6*s + 12, 5*n + 3*s = 57. Find a, given that 15*a**4 + 0 + n*a**2 - 3/2*a - 9/2*a**5 - 18*a**3 = 0.
0, 1/3, 1
Let m(y) be the second derivative of y**6/360 - y**5/120 - y**3/3 - 7*y. Let a(c) be the second derivative of m(c). Factor a(i).
i*(i - 1)
Let x(m) be the second derivative of -m**6/30 - m**5/20 + m**4/12 + m**3/6 + 5*m. Factor x(n).
-n*(n - 1)*(n + 1)**2
Let l(n) be the second derivative of n**5/70 - n**4/21 - 5*n. Factor l(p).
2*p**2*(p - 2)/7
Let h(g) be the second derivative of -1/21*g**7 + 0*g**3 + 0*g**4 - 11/135*g**6 + 4*g + 0*g**2 + 0 - 1/45*g**5. Factor h(c).
-2*c**3*(c + 1)*(9*c + 2)/9
Let i(x) be the first derivative of -2*x**5/3 - x**4/3 - 11. Factor i(r).
-2*r**3*(5*r + 2)/3
Suppose -4*c - 363 = -363. Factor -2/11*t**4 + c + 2/11*t**3 - 2/11*t + 2/11*t**2.
-2*t*(t - 1)**2*(t + 1)/11
Let g(a) = -a**2 - a - 1. Let w(p) be the first derivative of -2*p**3/3 - 3*p**2/2 - 2*p + 3. Let r(c) = -2*g(c) + 2*w(c). Factor r(f).
-2*(f + 1)**2
Let z = -4 + 7. Determine i so that -15*i**4 - 6*i**3 - 18*i**z - 26*i**2 - 3*i**5 + 14*i**2 = 0.
-2, -1, 0
Let s = 3 + 0. Let a(u) = -u + 2. Let n be a(0). Factor -3*t**2 - s*t**n - t**4 - t - 3*t**3 + 3*t**2.
-t*(t + 1)**3
Let f(u) be the first derivative of -2 - 2/5*u + 1/5*u**2 - 4/25*u**5 - 1/10*u**4 + 2/5*u**3. Solve f(o) = 0 for o.
-1, 1/2, 1
Let q = 135 - 539/4. Factor q*c + 0 - 1/4*c**2.
-c*(c - 1)/4
Let d(n) be the second derivative of n**4/4 + n**3/3 + n**2/2 + 2*n. Let o be d(-1). Factor 0*u**2 + u**2 - o*u + 3 - 2.
(u - 1)**2
Factor m**4 + 81 + 9*m**2 + 45*m**2 + 108*m - 3*m**3 + 15*m**3.
(m + 3)**4
Suppose 2*v - 2*o - 24 = -v, v + o = 3. Suppose 3*a = -0*a + v. Let -y**3 + y**3 + 2*y**4 + a*y**3 = 0. What is y?
-1, 0
Let n be -5 - -2 - (-6304)/2100. Let h(m) be the third derivative of 0*m**4 + 0*m**5 + 0*m + 0 + 0*m**3 - m**2 + 0*m**6 - n*m**7. Factor h(r).
-2*r**4/5
Suppose 5*i + 2*c = 96 + 138, 0 = -c - 3. Factor 0 + 47*s**2 + 2*s - 1 - i*s**2.
-(s - 1)**2
Let n = 34/33 + -4/11. Suppose 0 + 0*m**2 - 2/3*m**3 + 0*m + n*m**5 + 0*m**4 = 0. What is m?
-1, 0, 1
Factor -7 + 11 - 6*l - 7 + 2*l**3 - 1.
2*(l - 2)*(l + 1)**2
Let p(w) = 7*w**2 - 2*w + 3. Let q(r) = -18*r**2 + 3*r**2 - 7 + 3*r + 1. Let u(z) = 9*p(z) + 4*q(z). Solve u(f) = 0.
1
Let q(l) = l**2 - 7*l + 2. Let i be q(0). Factor 8/7*d - 8/7 - 2/7*d**i.
-2*(d - 2)**2/7
Let d(l) be the first derivative of 3*l**4/16 + 5*l**3/4 + 3*l**2 + 3*l - 22. Factor d(z).
3*(z + 1)*(z + 2)**2/4
Factor -5*m**3 - 10*m**2 - 10*m**3 - 8*m**5 - 14*m**5 + 27*m**5.
5*m**2*(m - 2)*(m + 1)**2
Let v = 3 + -3. Suppose v*b - b = 0. Solve -t**4 + 1/2*t**5 + t**2 + b*t**3 - 1/2*t + 0 = 0.
