Let c(g) = -g**3 + 5*g - 5. Let k(f) = -f**3 + f - 1. Let o(r) = -c(r) + 5*k(r). Find i such that o(i) = 0.
0
Let h be 15/(-6)*8/(-10). Let u(k) be the second derivative of -1/15*k**6 + 0 + 0*k**3 - 1/6*k**4 + 0*k**h - k - 1/5*k**5. Factor u(f).
-2*f**2*(f + 1)**2
Let x(c) = -3*c - 4. Let a be x(-2). Let s(f) be the second derivative of 1/3*f**3 + 1/12*f**4 + 0 + 3*f + 0*f**a. Let s(o) = 0. Calculate o.
-2, 0
Let v(f) be the first derivative of 3*f**5/25 + 9*f**4/10 + 12*f**3/5 + 3*f**2 + 9*f/5 - 11. Suppose v(w) = 0. What is w?
-3, -1
Let j(n) be the third derivative of n**9/15120 + n**8/2240 + n**7/1260 + n**4/12 + 2*n**2. Let r(f) be the second derivative of j(f). Factor r(g).
g**2*(g + 1)*(g + 2)
Factor 18*h - 30/7*h**2 - 14 + 2/7*h**3.
2*(h - 7)**2*(h - 1)/7
Factor 0 - 4/9*x**2 + 0*x - 22/9*x**3 - 14/9*x**5 - 32/9*x**4.
-2*x**2*(x + 1)**2*(7*x + 2)/9
Let u(b) be the third derivative of -b**7/2310 - b**6/1320 + 20*b**2. Factor u(p).
-p**3*(p + 1)/11
Let n(y) be the second derivative of y**6/60 - y**5/20 + 5*y. Let n(v) = 0. What is v?
0, 2
Let y be (-56)/(-30) + 8/60. Let n(d) be the third derivative of d**y - 1/24*d**4 + 0*d**3 - 1/60*d**5 + 0 + 0*d. Factor n(p).
-p*(p + 1)
Factor 3*f**2 + f**3 - 10 + 2*f + 10.
f*(f + 1)*(f + 2)
Let w(i) be the first derivative of i**6/42 + 2*i**5/35 - i**4/28 - 2*i**3/21 - 1. Factor w(p).
p**2*(p - 1)*(p + 1)*(p + 2)/7
Suppose 3*v - 2*p = 12, 2*v = -0*v - 3*p + 8. Factor 4*d**2 + v*d + 17 - 17.
4*d*(d + 1)
Suppose 31 = 3*z - 2*f, -f = -3*z - 0*f + 26. Solve 3 - z + 14*s**2 + 4*s**3 + 6*s - 10*s**4 - 10*s**3 = 0 for s.
-1, 2/5, 1
Let u(k) be the third derivative of -k**6/1260 + k**5/105 - k**4/21 + k**3/2 + 4*k**2. Let q(v) be the first derivative of u(v). Factor q(n).
-2*(n - 2)**2/7
Let l be 8/(-36) - ((-259)/45)/7. Factor 3/5 + 6/5*a + l*a**2.
3*(a + 1)**2/5
Let p(b) be the first derivative of b**6/180 - b**5/18 + 2*b**4/9 - 4*b**3/9 - 5*b**2/2 + 4. Let s(z) be the second derivative of p(z). Factor s(v).
2*(v - 2)**2*(v - 1)/3
Let l = 4 - 2. Factor -i**2 - 2*i**l + 2*i**2 + 3*i**2 - 8*i + 6.
2*(i - 3)*(i - 1)
Let b(u) = -233*u**4 + 160*u**3 + 8*u**2 - 7*u. Let x(h) = 58*h**4 - 40*h**3 - 2*h**2 + 2*h. Let m(v) = -4*b(v) - 18*x(v). Let m(w) = 0. What is w?
-2/7, 0, 1/2
Factor -292*s**2 - 10*s**5 + 36*s**4 + 12*s**3 + 366*s + 18*s + 14*s**5 + 0*s**5 - 144.
4*(s - 1)**3*(s + 6)**2
Let a(p) be the first derivative of -6*p**3/11 - 6*p**2/11 - 2*p/11 + 47. Determine g, given that a(g) = 0.
-1/3
Solve 0 - 1/3*q**5 - 2*q**3 + 4/3*q**2 + 4/3*q**4 - 1/3*q = 0.
0, 1
Suppose 5 + 0*a - 5/4*a**2 = 0. Calculate a.
-2, 2
Suppose 2*i - 23 = -5*g, 0*g + 31 = 5*g + 4*i. Factor 0 - 4/3*a**g + 8/3*a**2 - 4/3*a.
-4*a*(a - 1)**2/3
Let l(q) be the first derivative of 5*q**3/3 - 10*q**2 + 15*q - 10. Find a, given that l(a) = 0.
