t h(l) be the second derivative of 0 + 2/9*l**3 + 1/3*l**f + 1/18*l**4 + l. Find a, given that h(a) = 0.
-1
Let d = -276 - -1115/4. Factor -1/2 + 1/4*v**3 - 3*v**2 - d*v + v**4.
(v - 2)*(v + 1)**2*(4*v + 1)/4
Let q(s) be the first derivative of -s**7/21 + s**6/15 + s**5/10 - s**4/6 + 3*s + 3. Let a(x) be the first derivative of q(x). Factor a(r).
-2*r**2*(r - 1)**2*(r + 1)
Let i be (210/(-9))/(4/(-30)). Let t = -1573/9 + i. Factor -t*h**2 - 2/9 - 4/9*h.
-2*(h + 1)**2/9
Let f(m) be the third derivative of -1/20*m**4 + 0 + 0*m - 2/15*m**3 + m**2 - 1/150*m**5. Factor f(t).
-2*(t + 1)*(t + 2)/5
Let a(g) be the first derivative of -g**6/900 + g**5/150 - g**4/60 + 5*g**3/3 + 3. Let y(x) be the third derivative of a(x). Factor y(d).
-2*(d - 1)**2/5
Let o = 1/6 - -1/6. Let c(w) be the first derivative of 1/15*w**5 + o*w**3 - 1 - 1/4*w**4 - 1/6*w**2 + 0*w. Find a such that c(a) = 0.
0, 1
Let f be 2/((-2 - -2) + -2). Let d be f - (-1)/((-3)/(-4)). Factor 0*i + 0 - d*i**4 - 1/3*i**2 + 2/3*i**3.
-i**2*(i - 1)**2/3
Solve 0 + 2/9*o**2 + 0*o - 2/9*o**3 = 0 for o.
0, 1
Let i(v) be the first derivative of 5*v**6/4 + 39*v**5/10 + 27*v**4/8 - v**3/2 - 3*v**2/2 + 6. Factor i(n).
3*n*(n + 1)**3*(5*n - 2)/2
Let g be 1/(-3) + 230/60. Let z(t) be the first derivative of 10/3*t**3 - t**2 + 0*t - g*t**4 + 1 + 6/5*t**5. Solve z(x) = 0.
0, 1/3, 1
Suppose -2*c + 5*c - 12 = 0. Let z be (9/(-6))/(-3)*c. Factor 0*w + 2/5*w**3 - 2/5*w**5 - 2/5*w**4 + 2/5*w**z + 0.
-2*w**2*(w - 1)*(w + 1)**2/5
Let r(v) be the first derivative of -5*v**3/3 + 10*v**2 - 20*v - 18. Factor r(q).
-5*(q - 2)**2
Let -23*g**3 + 22*g**3 - g**2 + g**4 + 2*g - g = 0. What is g?
-1, 0, 1
Let g(l) be the second derivative of 3*l**5/100 + l**4/10 - l**3/10 - 3*l**2/5 - 5*l. Determine t, given that g(t) = 0.
-2, -1, 1
Let l(c) = c - 5. Let x be l(6). Suppose 7 - x = 2*m. Factor -8*i + 5 - 6*i**2 + 3 + i**4 - 3*i**3 + 7*i**m + i**4.
2*(i - 1)**2*(i + 2)**2
Let u = -7 + 9. Factor -b + 22*b**3 + u*b - 23*b**3.
-b*(b - 1)*(b + 1)
Let r(p) be the third derivative of p**2 + 0*p + 0 + 1/4*p**4 - 1/20*p**5 + 3/2*p**3. Solve r(h) = 0 for h.
-1, 3
Let a(l) = -4*l**5 - 8*l**4 + 3*l**3 + 11*l**2 + 2*l - 1. Let m(i) = -i**5 + i**3 - i**2 - i - 1. Let u(s) = -3*a(s) - 3*m(s). Factor u(t).
3*(t - 1)*(t + 1)**3*(5*t - 2)
Suppose 0 = -a + 12 - 1. Let d(z) = -2*z**2 + 13*z - 11. Let u(x) = x**2 - 7*x + 6. Let o(w) = a*u(w) + 6*d(w). Factor o(i).
-i*(i - 1)
Let q(l) be the first derivative of -l**6/54 + 2*l**5/45 - 2*l**3/27 + l**2/18 - 9. Solve q(k) = 0 for k.
-1, 0, 1
Let k(t) be the first derivative of t**5 - 5*t**3 + 5*t**2 + 42. Factor k(g).
5*g*(g - 1)**2*(g + 2)
Let v be 9/(-6)*(-104)/6. Factor 6*u + v*u + 5*u**2 - u**2 + 64.
4*(u + 4)**2
Suppose 3*u + 10 = -4*r - 8, -21 = 3*u + 3*r. Let c be 0 - (-1)/(-11)*u. Factor 6/11*l**3 + 0 + c*l**2 + 4/11*l.