-1, 0, 1
Let p(b) be the third derivative of 2/105*b**7 + 0*b**4 - 1/168*b**8 + 0*b + b**2 + 0*b**3 + 0*b**5 + 0 - 1/60*b**6. Factor p(h).
-2*h**3*(h - 1)**2
Suppose 4*h - 17 + 5 = 0. Let v = 13 - 9. Let a**2 - a**4 + 2*a**3 + a + 0*a**v - 3*a**h = 0. Calculate a.
-1, 0, 1
Let v = 95/268 - 7/67. Let y be 34/72 - (-10)/(-45). Solve y*x**4 + v*x**2 + 0 + 0*x - 1/2*x**3 = 0 for x.
0, 1
Let y(s) be the first derivative of -1/6*s**4 + 10/9*s**3 - 7/3*s**2 + 2*s - 7. Find t, given that y(t) = 0.
1, 3
Let -12*t + 2*t**4 + 2*t**4 - 20*t**2 - 9*t**3 + 5*t**3 = 0. What is t?
-1, 0, 3
Let u(h) be the first derivative of 2*h**5/15 + 19*h**4/6 + 28*h**3 + 108*h**2 + 144*h - 29. Factor u(j).
2*(j + 1)*(j + 6)**3/3
Let h(x) = -x - 5. Let u be h(-7). Suppose -3*l + 8 = -d, d + 3*d = u*l - 2. Factor 0 - 5/3*c**2 + c**l - 2/3*c.
c*(c - 2)*(3*c + 1)/3
Let s be (70/40)/((-1)/(-4)). Solve -8*r**4 + 4 + 6*r**4 + 5*r**4 - r**5 - s*r**2 + r**3 = 0.
-1, 1, 2
Let a(h) be the second derivative of h**5/10 - h**4/4 + h**3/6 - 15*h. Factor a(c).
c*(c - 1)*(2*c - 1)
Factor 0 + 6/5*z + 9/5*z**3 + 3*z**2.
3*z*(z + 1)*(3*z + 2)/5
Let m(t) be the third derivative of -t**8/1680 - t**7/280 - t**6/120 - t**5/120 + t**3/3 + 3*t**2. Let n(s) be the first derivative of m(s). Factor n(k).
-k*(k + 1)**3
Let y be (2/6)/(9/81). Let k(n) be the third derivative of 0*n**5 - 1/168*n**8 + 0*n**y + 3*n**2 + 0*n**4 + 2/105*n**7 + 0*n + 0 + 0*n**6. Factor k(d).
-2*d**4*(d - 2)
Let c(j) = j**3 - 2*j**2 - 4*j + 4. Let x be c(3). Let w be (x/(-2))/((-3)/18). Determine r so that -2*r**3 + r**w + 2*r - r = 0.
-1, 0, 1
Let p(f) = 2*f**2 - 2*f. Let y be p(2). Suppose y*x - z = -6*z + 1, 2*x - 5 = -z. Factor -g**3 - 2 + x + g + g**2 - 3.
-(g - 1)**2*(g + 1)
Let r(b) = 2*b**3 + 5*b**2 + 3*b - 1. Let m(i) = -i**3 - i**2 + 1. Let z(o) = 4*m(o) + 4*r(o). Factor z(x).
4*x*(x + 1)*(x + 3)
Factor -n**5 + 188*n**4 - 188*n**4 + n**3.
-n**3*(n - 1)*(n + 1)
Let y(d) be the third derivative of -d**7/1050 - d**6/200 + d**4/30 + 29*d**2. Suppose y(c) = 0. What is c?
-2, 0, 1
Let q(g) be the first derivative of 0*g**4 - 2/5*g**5 - 1/3*g**6 + 0*g**3 - 1 + 0*g**2 + 0*g. Suppose q(m) = 0. Calculate m.
-1, 0
Factor -48*h**2 - 89*h + 89*h + 24*h**3 - 3*h**4.
-3*h**2*(h - 4)**2
Let p(d) = -9*d - d**3 + d**3 - 2 - d**3 + 4*d**2 + 4. Let z(g) = 9*g**3 - 33*g**2 + 72*g - 15. Let f(u) = -33*p(u) - 4*z(u). Suppose f(i) = 0. What is i?
-2, 1
Let z = -23 - -27. Let q(v) be the first derivative of 1 + 1/4*v + 2*v**3 + 9/8*v**2 + v**z. Find f, given that q(f) = 0.
-1, -1/4
Let w(u) be the first derivative of -u**5/20 - u**4/3 - 5*u**3/6 - u**2 + u - 3. Let p(s) be the first derivative of w(s). Find q, given that p(q) = 0.
-2, -1
Let i(u) be the second derivative of -u**7/105 + u**6/15 - 9*u**5/50 + 7*u**4/30 - 2*u**3/15 - u. Factor i(a).