1, 3
Let g(z) be the third derivative of 7*z**6/360 - 2*z**5/135 - 11*z**4/216 - z**3/27 + 4*z**2. What is v in g(v) = 0?
-1/3, -2/7, 1
Let r be 5 - (-2)/4*-6. Suppose 2*f = r*y - 10, -3*y + 5*f = y - 22. Factor -3*h - 3*h**4 - 1 - 6*h**2 - 9*h**3 + 1 - y*h**2.
-3*h*(h + 1)**3
Let j(h) be the third derivative of h**7/840 + h**6/96 + 3*h**5/80 + 7*h**4/96 + h**3/12 + 9*h**2. Factor j(z).
(z + 1)**3*(z + 2)/4
Let o = -5 - -7. Let 0*q + 2*q**4 + 2*q**3 - 31*q**2 + 29*q**2 - o*q = 0. What is q?
-1, 0, 1
Let v(g) = -g**3 - g**2 - g + 1. Let z(n) = -9*n**3 - 12*n**2 - 9*n + 6. Let b(t) = 6*v(t) - z(t). Solve b(d) = 0.
-1, 0
Let f(d) be the second derivative of 7/6*d**4 - 1/2*d**3 + 0 - d**2 - 2/5*d**6 - 3*d + 1/6*d**7 - 1/5*d**5. Solve f(b) = 0 for b.
-1, -2/7, 1
Suppose -3*l - l = 4*h - 4, 5*l = -20. Suppose -4 + 19 = h*r. Factor -2/5*c**r - 1/5 + 2/5*c + 1/5*c**4 + 0*c**2.
(c - 1)**3*(c + 1)/5
Factor -2/3*i + 2/3 - 2/3*i**2 + 2/3*i**3.
2*(i - 1)**2*(i + 1)/3
Suppose 2*a + 4*v = -3*a + 10, -4*a = -4*v - 8. Let o be (-9)/a*20/(-30). Determine k so that 36*k**o + 162*k + 6*k**4 + 486/5 + 108*k**2 + 2/5*k**5 = 0.
-3
Let o(a) be the third derivative of a**5/150 + 19*a**2. Determine k, given that o(k) = 0.
0
Factor 1/5*i**3 + 4/5 + 8/5*i + i**2.
(i + 1)*(i + 2)**2/5
Suppose 0*m = 5*m - 120. Let o = 24 - m. Find x such that o - 1/3*x**2 + 0*x = 0.
0
Factor -1/4*f**2 + 1/4*f + 1/2.
-(f - 2)*(f + 1)/4
Let r(n) = -n**3 + 6*n**2 - 5*n + 4. Let g be r(5). Suppose g*v - 12 = 4*q, -3 = -2*q - 5. Factor 0 + 3*w**2 + 0*w**2 + 5*w - 2 - 5*w**v.
-(w - 2)*(2*w - 1)
Suppose -9 = -3*h + 3. Let a be (-9)/(-36) - 1/h. Factor -2/3*q**3 + 2/3*q**4 - 2/9*q**5 + 0*q + 2/9*q**2 + a.
-2*q**2*(q - 1)**3/9
Let m(q) be the first derivative of 0*q**2 - 2/15*q**3 - 2 + 0*q. Factor m(l).
-2*l**2/5
Let d = 199 - 196. Factor -4/3*z**4 + 0*z**2 + 0*z + 0 + 2/3*z**d + 2/3*z**5.
2*z**3*(z - 1)**2/3
Let g(t) be the second derivative of t**6/12 + 3*t**5/40 - t**4/12 + 2*t. Factor g(u).
u**2*(u + 1)*(5*u - 2)/2
Let m(z) = 15*z**2 - 98*z + 135. Let q(n) = -10*n**2 + 65*n - 90. Let w(l) = -5*m(l) - 8*q(l). Let w(v) = 0. What is v?
3
Solve -2/7*x + 6/7 - 2/7*x**5 + 4/7*x**3 - 12/7*x**2 + 6/7*x**4 = 0.
-1, 1, 3
Let o(b) = 3*b**2 + 3*b + 2. Let m be o(-1). Factor a + 2*a + 4 - 3*a - a**m.
-(a - 2)*(a + 2)
Let x(p) = 8*p**4 + 7*p**3 - 10*p**2 + 2*p - 7. Let h(u) = u**4 + u**3 - u**2 - 1. Let w(k) = -14*h(k) + 2*x(k). Determine n so that w(n) = 0.
-2, 0, 1
Let b = -29 + 29. Factor -20*k**2 + b - 2*k - 81/2*k**4 - 117/2*k**3.
-k*(k + 1)*(9*k + 2)**2/2
Suppose 3*l + 3 = -2*r, 0*l - l = r + 2. Factor l + 14*v - 53*v + 5 + 54*v**2.
