) be the first derivative of 3/7*k**2 - 3 + 2/7*k**3 + 1/14*k**4 + 2/7*k. Suppose o(n) = 0. What is n?
-1
Let t(w) be the first derivative of 5*w**6/6 + 3*w**5 + 5*w**4/4 - 5*w**3 - 5*w**2 + 15. Let t(u) = 0. Calculate u.
-2, -1, 0, 1
Let v be (-362)/(-120) + -7 + 4/1. Let y(m) be the second derivative of 1/84*m**7 - 3/40*m**5 + v*m**6 + 1/6*m**3 - 4*m - 1/24*m**4 + 0 + 0*m**2. Factor y(t).
t*(t - 1)**2*(t + 1)*(t + 2)/2
Suppose 4*x = n + 4, 2*n + 5 + 3 = 4*x. Let t(y) be the third derivative of 1/108*y**4 - 2/27*y**3 + y**2 + 0*y + 1/270*y**5 + x. Factor t(w).
2*(w - 1)*(w + 2)/9
Factor -2*h**4 - 2*h**3 - 2*h**3 + 2*h**4 - 2 + 2*h**4 + 4*h.
2*(h - 1)**3*(h + 1)
Let m(p) be the third derivative of -p**7/420 + p**6/240 + p**5/120 - p**4/48 + p**2. Factor m(j).
-j*(j - 1)**2*(j + 1)/2
Let j(w) = 3*w**2 - 23*w. Let s(i) = 3*i**2 - 24*i. Let f(t) = 3*j(t) - 2*s(t). Factor f(x).
3*x*(x - 7)
Let l(p) be the second derivative of p**5/15 - 4*p**4/3 + 32*p**3/3 - 3*p**2 + 5*p. Let h(w) be the first derivative of l(w). Factor h(b).
4*(b - 4)**2
Suppose 2*j**5 - 15*j**2 + 20*j**3 + 25*j**4 - 9*j**5 - j**5 - 2*j**5 = 0. What is j?
-1, 0, 1/2, 3
Let n(h) = 5*h**2 - 15*h + 1. Let j(x) = -1. Let u(c) = j(c) + n(c). What is t in u(t) = 0?
0, 3
Let r = 13 + -8. Suppose b - r*a + 10 = 0, 0*b + a - 2 = -2*b. Factor 1/3*j + 1/3*j**2 + b.
j*(j + 1)/3
Let x(q) = q + 14. Let k be (10/6)/((-2)/12). Let t be x(k). Factor 6*r**4 + 4 - 5*r**t - 3 - 2*r**2.
(r - 1)**2*(r + 1)**2
Factor -2*p**2 - 2/5*p**3 - 14/5*p - 6/5.
-2*(p + 1)**2*(p + 3)/5
Let m(v) be the first derivative of 2*v**5/35 - v**4/14 - 2*v**3/21 + v**2/7 - 16. Suppose m(f) = 0. Calculate f.
-1, 0, 1
Let q(l) be the second derivative of -l**7/1680 + l**6/360 - l**5/240 + l**3/3 + 4*l. Let t(f) be the second derivative of q(f). What is c in t(c) = 0?
0, 1
Let w(j) = 2*j**4 + 17*j**3 + 69*j**2 + 109*j + 64. Let z(a) = a**3 + a**2 + a. Let p(n) = 2*w(n) + 6*z(n). Find i, given that p(i) = 0.
-4, -2
Let n = 14 - -2. Let d be 1*4/(n/2). Factor -d*q**2 + 0*q + 1/2.
-(q - 1)*(q + 1)/2
Suppose 0 = -2*s - 3*s. Let a(r) be the third derivative of -1/48*r**4 + s - r**2 + 1/120*r**5 + 0*r**3 + 0*r. Factor a(x).
x*(x - 1)/2
Suppose 0*a = -a + 7. Factor -l**2 - a*l**2 - 2*l**2 + 2*l - 8 - 26*l.
-2*(l + 2)*(5*l + 2)
Let u(n) = n**2 + 10*n + 5. Let l be u(-9). Let f be (-21)/(-308) - l/22. Factor 1/4*a**3 + 1/4*a**2 + 0 - 1/4*a**4 - f*a.
-a*(a - 1)**2*(a + 1)/4
Suppose 12 = -0*b + 6*b. Let g(q) be the first derivative of 3*q**b - 2*q**3 + 1/2*q**4 + 2 - 2*q. Factor g(x).
2*(x - 1)**3
Let l = 21 + -19. Let c(w) be the first derivative of w**l - 2 + 0*w + 1/2*w**4 + 4/3*w**3. Factor c(u).
2*u*(u + 1)**2
Let i(b) = -b + 19. Let p be i(17). Let h(q) be the first derivative of -2*q + 2/3*q**3 + 2 + 0*q**p. Solve h(z) = 0.
