 2 - 0. Let u be 2*(-4)/(-3) - 1. Find a such that 2/3*a**o + u*a**3 + a**2 - 1/3*a - 1/3 = 0.
-1, 1/2
Let c = -9 + 11. Let g = 110 + -320/3. Factor -g*j**c - 2/3*j + 2/3 - 2*j**3.
-2*(j + 1)**2*(3*j - 1)/3
Let f(m) be the first derivative of 2/5*m**5 + 0*m**2 - 1/6*m**6 + 0*m - 1/4*m**4 + 0*m**3 + 1. Determine z so that f(z) = 0.
0, 1
Suppose -38*r + 67*r - 33*r + 4*r**2 = 0. Calculate r.
0, 1
Let p be 9/6 + 11/(-2). Let z(l) = 5*l**4 - 4*l**3 + 7*l**2 + 4. Let y(t) = -11*t**4 + 8*t**3 - 15*t**2 - 9. Let u(q) = p*y(q) - 9*z(q). Factor u(r).
-r**2*(r - 3)*(r - 1)
Let r = 10/19 + 55/76. Let z(o) be the first derivative of -1 + r*o**4 + 4/3*o**3 + 0*o + 2/5*o**5 + 1/2*o**2. Factor z(l).
l*(l + 1)**2*(2*l + 1)
Let h(g) be the third derivative of 0*g + 0 - 7/20*g**6 - 1/10*g**5 + 43/105*g**7 + 0*g**3 + 2*g**2 - 1/8*g**8 + 1/6*g**4. Solve h(d) = 0.
-2/7, 0, 1/3, 1
Let f(g) be the first derivative of g**9/2016 - g**8/280 + 3*g**7/280 - g**6/60 + g**5/80 - 5*g**3/3 - 6. Let c(b) be the third derivative of f(b). Factor c(o).
3*o*(o - 1)**4/2
Let y(s) be the first derivative of -2*s**6/3 + 12*s**5/5 - 3*s**4 + 4*s**3/3 - 7. Factor y(b).
-4*b**2*(b - 1)**3
Let w(v) be the first derivative of -v**7/105 + 2*v**6/75 - v**5/50 + 3*v - 2. Let j(m) be the first derivative of w(m). Factor j(u).
-2*u**3*(u - 1)**2/5
Let g(a) be the first derivative of -a**3/12 - a**2/4 + 2*a + 31. Solve g(y) = 0.
-4, 2
Suppose -2/3*f - 1/6*f**2 - 2/3 = 0. Calculate f.
-2
Let f(z) = -z**3. Let i(y) = -693*y**3 - 855*y**2 - 192*y - 12. Let q(b) = 18*f(b) - i(b). Factor q(h).
3*(h + 1)*(15*h + 2)**2
Let b(h) be the first derivative of 3*h**4/16 + 5*h**3/4 + 3*h**2 + 3*h - 2. Factor b(s).
3*(s + 1)*(s + 2)**2/4
Let h(t) be the second derivative of -t**6/45 + t**5/30 - t**2/2 + 2*t. Let u(v) be the first derivative of h(v). Suppose u(r) = 0. Calculate r.
0, 3/4
Let i = 31/92 - 2/23. Let k be (-5)/(-50)*100/40. Find r, given that -k*r**3 + 0 + 0*r**2 + i*r = 0.
-1, 0, 1
Let t(y) be the second derivative of -y**7/231 - 4*y**6/165 - 2*y**5/55 + y**4/33 + 5*y**3/33 + 2*y**2/11 - 6*y. Let t(v) = 0. What is v?
-2, -1, 1
Let d = 877/12 + -217/3. Factor 1/2*j**3 + 1/2*j + 7/4*j**2 - d.
(j + 1)*(j + 3)*(2*j - 1)/4
Let u(s) = -4*s**2 - 2*s + 2. Let q(v) = 17*v**2 + 8*v - 9. Let m(w) = -6*q(w) - 26*u(w). Determine k so that m(k) = 0.
-1
Let t be (-226)/(-120) - (-6)/(-45). Find h such that -9/4*h**2 - 1/2*h - t*h**3 + 0 = 0.
-1, -2/7, 0
Suppose l = 4*d - 6, -d - 2 + 8 = 2*l. Let o = -43 + 47. Factor b**d - 5 + 0*b**2 + 1 + o*b - 2*b**2.
-(b - 2)**2
Let y = 169251 - 20648435/122. Let u = -2/61 + y. Determine s, given that s + s**3 - 1/4*s**4 - u*s**2 - 1/4 = 0.