3*(2*v - 1)*(9*v - 2)
Let x(g) be the first derivative of -g**4/4 - 11*g**3/3 - 19*g**2/2 - 9*g + 48. Determine j, given that x(j) = 0.
-9, -1
Let t(p) be the first derivative of -3/4*p + 3/2*p**2 + 1/4*p**3 + 3 - 3/4*p**4. What is y in t(y) = 0?
-1, 1/4, 1
Let m(p) be the first derivative of p**5/300 + p**4/60 + p**3/30 - p**2/2 - 2. Let n(j) be the second derivative of m(j). Solve n(u) = 0.
-1
Let m(n) = -7*n**3 + 5*n**2 + 9*n - 9. Let z(j) = 1 - 2*j**3 + j**2 + 2*j + 2 - 5. Let w(g) = 2*m(g) - 9*z(g). Determine i so that w(i) = 0.
-1/4, 0
Factor -5/4*d**2 + 55/4*d - 25/2.
-5*(d - 10)*(d - 1)/4
Let n(m) = 9*m**3 - 4*m**2 - 4*m - 6. Let g(p) = -10*p**3 + 5*p**2 + 4*p + 7. Let z(c) = 5*g(c) + 6*n(c). Suppose z(k) = 0. Calculate k.
-1, -1/4, 1
Let p(o) be the third derivative of o**5/75 + o**4/6 + 8*o**3/15 - 2*o**2. Factor p(k).
4*(k + 1)*(k + 4)/5
Let u(d) be the third derivative of 0*d**5 - d**3 + 1/40*d**6 - 2*d**2 + 0*d + 0 - 3/8*d**4. Let u(q) = 0. What is q?
-1, 2
Factor -1/6*v**2 - 1/3 - 1/2*v.
-(v + 1)*(v + 2)/6
Suppose 4*x = 2*x - 2. Let p be (0 - 2)/(0 + x). Factor -2*q**p + 0 - 1 + 2*q + 5.
-2*(q - 2)*(q + 1)
Let x(d) be the third derivative of d**7/840 - d**6/480 + 13*d**2. Factor x(o).
o**3*(o - 1)/4
Let b(l) be the first derivative of l**8/840 - l**6/180 - 2*l**3/3 - 3. Let s(y) be the third derivative of b(y). Factor s(w).
2*w**2*(w - 1)*(w + 1)
Let j(m) be the first derivative of -9*m**4/7 - m**3/21 + m**2/7 - 54. Factor j(x).
-x*(4*x + 1)*(9*x - 2)/7
Let w(i) be the third derivative of i**6/60 - i**5/15 - 5*i**2. What is v in w(v) = 0?
0, 2
Let o(u) be the first derivative of -6/7*u**2 - 4 + 18/7*u + 2/21*u**3. Factor o(i).
2*(i - 3)**2/7
Factor 0*u - 1/4*u**4 + 1/2*u**3 - 1/4*u**2 + 0.
-u**2*(u - 1)**2/4
Let l(t) = -2*t**2 - 9*t. Let s be l(-4). Let n(z) be the third derivative of 0*z - 3/70*z**5 - 1/21*z**3 + 0 + 2*z**2 - 1/14*z**s. Factor n(g).
-2*(3*g + 1)**2/7
Determine v, given that 2*v**5 + 18*v + 35*v**3 + 48*v**2 + 26*v**3 - 17*v**3 + 25*v**4 - 9*v**4 = 0.
-3, -1, 0
Let j(b) be the third derivative of 0*b + 0*b**3 + 1/96*b**4 + 0 - 1/240*b**5 + 4*b**2. Solve j(h) = 0 for h.
0, 1
Let z(s) be the first derivative of -5*s**9/6048 + s**8/420 - s**7/1680 - s**6/360 - s**3 - 3. Let u(w) be the third derivative of z(w). Factor u(m).
-m**2*(m - 1)**2*(5*m + 2)/2
Suppose 2 = 4*s - 6. Let f(b) = b + 2. Let w be f(s). Let -n**5 - w*n**5 + 3*n**5 - 2*n**4 = 0. Calculate n.
-1, 0
Let w = -2 + -12. Let p be (-38)/w + (-12)/(-42). Let -2/11*d**2 - 2/11*d + 2/11 + 2/11*d**p = 0. Calculate d.
-1, 1
Let m be (-1)/6 - 1/(-2). Factor m - 1/3*z**3 - z + z**2.
-(z - 1)**3/3
Let i(a) = -21*a**3 + 12*a**2 + 37*a + 16. Let c(p) = -p**3 - p. Let m(j) = 6*c(j) - 2*i(j). Factor m(u).
4*(u - 2)*(3*u + 2)**2
Suppose 3*q + 0*q = 9. S