-1, 1
Factor 16*r + 73*r**2 + 86*r**2 - 149*r**2 + 8 + 2*r**3.
2*(r + 1)*(r + 2)**2
Suppose 0 = 9*m - 7*m - 8. Factor 2 + j - 3*j**2 + 2 + 11*j - m*j**2.
-(j - 2)*(7*j + 2)
Solve -4/5*d - 8/5*d**4 - 26/5*d**3 - 22/5*d**2 + 0 = 0 for d.
-2, -1, -1/4, 0
Let b(r) be the second derivative of 2*r**7/21 - 8*r**6/15 - 2*r**5/5 + 4*r**4 + 6*r**3 - 7*r + 1. Let b(f) = 0. Calculate f.
-1, 0, 3
Let k be (2 - 8)*(-1)/3. Determine u, given that 1512*u**3 - 2548*u**4 + 18*u + 14*u - 183*u**k + 1372*u**5 - 185*u**2 = 0.
0, 2/7, 1
Let f = -37/2 + 223/12. Let v(a) be the third derivative of a**2 + 2/9*a**3 + 1/90*a**5 + 0*a + 0 + f*a**4. Factor v(m).
2*(m + 1)*(m + 2)/3
Let n(b) be the first derivative of 5*b**6/33 - 2*b**5/5 + 7*b**4/22 - 2*b**3/33 + 13. Factor n(p).
2*p**2*(p - 1)**2*(5*p - 1)/11
Let i(u) be the second derivative of u**5/5 + 5*u**4/12 - 7*u**3/6 - u**2 - 6*u. Factor i(b).
(b - 1)*(b + 2)*(4*b + 1)
Let t = 8/3 - 2. What is r in r**4 - t*r**2 + 1/3*r**5 - r + 2/3*r**3 - 1/3 = 0?
-1, 1
Let a be 4/(-12) - (-388)/12. Let d be a/(-60)*(-3)/2. Factor d*k + 1/5*k**3 + 0 - 4/5*k**2.
k*(k - 2)**2/5
Let o(y) be the second derivative of -1/9*y**3 + 1/9*y**4 + 1/30*y**5 - 2/3*y**2 + 0 - y. Factor o(u).
2*(u - 1)*(u + 1)*(u + 2)/3
Let m(d) = 2*d + 14. Let a be m(-7). Factor a - i - 1/2*i**2.
-i*(i + 2)/2
Suppose 2 = -2*x, -w - 4*x - 3 = -2. Solve -1/4*r**2 + 0 + 1/4*r**4 + 0*r + 0*r**w = 0 for r.
-1, 0, 1
Let a(b) = 9*b**5 - 5*b**4 - 13*b**3 + 5*b**2 - b. Let q(i) = -5*i**5 + 3*i**4 + 7*i**3 - 3*i**2 + i. Let o(y) = 3*a(y) + 5*q(y). Suppose o(t) = 0. What is t?
-1, 0, 1
Let b be (-7)/4 + (-1)/4. Let z be 7 - (-1)/(b/(-4)). Suppose 3*q**2 + 5*q - z*q**2 - 3*q = 0. What is q?
0, 1/3
Solve 0*j - 1/6*j**2 + 0 + 1/6*j**3 = 0 for j.
0, 1
Let i be 1/(-5) + (-7)/210*-6. Factor 1/2*v**4 + i + 0*v - 1/2*v**3 + 1/2*v**5 - 1/2*v**2.
v**2*(v - 1)*(v + 1)**2/2
Factor 5*n**2 - 7*n**4 - n**3 + 13*n**3 - n**2.
-n**2*(n - 2)*(7*n + 2)
Factor 26*y - 12*y**2 - 4 - 2*y**3 + 6*y**3 - 14*y.
4*(y - 1)**3
Let b(w) be the third derivative of -w**10/45360 + w**9/11340 - w**8/10080 + w**4/24 + w**2. Let a(z) be the second derivative of b(z). Factor a(m).
-2*m**3*(m - 1)**2/3
Let r = 21 - -14. Let s be (-3)/21 - (-5)/r. Factor s + 1/3*w + 1/3*w**2.
w*(w + 1)/3
Let z(x) be the first derivative of 6*x**5/5 + 2*x**4 - 2*x**2 - 2*x + 3. Let b(k) = -7*k**4 - 9*k**3 + 4*k + 2. Let q(u) = 4*b(u) + 5*z(u). Factor q(w).
2*(w - 1)*(w + 1)**3
Let d(t) be the second derivative of 1/15*t**6 + 0 + 0*t**2 + 3*t - 1/6*t**4 + 1/21*t**7 + 0*t**3 - 1/10*t**5. Factor d(j).