1
Suppose 4*c - c - 12 = 0. Factor 2*z**c + 2*z**3 - z**4 - z**2 + 0*z - z**3 - z.
z*(z - 1)*(z + 1)**2
Let c(z) be the second derivative of z**9/15120 - z**8/6720 - z**4/4 - z. Let m(b) be the third derivative of c(b). Factor m(k).
k**3*(k - 1)
Let p(v) = -6*v**2 - 4*v. Suppose -2 - 4 = 3*t. Let k(j) = 5*j**2 + 3*j. Let d(a) = t*p(a) - 3*k(a). Factor d(b).
-b*(3*b + 1)
Suppose -h = 2*h + 12*h. Factor -4/5*m + h - 2*m**4 - 24/5*m**3 - 18/5*m**2.
-2*m*(m + 1)**2*(5*m + 2)/5
Let b be 9/(-6) - (-3 - -1). Determine c, given that -1/4*c**3 - 1/4*c + b*c**2 + 0 = 0.
0, 1
Let l = -5 - -8. Suppose 0 = -s - 3, -4*v + 3*s = v - 29. Suppose 8/5*m**v + 0 + 2/5*m + 8/5*m**2 + 12/5*m**l + 2/5*m**5 = 0. What is m?
-1, 0
Let u(z) be the third derivative of -z**7/280 - z**6/40 - z**5/20 + 17*z**2. Factor u(s).
-3*s**2*(s + 2)**2/4
Find h, given that 0*h - 10*h - 20*h**3 + 0*h**5 - 2*h**5 + 10*h**4 - 2*h**2 + 2 + 22*h**2 = 0.
1
Let c(u) = -u**2 + 7*u - 3. Let h be c(6). Let j(r) = r**2 - 7*r + 8. Let f be j(6). Factor f*o**3 + o - 2*o**4 + o**h - 4*o**3 - 2*o**3.
-o*(o + 1)**2*(2*o - 1)
Let a = 446/297 - 16/27. Let k(r) = r**2 - 3*r + 2. Let f be k(3). Factor a*i**f + 14/11*i + 4/11.
2*(i + 1)*(5*i + 2)/11
Let -25*p**5 - p**2 - 4 - 11*p + p + 5*p**4 - 6*p + 41*p**3 + 0 = 0. What is p?
-1, -2/5, 1
Let l be ((-12)/9)/2*-3. Find x, given that -3*x**3 - 3*x**4 + 3*x - x**2 + 4*x**4 + 0*x**l = 0.
-1, 0, 1, 3
Let c(g) = g**3 + 13*g**2 + 11*g - 10. Let a be c(-12). Suppose -a*l + 6*l = 0. Let l + 1/4*v**2 + 0*v = 0. What is v?
0
Let b(m) = -4*m**2 - 4*m. Let y(o) = -9*o**2 - 9*o. Let i(a) = -13*b(a) + 6*y(a). Find l, given that i(l) = 0.
-1, 0
Let f(o) be the first derivative of 3*o**4/5 + 56*o**3/15 + 8*o**2 + 32*o/5 + 15. Solve f(w) = 0 for w.
-2, -2/3
Let o = 15 + -13. Let n be o/(-3)*9/(-21). Suppose -2/7*c**2 + 2/7 + 2/7*c - n*c**3 = 0. Calculate c.
-1, 1
Let c(u) = u**5 + 4*u**4 - u**3 - 2*u - 2. Let z be 2*(-3 + (2 - 0)). Let h(j) = -j**5 - j**4 + j**3 - j**2 + j + 1. Let q(s) = z*h(s) - c(s). Factor q(d).
d**2*(d - 2)*(d - 1)*(d + 1)
Suppose 2*u = -3*u. What is y in 0*y + 0*y**2 - 6/7*y**4 + 10/7*y**5 + u - 4/7*y**3 = 0?
-2/5, 0, 1
Factor -p**2 + 60*p - 60*p.
-p**2
Factor 1/10*h**2 - 1/2*h + 2/5.
(h - 4)*(h - 1)/10
Let a(l) be the first derivative of l + 1/4*l**2 - 1/2*l**3 + 1. Factor a(k).
-(k - 1)*(3*k + 2)/2
Let n(f) = 4*f + 16. Let a be n(-4). Suppose 3*j = -p - 1, j + a = -1. Factor 0*y + 1/6*y**4 - 1/3*y**p + 0*y**3 + 1/6.
(y - 1)**2*(y + 1)**2/6
Let f(a) be the second derivative of -1/30*a**6 - 4*a - 1/10*a**5 + 0*a**2 + 0 + 0*a**3 - 1/12*a**4. Solve f(o) = 0.
-1, 0
Factor 2*s**5 + 2*s - 8*s**4 + 2*s**4 + 6*s + 6*s**2 - 10*s**3.
2*s*(s - 4)*(s - 1)*(s + 1)**2
Let j(o) = -4*o**2 + 4*o + 7. Let p = 11 - 7. Let t(u) = 2*u**2 - 2*u - 4. Let a(d) = p*j(d) + 7*t(d). Let a(c) = 0. What is c?