2*l*(l + 1)*(3*l + 2)/11
Let p = -437/12 + 110/3. Solve 1/4*m**2 + p - 1/2*m = 0 for m.
1
Let o(h) be the third derivative of 0*h**4 + 1/2*h**3 - 1/20*h**5 - 9*h**2 + 0*h + 0. Find c, given that o(c) = 0.
-1, 1
Factor -4/9*y**3 - 2/9*y**4 + 0*y + 0*y**2 + 0 + 2/9*y**5.
2*y**3*(y - 2)*(y + 1)/9
Let t(n) be the third derivative of n**8/1008 + n**7/126 + n**6/45 + n**5/45 - 4*n**2. Factor t(k).
k**2*(k + 1)*(k + 2)**2/3
Factor -9/4*l**2 + 0 - 3/4*l.
-3*l*(3*l + 1)/4
Let c(x) be the first derivative of 2*x - 9/2*x**4 + 5*x**2 + 3 + 2*x**3. Factor c(m).
-2*(m - 1)*(3*m + 1)**2
Let d be -1 + 0 + 2 + -3. Let r be (-1 + -2)*(1 + d). Let 4*o**3 - 6*o**2 + o**r - 2*o**4 + o**3 + 2*o = 0. What is o?
0, 1
Factor m**2 + 2 + 11/3*m.
(m + 3)*(3*m + 2)/3
Let z(r) be the second derivative of -2*r**7/3 - 8*r**6/5 - 3*r**5/5 + 2*r**4/3 - 2*r. Factor z(b).
-4*b**2*(b + 1)**2*(7*b - 2)
Let h be 77/(-42) + (4 - 2). Suppose -h*x**3 + 0 + 0*x**2 + 1/6*x = 0. Calculate x.
-1, 0, 1
Factor -3*x + 0*x**3 - 6*x**2 + 0*x**3 - 3*x**3.
-3*x*(x + 1)**2
Suppose -a = -w - 0*a + 7, -4*w + 68 = 4*a. Solve 2*g**4 - g**4 + 0*g**4 - 8*g**3 - 5*g**4 + w*g**2 = 0.
-3, 0, 1
Factor -6*f + 99/2*f**3 + 0 + 24*f**2.
3*f*(3*f + 2)*(11*f - 2)/2
Factor 2/9*s**5 + 2/9*s**2 + 0*s - 2/9*s**3 + 0 - 2/9*s**4.
2*s**2*(s - 1)**2*(s + 1)/9
Let h be (-18)/42 + 27/14 + -1. Suppose -1/4*l**3 - h - 1/4*l**4 + 1/4*l + 3/4*l**2 = 0. Calculate l.
-2, -1, 1
Let b(h) be the first derivative of 2/21*h**3 + 3 + 0*h - 1/7*h**2. Factor b(f).
2*f*(f - 1)/7
Let z(a) = a**2 - 6*a + 7. Suppose -2*s + 5*s - 15 = 0. Let d be z(s). Find o, given that -1/2 + 5/2*o - 7/2*o**d + 3/2*o**3 = 0.
1/3, 1
Let w = -109/9 - -13. Solve 8/9 - w*c + 2/9*c**2 = 0.
2
Let y(r) = 2*r**3 + 25*r**2 - 14*r - 9. Let v be y(-13). Factor 1/4*z**v - 1 + z**3 + 3/4*z**2 - z.
(z - 1)*(z + 1)*(z + 2)**2/4
Determine d so that -4*d**3 - 1/3*d**2 + 1/3 + 4*d = 0.
-1, -1/12, 1
Suppose 5*t = -g + 11, -3*g = 2*g + 20. Factor 0*u**4 + 0*u + 2/3*u**t - 2/3*u**5 + 0 + 0*u**2.
-2*u**3*(u - 1)*(u + 1)/3
Let m be 112/49 + (-4)/14. Suppose 0 = -3*j + 12, -3*r + 3*j - 3 = -0*j. Factor -1/3*g**r + 0 + 1/3*g + 0*g**m.
-g*(g - 1)*(g + 1)/3
Factor -2*l**2 + 12*l + 4*l**2 - 4*l**2.
-2*l*(l - 6)
Factor 0*n + n**3 - 1/2 + 3/2*n**2.
(n + 1)**2*(2*n - 1)/2
Let w(z) be the first derivative of 2*z**3/21 + 4*z**2/7 + 8*z/7 + 2. Factor w(m).
2*(m + 2)**2/7
Let j(k) = 3*k**2 + 6*k + 3. Let p be j(-2). Factor 4/5 + 0*y**2 + 2/5*y**p - 6/5*y.
2*(y - 1)**2*(y + 2)/5
Factor 3/7*v**2 + 0 + 0*v.
3*v**2/7
Let x(s) be the third derivative of s**6/120 - s**4/24 - s**3/6 - 5*s**2. Let t(b) = -b**3 + 2*b**2 + 2*b + 2. Let l(u) = -t(u) - 2*x(u). Factor l(k).