2*j**2*(j - 1)*(j + 1)**2
Let p(a) be the first derivative of 36*a**5/5 + 141*a**4/4 + 31*a**3 - 21*a**2/2 - 9*a - 1. Let p(j) = 0. What is j?
-3, -1, -1/4, 1/3
Factor -17*u**2 + 9*u + 15*u**2 - 18 + 3*u.
-2*(u - 3)**2
Let i(p) be the second derivative of p**6/2 - p**5/2 - 15*p**4/4 + 10*p**2 + p. Find w such that i(w) = 0.
-1, 2/3, 2
Let n(p) be the second derivative of -1/6*p**3 + 1/90*p**5 + 0*p**4 + 0 + p - 1/540*p**6 + 0*p**2. Let q(k) be the second derivative of n(k). Factor q(r).
-2*r*(r - 2)/3
Suppose 0 = -2*q - 3*t + 9, -2*q - 6 = 3*q - 2*t. Factor q*p + 2/9 - 2/9*p**2.
-2*(p - 1)*(p + 1)/9
Let x be (-161)/35 + 8 + (-4)/10. Solve -4/7*d**x + 0*d**2 + 2/7*d**4 + 0*d + 0 = 0.
0, 2
Let d(r) = -2*r**3 + 14*r**2 + 2*r + 10. Let c(f) = f**2 + 1. Let i(n) = 12*c(n) - d(n). What is k in i(k) = 0?
-1, 1
Let i be 14/(-7) + (-39)/(-9) + -1. Factor -i - 2/3*v**2 - 2*v.
-2*(v + 1)*(v + 2)/3
Let n(z) = z**2 + 8*z + 9. Let q be n(-7). Solve 16/3*u**3 + 2/3*u**q - 4/3*u + 0 + 10/3*u**4 = 0.
-1, 0, 2/5
Let a(k) be the third derivative of k**10/75600 + k**9/18900 - k**7/3150 - k**6/1800 - k**4/24 - 3*k**2. Let u(z) be the second derivative of a(z). Factor u(l).
2*l*(l - 1)*(l + 1)**3/5
Let q = -13/24 + 7/8. Suppose -d + 4/3*d**2 - q = 0. What is d?
-1/4, 1
Let f(m) be the second derivative of m**4/84 - m**3/14 + m**2/7 - 8*m. Factor f(u).
(u - 2)*(u - 1)/7
Let u be (-9)/(-3) - (-7 + 10). Suppose -1/5*z**2 + u*z + 0 = 0. What is z?
0
Let 946*o - 25*o**3 - 20*o**2 - 15*o**2 - 961*o - 5*o**4 = 0. Calculate o.
-3, -1, 0
Let f(n) be the first derivative of -n**6/260 - 4*n**5/195 + n**4/39 + 2*n**3/3 - 1. Let x(k) be the third derivative of f(k). Find c such that x(c) = 0.
-2, 2/9
Let q = -1 - -3. Let j be (0 + q)/((-2)/(-3)). Factor 0*d**2 - 2*d + 2*d**3 - j*d**4 + d**4 + 2*d**2.
-2*d*(d - 1)**2*(d + 1)
Let l(s) = 10*s**5 - 20*s**4 + 5*s**3 + 25*s**2 - 10*s + 5. Let n(z) = -5*z**5 + 10*z**4 - 2*z**3 - 12*z**2 + 5*z - 2. Let a(q) = -2*l(q) - 5*n(q). Factor a(i).
5*i*(i - 1)**3*(i + 1)
Let z(r) be the first derivative of r**6/480 - r**5/40 + r**4/8 - r**3 - 6. Let d(b) be the third derivative of z(b). Find i, given that d(i) = 0.
2
Let g be (-9)/45 - 38/60. Let r = -7/30 - g. Let 3/5*c + 0 - r*c**2 = 0. Calculate c.
0, 1
Let o(g) be the third derivative of -g**7/2520 - g**6/360 - g**5/180 + 5*g**3/6 + 3*g**2. Let i(d) be the first derivative of o(d). What is y in i(y) = 0?
-2, -1, 0
Let s(l) be the first derivative of -2*l**5/65 - l**4/13 + 2*l**2/13 + 2*l/13 + 1. Suppose s(y) = 0. What is y?
-1, 1
Let x(u) be the second derivative of u**4/78 - 9*u. Find w such that x(w) = 0.
0
Let m(u) = u**2 - 1. Let c be m(-2). Factor c*w**2 - w + 2*w**2 + 3*w**4 - 2*w**4 + w**3 - 6*w**2.
w*(w - 1)*(w + 1)**2
Let g(i) be the third derivative of i**5/12 - 35*i**4/24 - 20*i**3/3 + 18*i**2. Solve g(p) = 0.
-1, 8
Factor 2/3*a**2 