*o + 1)**2
Suppose n - 3 = -8. Let x be (-4)/(-30) - 1/n. Let -1/3*v**2 + 2/3 - x*v = 0. Calculate v.
-2, 1
Let j(m) be the first derivative of 0*m**2 + 8/15*m**5 - 7/36*m**6 - 3 - 11/24*m**4 + 1/9*m**3 + 0*m. What is g in j(g) = 0?
0, 2/7, 1
Let u(d) be the first derivative of -4*d**3/21 + 3*d**2/7 - 2*d/7 + 15. Factor u(z).
-2*(z - 1)*(2*z - 1)/7
Factor -2/3 - 4/3*a - 2/3*a**2.
-2*(a + 1)**2/3
Let v(u) = -u**3 + 5*u**2 - 2*u + 8. Let m be v(5). Let f be 7/m*(-45)/70. Find r, given that -3/4*r**2 - 3/2 - f*r = 0.
-2, -1
Suppose -t - 3*t = 3*o - 2, 3*t = 5*o - 13. Factor n**o + 4*n - 3*n**2 + 2 + 4*n**2 + 0*n**2.
2*(n + 1)**2
Let q = 30 - 28. Let x(c) be the first derivative of 0*c + 6/5*c**5 + 2 + 0*c**q - c**4 + 2/9*c**3 - 4/9*c**6. Let x(d) = 0. Calculate d.
0, 1/4, 1
Factor 2/7*r**4 + 0*r + 4/7*r**3 + 2/7*r**2 + 0.
2*r**2*(r + 1)**2/7
Suppose x - 6 = -4. Factor -4*t**2 + 3*t**2 + 2*t**x.
t**2
Suppose -8 = 3*a + 4*u, a + a = u + 2. Factor -2/3*k**2 + a + 1/3*k.
-k*(2*k - 1)/3
Let n(v) be the third derivative of -v**7/630 - v**6/120 - v**5/180 + v**4/24 + v**3/9 - v**2. Factor n(m).
-(m - 1)*(m + 1)**2*(m + 2)/3
Let f(k) be the first derivative of -4*k**3/21 + 4*k/7 - 1. Suppose f(d) = 0. What is d?
-1, 1
Let u = -13 + 18. Suppose o + 89 = u*d, -5*d + 17 + 69 = -4*o. Suppose 8/3 + d*b**2 + 3*b**5 - 12*b - 4*b**4 - 23/3*b**3 = 0. What is b?
-2, 2/3, 1
Let m(d) = 3*d + 3. Let z(r) = -7*r - 7. Let g(l) = 5*m(l) + 2*z(l). Let b(s) = s**2 - 3*s - 4. Let i(q) = -2*b(q) - 6*g(q). Find h, given that i(h) = 0.
-1, 1
Let u(k) = -k**3 + 19*k**2 + 22*k - 38. Let z be u(20). Solve 0 + 3/5*m**z + 0*m + 9/5*m**3 = 0 for m.
-1/3, 0
Let c be 488/(-2016) + 2/8. Let h(q) be the second derivative of 0*q**6 - c*q**7 + q + 0*q**4 + 0*q**2 + 0 + 1/30*q**5 - 1/18*q**3. Let h(p) = 0. Calculate p.
-1, 0, 1
Let k(y) be the first derivative of -y**3/15 - y**2 - 5*y - 5. Factor k(o).
-(o + 5)**2/5
Let f(i) = -i**3 - 4*i**2 - 2*i - 3. Let x be f(-4). Let r = 64 + -62. Find z such that 6*z + 2*z**r + 5*z**2 + x*z**3 - 2*z**3 + 2*z**2 = 0.
-2, -1, 0
Factor 2/11*m**3 + 10/11*m + 8/11*m**2 + 4/11.
2*(m + 1)**2*(m + 2)/11
Let w be (-4)/10 + 119/35. Let a(q) = 13*q**3 - 2*q**2 - 5. Let s(p) = -7*p**3 + p**2 + 3. Let k(f) = w*a(f) + 5*s(f). Factor k(h).
h**2*(4*h - 1)
Let q(m) = 7*m**5 - 9*m**4 + 8*m**3 - 3*m**2 - 3. Let l(x) = 34*x**5 - 46*x**4 + 40*x**3 - 14*x**2 - 14. Let j(b) = -3*l(b) + 14*q(b). What is w in j(w) = 0?
0, 1, 2
Let p(q) be the second derivative of q**5/5 + 4*q**4/3 + 10*q**3/3 + 4*q**2 + 34*q. Factor p(k).
4*(k + 1)**2*(k + 2)
Suppose 19 = 7*j - 9. Let s(d) be the third derivative of 1/150*d**5 + 0 + 0*d + 3*d**2 - 1/15*d**3 + 0*d**j. Factor s(f).