-2*a*(a - 2)*(a - 1)**3/5
Let 0 - 1/3*g**3 - 1/3*g**4 + 1/3*g**2 + 1/3*g = 0. What is g?
-1, 0, 1
Let k(o) be the third derivative of o**7/280 - o**6/120 - o**3/2 + 6*o**2. Let c(m) be the first derivative of k(m). Factor c(t).
3*t**2*(t - 1)
What is d in 54/5 - 66/5*d + 38/15*d**2 - 2/15*d**3 = 0?
1, 9
Let j = 26 - 18. Suppose 0*a - 2*a + j = 0. Suppose -2*h - 3*h**3 + 5*h**5 - 5*h**a + 0*h**4 + 7*h**2 - 2*h**4 = 0. Calculate h.
-1, 0, 2/5, 1
Let a(h) be the second derivative of 2*h - 1/3*h**4 + 0*h**2 + 0 + 1/10*h**5 + 0*h**3 + 1/15*h**6. Solve a(r) = 0.
-2, 0, 1
Suppose g - 10 = -4*g. Suppose g*j - 82 = -28. Solve 24*k**3 + 8*k**4 + 3*k + 42*k**2 + 4*k**4 - j*k**2 = 0.
-1, -1/2, 0
Factor b**2 + b**2 - 10 - 8*b + 0*b**2.
2*(b - 5)*(b + 1)
Let l(k) be the first derivative of 5*k**4/4 - 5*k**3 - 2. Factor l(j).
5*j**2*(j - 3)
Let c be (15/6)/(25/20). Let b(q) be the second derivative of -1/30*q**5 + 0 - 1/18*q**6 + 0*q**c + 5/36*q**4 + 1/9*q**3 - q. Find r such that b(r) = 0.
-1, -2/5, 0, 1
Let j(l) be the second derivative of 0 + 0*l**2 + 1/3*l**6 - 4/15*l**3 - 9/10*l**5 - 3*l + 4/5*l**4. Factor j(s).
2*s*(s - 1)*(5*s - 2)**2/5
Let i(r) be the third derivative of r**11/997920 - r**9/90720 + r**7/15120 + r**5/60 + 2*r**2. Let c(z) be the third derivative of i(z). Factor c(g).
g*(g - 1)**2*(g + 1)**2/3
Let c(y) be the second derivative of 1/3*y**4 - 1/2*y**2 - 3/40*y**5 + 0 - y - 1/4*y**3. Factor c(w).
-(w - 2)*(w - 1)*(3*w + 1)/2
Factor 20/3*a + 100/3 + 1/3*a**2.
(a + 10)**2/3
Let i be 3/2*(-80)/(-30). Let s(c) be the second derivative of 1/42*c**i + 0 - c + 1/7*c**2 + 2/21*c**3. Factor s(q).
2*(q + 1)**2/7
Let m(y) be the first derivative of -y**6/16 - 3*y**5/20 - 3*y**4/32 - 5. What is k in m(k) = 0?
-1, 0
Let h be 3*(14/(-3) - -2). Let g(d) = -2*d - 12. Let z be g(h). What is q in -1/2 - 8*q**2 - z*q = 0?
-1/4
Let k = 10 - 13. Let c(s) = 3*s**3 - 23*s**2 + 32*s - 8. Let r(l) = -10*l**3 + 70*l**2 - 96*l + 24. Let h(a) = k*r(a) - 8*c(a). Factor h(x).
2*(x - 2)**2*(3*x - 1)
Let z(f) be the first derivative of f**7/840 - f**6/360 + 7*f**3/3 + 8. Let m(o) be the third derivative of z(o). Factor m(v).
v**2*(v - 1)
What is k in 2/5*k**3 - 14/5*k - 4/5*k**2 - 8/5 = 0?
-1, 4
Let w(o) be the second derivative of -o**5/120 + 9*o. Determine k, given that w(k) = 0.
0
Let -4/3*s**3 - 8/3*s**2 - 1/3 - 5/3*s = 0. Calculate s.
-1, -1/2
Suppose 0 = 13*j + j - 56. Determine h so that 0 + 0*h + 2/11*h**2 - 2/11*h**j + 0*h**3 = 0.
-1, 0, 1
Let y(t) = t**2 + 31*t - 41. Let j(i) = -8*i + 10. Let v(a) = -9*j(a) - 2*y(a). Factor v(g).
-2*(g - 4)*(g - 1)
Let s be 2/(-4)*6/(-1). Suppose l - s - 3 = 0. Factor -l*u - u**2 + 4*u**2 + 4 - u**2.
2*(u - 2)*(u - 1)
Let m(r) be the second derivative of r**8/3360 + r**7/630 + r**6/360 - r**4/6 - 3*r. Let u(