + 2)
Let n = -626 + 1879/3. Determine r, given that 1/3*r**2 + 1/3*r**5 - 1/3*r**3 - n*r**4 + 0 + 0*r = 0.
-1, 0, 1
Let o = 72 + -72. Let z(w) be the third derivative of -1/90*w**5 + 0*w - 1/180*w**6 + 0 - 2*w**2 - 1/108*w**4 - 1/945*w**7 + o*w**3. Factor z(i).
-2*i*(i + 1)**3/9
Let x(f) be the third derivative of f**9/90720 - f**8/15120 - f**7/7560 + f**6/540 + f**5/30 + f**2. Let j(g) be the third derivative of x(g). Factor j(p).
2