2*(f - 1)*(f + 1)/5
Let f be (9/15)/((-9)/(-45)). Factor -2/5*u**4 - 8/5*u**2 + 8/5*u**f + 0*u + 0.
-2*u**2*(u - 2)**2/5
Let q = 8/5 + -19/15. What is l in 2/3*l - q*l**2 + 0 = 0?
0, 2
Factor -9*s - 41 - 3*s**3 + 41 + 4*s**2 + 8*s**2.
-3*s*(s - 3)*(s - 1)
Let j = 4/79637 - -14413193/21979812. Let l = j - -1/92. Solve -l*r**2 + 0 + 2/3*r = 0 for r.
0, 1
Determine w, given that -69/4*w**2 - 3 + 15*w + 21/4*w**3 = 0.
2/7, 1, 2
What is v in -6/5*v**2 - 9/5*v + 0 - 1/5*v**3 = 0?
-3, 0
Let m(s) = 4*s**3 + s - 1. Let c be m(1). Let 54*k**5 - 53*k**5 + 3*k**3 + k**2 - k**4 + 0*k**c - 4*k**3 = 0. What is k?
-1, 0, 1
Let q(n) = -n**3 - 5*n**2 - 2*n - 8. Let y be q(-5). Let s(h) be the second derivative of 3*h - h**y - 1/24*h**4 + 1/3*h**3 + 0. Factor s(w).
-(w - 2)**2/2
Let j = -8 - -12. Let o = -269/5 + 54. Solve 1/5*r**2 - o*r**3 + 1/5*r + 0 - 1/5*r**j = 0 for r.
-1, 0, 1
Suppose -5*i + 5 = 5*t, -12 = 3*t - 5*t + 3*i. Let c(d) be the first derivative of 2/21*d**t + 1/7*d**2 + 0*d + 1. Factor c(r).
2*r*(r + 1)/7
Let r = -44 - -47. Solve -2/7*m**2 - 2/7*m**5 - 6/7*m**4 + 0 + 0*m - 6/7*m**r = 0.
-1, 0
Suppose 7*m = 4*m + 6. Factor -8/9 - 2/9*n**m - 8/9*n.
-2*(n + 2)**2/9
Let q(u) be the first derivative of -5*u**6/6 - 2*u**5 - 5*u**4/4 + 56. Factor q(a).
-5*a**3*(a + 1)**2
Let y(i) be the first derivative of -i**6/10 + 3*i**5/25 + 3*i**4/10 - 24. Determine f, given that y(f) = 0.
-1, 0, 2
Let w(k) = -k**3 + 11*k**2 + 12*k - 2. Let p be w(12). Let s be (8/(-42))/(p/15). Factor 6/7*g**3 + s*g + 2*g**2 + 2/7.
2*(g + 1)**2*(3*g + 1)/7
Suppose 0 = -2*s - 5*r - 15, -2*s + 5*r + 52 = 17. Let m be 2 + 4 + (-1 - 1). Solve -2/3*a**3 - 2/9*a**2 + 0 - 2/3*a**m + 0*a - 2/9*a**s = 0.
-1, 0
Let g(d) be the first derivative of -d**6/27 + 8*d**5/45 - 5*d**4/18 + 4*d**3/27 - 2. Solve g(l) = 0.
0, 1, 2
Let q(d) = -d**3 + 20*d**2 - 38*d + 39. Let v be q(18). Factor 1/5*g**2 + 0*g + 0 - 1/5*g**v.
-g**2*(g - 1)/5
Suppose -4*d + 8*d = 12. Factor 54*t**2 + 3 - 36*t**d - 27 - 45*t**3 + 36*t.
-3*(3*t - 2)**2*(3*t + 2)
Let v(z) be the second derivative of z**6/45 - 17*z**5/120 + 17*z**3/36 - z**2/3 - 39*z. What is d in v(d) = 0?
-1, 1/4, 1, 4
Suppose 2*m - 9 = -5. Let k(s) = 6*s - 6. Let p(t) = 5*t - 5. Let w(g) = -4*k(g) + 5*p(g). Let q(j) = -j**2 - 4*j + 2. Let a(c) = m*w(c) + q(c). Factor a(i).
-i*(i + 2)
Let y(v) be the first derivative of -v**6/2 + 6*v**5/5 + 3*v**4/2 - 8*v**3 + 21*v**2/2 - 6*v + 19. Determine g, given that y(g) = 0.
-2, 1
Let v(h) be the third derivative of -h**10/378000 + h**8/50400 + 2*h**5/15 - 5*h**2. Let l(n) be the third derivative of v(n). Factor l(b).
-2*b**2*(b - 1)*(b + 1)/5
Let p(i) be the third derivative of i**8/1680 - i**7/525 + i**5/150 - i**4/120 + i**2. Factor p(h).
h*(h - 1)**3*(h + 1)/5
Let u(m) be the first derivative of 18*m**7/35 + 18*m**6/5 + 6*m**5 + 14*m**4/3 + 2*m**3 + 7*m**2/2 + 7. Let c(s) be the second derivative of u(s). Factor c(z).