-k**2*(k + 2)
Let v(b) be the first derivative of -7/30*b**3 + b + 2 - 1/12*b**4 - 1/5*b**2. Let g(z) be the first derivative of v(z). Factor g(w).
-(w + 1)*(5*w + 2)/5
Let s(o) be the third derivative of o**2 + 0 + 1/4*o**3 - 1/140*o**7 + 0*o + 0*o**5 + 1/8*o**4 - 1/40*o**6. Factor s(z).
-3*(z - 1)*(z + 1)**3/2
Let p(c) be the second derivative of -1/30*c**6 - 1/10*c**5 + 0*c**3 + 0 + 4*c + 0*c**4 + 0*c**2. Let p(h) = 0. What is h?
-2, 0
Let l be -2 + 2 - (-2 - 3). Suppose -l*q + 15 = -0*q. Suppose x - 2*x**q + 0*x**3 - 2*x**5 + 6*x**5 - 3*x**5 = 0. Calculate x.
-1, 0, 1
Let g(u) be the third derivative of 2*u**5/15 + 3*u**4/4 + 2*u**3/3 - 3*u**2. Suppose g(d) = 0. What is d?
-2, -1/4
Let i(v) be the first derivative of v**9/3780 + v**8/525 + v**7/210 + v**6/225 - 5*v**3/3 - 2. Let j(o) be the third derivative of i(o). Factor j(c).
4*c**2*(c + 1)**2*(c + 2)/5
Let w(g) be the second derivative of g**4/6 - 2*g**3/3 + g**2 + 13*g. Suppose w(z) = 0. Calculate z.
1
Suppose 121*q - 117*q = 0. Let q*c - 4/11*c**2 + 0*c**3 + 2/11*c**4 + 2/11 = 0. What is c?
-1, 1
Let z = 651 + -649. Factor 16/9*g**z - 2/9*g**5 + 0*g - 8/3*g**3 + 4/3*g**4 + 0.
-2*g**2*(g - 2)**3/9
Factor 0*w**3 - 2/3*w**2 + 0*w + 1/3*w**4 + 1/3.
(w - 1)**2*(w + 1)**2/3
Let u(d) be the first derivative of 5 + 1/2*d**6 + 5*d**3 - 3/5*d**5 - 9/4*d**4 - 3*d**2 + 0*d. Factor u(b).
3*b*(b - 1)**3*(b + 2)
Let i = 491 + -486. Factor 1/4*n**i + 0 - 1/4*n**4 - 1/2*n**3 + 0*n + 0*n**2.
n**3*(n - 2)*(n + 1)/4
What is q in 0 + 3/4*q - 1/4*q**2 = 0?
0, 3
Determine o so that 2/7*o**3 - 2/7*o - 6/7*o**2 + 2/7*o**4 + 4/7 = 0.
-2, -1, 1
Let c be 0/((3 - 4)*1). Solve y**2 - y + c*y + y = 0 for y.
0
Factor -2/11*n**3 + 2/11*n + 4/11*n**2 - 4/11.
-2*(n - 2)*(n - 1)*(n + 1)/11
Let m(j) be the third derivative of -j**7/70 + 7*j**6/40 + j**5/20 - 7*j**4/8 + 2*j**2 - 17*j. Factor m(n).
-3*n*(n - 7)*(n - 1)*(n + 1)
Determine x so that 8/7*x**2 - 60/7*x - 36/7 + 8*x**3 + 4*x**4 + 4/7*x**5 = 0.
-3, -1, 1
Suppose -1 = -3*b + 3*t - 2*t, 3*b + 3*t = 21. Solve -3 + 2*m**3 - 8*m**b - 1 + 6*m + 4*m = 0.
1, 2
Let n(x) be the second derivative of x**6/30 + x**5/20 - x**4/12 - x**3/6 - 3*x. Determine o, given that n(o) = 0.
-1, 0, 1
Let f(p) = -7*p**4 + 9*p**3 - 13*p**2 - 39*p + 50. Let w(v) = 15*v**4 - 18*v**3 + 26*v**2 + 77*v - 100. Let m(n) = 13*f(n) + 6*w(n). Factor m(s).
-(s - 5)**2*(s - 1)*(s + 2)
What is h in 0 + 4/9*h**4 - 16/9*h**2 + 4/9*h**3 - 16/9*h = 0?
-2, -1, 0, 2
Let v(g) be the second derivative of -1/22*g**5 + 0*g**2 + 0 - 4/33*g**4 + 9*g + 4/33*g**3. Factor v(y).
-2*y*(y + 2)*(5*y - 2)/11
Let b(r) be the first derivative of -2*r**5/25 - 3*r**4/5 - 8*r**3/5 - 8*r**2/5 + 6. Find v, given that b(v) = 0.
-2, 0
Suppose 2*i -