0, 1
Let g be (-2)/3 + (1 - 2/6). Let 2/7*n**2 + 2/7*n**3 + g*n + 0 = 0. What is n?
-1, 0
Let b(i) be the first derivative of -2*i**3/15 - 3*i**2/5 - 4*i/5 - 11. Determine d, given that b(d) = 0.
-2, -1
Let -2/7*r**4 + 0 - 4/7*r**3 + 4/7*r + 2/7*r**2 = 0. Calculate r.
-2, -1, 0, 1
Let u(c) be the third derivative of -c**5/50 + c**4/10 - c**3/5 + 27*c**2. Factor u(v).
-6*(v - 1)**2/5
Let g(z) be the first derivative of 3*z**3 + 3*z**2/2 - 6*z + 10. Factor g(l).
3*(l + 1)*(3*l - 2)
Let z(r) be the first derivative of r**3 - 3*r**2 + 3*r + 2. Factor z(o).
3*(o - 1)**2
Let y = -69/4 + 35/2. Factor -y*l - 1/2 + 1/4*l**3 + 1/2*l**2.
(l - 1)*(l + 1)*(l + 2)/4
Let w be 2/(-22*5) - (-11)/55. Factor -w*j**2 - 2/11*j + 0.
-2*j*(j + 1)/11
Solve -12*u**3 - 5*u**3 - 58*u**2 - 48*u - 8 - u**3 = 0 for u.
-2, -1, -2/9
Let n(v) be the third derivative of -v**8/28 - 2*v**7/105 + 17*v**6/90 + 7*v**5/45 - 4*v**4/9 - 8*v**3/9 + v**2 + 5*v. What is t in n(t) = 0?
-1, -2/3, 1
Let w = -194 - -1360/7. Let 0*a**2 - 2/7*a**3 + w*a + 0 = 0. Calculate a.
-1, 0, 1
Let p(r) = 6*r**5 + 2*r**4 + 3*r**3 - r**2 + 5. Let v(w) = -7*w**5 - 3*w**4 - 3*w**3 + w**2 - 6. Let k(t) = 6*p(t) + 5*v(t). Factor k(l).
l**2*(l - 1)**3
Let l(c) be the third derivative of -c**8/1680 + 2*c**7/525 - c**6/300 - c**5/75 + c**4/40 - 9*c**2 - 4*c. Suppose l(w) = 0. What is w?
-1, 0, 1, 3
Let v(a) be the first derivative of 2/9*a + 2/27*a**3 - 3 + 2/9*a**2. Factor v(j).
2*(j + 1)**2/9
Let j(n) be the third derivative of n**7/315 + 7*n**6/270 + 2*n**5/27 + 2*n**4/27 + 22*n**2. Factor j(t).
2*t*(t + 2)**2*(3*t + 2)/9
Suppose -s + 3*u = -18, -5*u + 2*u - 12 = s. Factor 5*n**2 + 3*n**3 - n**3 - s*n**2.
2*n**2*(n + 1)
Suppose -8*p = -3*p + 90. Let o = p - -20. Suppose 0 + 1/2*l**o + 1/2*l = 0. What is l?
-1, 0
Suppose 20 = u - 6*u. Let t = u - -4. Factor -1/5*c**3 + 1/5*c + t*c**2 + 0.
-c*(c - 1)*(c + 1)/5
Suppose 2*i = 4*f, -5*i - 4*f = -14 - 0. Let y be ((-36)/(-16))/3*i. Solve 0 - y*b**4 + 3*b - 15/2*b**2 + 6*b**3 = 0 for b.
0, 1, 2
Let n = 26 + -24. Let y be 60/(-135)*(-3)/n. Let y + 2/3*r**2 - 4/3*r = 0. What is r?
1
Let j(f) be the second derivative of 5*f**4/12 - 15*f**3/2 - 27*f. Factor j(v).
5*v*(v - 9)
Let o(x) be the first derivative of -x**6/21 - 4*x**5/35 + x**4/14 + 4*x**3/21 - 22. Let o(u) = 0. What is u?
-2, -1, 0, 1
Let n(z) = z**2 + 3*z - 1. Let k = -24 + 20. Let m be n(k). Factor 0*j + 1/4*j**5 + 1/4*j**2 + 3/4*j**m + 3/4*j**4 + 0.
j**2*(j + 1)**3/4
Let p(m) be the first derivative of -m**5/4 + 45*m**4/16 - 45*m**3/4 + 135*m**2/8 - 11. Factor p(z).
-5*z*(z - 3)**3/4
Let x be 4 + 0/(2 + -5). Let y be x/(-56)*4*-1. Let -16/7*m**4 - 16/7 + 50/7*m**3 + y*m**5 - 76/7*m**2 + 8*m = 0. Calculate m.
1, 2
Suppose -2