4*(z + 3)*(3*z + 1)**3
Let a(x) be the first derivative of -x**6/2 - 6*x**5/5 - 3*x**4/4 - 13. Solve a(r) = 0 for r.
-1, 0
Let y(a) = a**3 - 2*a**2 + 2*a + 2. Let k be y(2). Factor 2*o**3 - k*o - o**3 + 5*o.
o*(o - 1)*(o + 1)
Let a(f) = f**3 - f. Let h(o) = -6*o**3 + 8*o + 2. Let u(b) = 15*a(b) + 3*h(b). Factor u(g).
-3*(g - 2)*(g + 1)**2
Let j(z) = -z**3 + 4*z**2 + 8*z - 5. Let h be j(5). Solve h*y**2 - 98/9*y**4 - 56/9*y**3 + 56/9*y + 8/9 = 0.
-1, -2/7, 1
Let v(q) = 3*q**2 - 2*q + 5. Let a(c) = 6*c**2 - 5*c + 9. Let p(f) = 3*a(f) - 5*v(f). Suppose p(k) = 0. What is k?
2/3, 1
Let h(j) = -j**3 - 7*j**2 - 7*j - 4. Let v be h(-6). Factor 1 + 9*s**2 - 5*s**3 - 1 + v + s**4 - 10*s + 3*s.
(s - 2)*(s - 1)**3
Let s(f) = -4*f**4 - 12*f**3 - 10*f**2 - 2*f + 2. Let b(y) be the first derivative of -y**3/3 - y**2/2 + y + 10. Let g(i) = -2*b(i) + s(i). Factor g(p).
-4*p**2*(p + 1)*(p + 2)
Let y(o) = -5*o**3 + 37*o**2 + 21*o - 9. Let r(l) = l**2 + l - 1. Let h(j) = -18*r(j) + 2*y(j). Factor h(x).
-2*x*(x - 6)*(5*x + 2)
What is j in -9*j**4 - 1 - 9*j + 62*j**2 + 6*j**3 + 3*j**5 - 56*j**2 + 4 = 0?
-1, 1
Let c(h) be the first derivative of -h**7/2940 + h**6/1260 + h**5/210 - h**3 + 3. Let n(r) be the third derivative of c(r). Factor n(k).
-2*k*(k - 2)*(k + 1)/7
Let i(j) be the third derivative of j**6/24 - j**5/12 - 5*j**4/24 + 5*j**3/6 - 27*j**2. Factor i(v).
5*(v - 1)**2*(v + 1)
Let n(f) be the third derivative of f**10/15120 + f**9/7560 - f**4/24 + 2*f**2. Let p(s) be the second derivative of n(s). Factor p(b).
2*b**4*(b + 1)
Let v = -561 - -6175/11. What is y in 2/11*y + 0 - 2/11*y**5 - 4/11*y**2 + v*y**4 + 0*y**3 = 0?
-1, 0, 1
Let r = 141 - 141. Factor 0*a + r - 2/5*a**2 + 2/5*a**5 - 2/5*a**3 + 2/5*a**4.
2*a**2*(a - 1)*(a + 1)**2/5
Solve 27/2 - 36*n + 3/2*n**4 + 33*n**2 - 12*n**3 = 0.
1, 3
Factor 3*c**3 + 1872*c - 1872*c - 5*c**3 + 2*c**2.
-2*c**2*(c - 1)
Let x = -7 + 10. Let s(u) = -4*u**2 - 9*u - 12. Let t(d) = -3*d**2 - 8*d - 11. Let v(i) = x*t(i) - 2*s(i). Factor v(a).
-(a + 3)**2
Let v(d) be the second derivative of -2*d + 11/21*d**3 - 2/7*d**2 - 8/21*d**4 + 1/10*d**5 + 0. Factor v(x).
2*(x - 1)**2*(7*x - 2)/7
Let k(r) be the third derivative of -r**6/180 - r**5/90 + r**4/36 + r**3/9 - r**2. Determine q, given that k(q) = 0.
-1, 1
Let -1/3*m**5 + 0*m + 2/3*m**2 + 0 + m**3 + 0*m**4 = 0. What is m?
-1, 0, 2
Let o(k) = k**2 - 12*k + 6. Let a be o(6). Let q be 0 - (a/(-9))/(-5). Factor -q*u**3 + 0*u + 0*u**2 + 5/3*u**4 + 0.
u**3*(5*u - 2)/3
Let j = -482 - -485. Suppose 0*u + 8/13 - 2/13*u**j - 6/13*u**2 = 0. Calculate u.
-2, 1
Suppose -6*i = -4*i - 4. Let z(r) be the second de