2 + 2/13 - 2/13*j**5 - 10/13*j + n*j**4.
-2*(j - 1)**5/13
Let b(j) be the first derivative of -1/30*j**6 + 8 + 0*j**2 + 1/15*j**3 + 0*j - 3/20*j**4 + 3/25*j**5. Solve b(n) = 0 for n.
0, 1
Let c(z) be the third derivative of z**6/1620 - z**5/540 + z**3 + 6*z**2. Let b(a) be the first derivative of c(a). Factor b(g).
2*g*(g - 1)/9
Let a(k) = -7*k**3 - 10*k**2 - 3*k. Let v(d) = 0*d + 3 + 0*d + d**2 - 4. Let o(y) = -a(y) + 2*v(y). Factor o(q).
(q + 1)**2*(7*q - 2)
Let g = -3 - -5. Determine t so that -2*t**5 - 2*t**5 + 0*t**4 - 2*t**g + 2*t**4 + 4*t**4 = 0.
-1/2, 0, 1
Let y(w) be the first derivative of -w**4/2 + 14*w**3/9 - 2*w**2/3 + 19. Factor y(t).
-2*t*(t - 2)*(3*t - 1)/3
Suppose 4*t = 2*a - 32, 4*a - 44 = -0*t + 4*t. Let f(z) = -z**2 - 9*z + 6. Let w(y) = y - 1. Let p(r) = a*w(r) + f(r). Factor p(o).
-o*(o + 3)
Find n such that 23*n + 3*n**3 + 52/3*n**2 - 6 = 0.
-3, 2/9
Let j(a) be the first derivative of 7*a**4/2 - 4*a**3/3 - 28*a**2 + 16*a - 15. Factor j(z).
2*(z - 2)*(z + 2)*(7*z - 2)
Let i(c) be the third derivative of 2*c**6/75 - 2*c**5/25 + c**4/10 - c**3/15 + 18*c**2. Factor i(b).
2*(2*b - 1)**3/5
Let h = 351/5 + -70. Let t(a) = -3*a. Let k be t(-1). Factor 2/5*u**k - 1/5 + 0*u**2 + h*u**4 - 2/5*u.
(u - 1)*(u + 1)**3/5
Let a = -17/30 + -409/30. Let k = -14 - a. Factor 1/5*v**5 + k*v**4 + 0 - 1/5*v**2 - 1/5*v**3 + 0*v.
v**2*(v - 1)*(v + 1)**2/5
Let s(a) be the third derivative of -7*a**6/1020 + 19*a**5/510 + a**4/34 + 47*a**2. Factor s(d).
-2*d*(d - 3)*(7*d + 2)/17
Let l(z) be the second derivative of 2*z**6/15 - 7*z**5/10 + 3*z**4/2 - 5*z**3/3 + z**2 - 28*z. Factor l(h).
2*(h - 1)**3*(2*h - 1)
Let v = 24 - 24. Let -2/7*c**4 + v*c**2 + 0 - 8/7*c + 6/7*c**3 = 0. What is c?
-1, 0, 2
Suppose 2*c = 1 - 9, 4*w - c - 20 = 0. Suppose 6/11*m**w + 0 + 0*m + 4/11*m**3 - 2/11*m**2 = 0. What is m?
-1, 0, 1/3
Suppose 4*w = 16 + 20. Suppose -5*a = -w - 1. Factor 4/3*o - 2/3 - 2/3*o**a.
-2*(o - 1)**2/3
Let g(d) be the second derivative of 0 + 1/39*d**3 + 3/130*d**5 - 3*d + 2/39*d**4 + 0*d**2. Suppose g(i) = 0. Calculate i.
-1, -1/3, 0
Suppose 5*w + 4*r = r - 9, 2*w - 4*r = 12. Suppose w = 3*a - 30 + 12. Let t(m) = m**2 + 10*m - 2. Let p(d) = -d + 1. Let u(o) = a*p(o) + t(o). Factor u(s).
(s + 2)**2
Factor -6*v**2 - 21/2*v - 9/2.
-3*(v + 1)*(4*v + 3)/2
Factor 8*r**2 - 5*r**4 - 2*r - 7*r - r + 7*r**2.
-5*r*(r - 1)**2*(r + 2)
Let z(y) be the first derivative of -y**6/3 + y**4 - y**2 - 24. Factor z(t).
-2*t*(t - 1)**2*(t + 1)**2
Let z(l) be the first derivative of 0*l + 4 + 3/5*l**5 + 1/3*l**3 - 3/4*l**4 - 1/6*l**6 + 0*l**2. Suppose z(x) = 0. Calculate x.
0, 1
Let i(d) be the first derivative of -d**8/6720 + d**7/1680 - d**6/1440 - d**3 - 6. Let g(k) be the third derivative of i(k). Suppose g(w) = 0. What is w?
0, 1
Let q(o) be the second derivative of -o**4/6 - 2*o**3/3 + 3*o**2 + 10*o. Factor q(r).
-2*(r - 1)*(r + 3)
Let z(h) be the third derivative of h**6/12 - h**5/12 + 9*h**2. Solve z(o) = 0.
0, 1/2
Let y(k) = -k**4 - k**3 + k**2 + 6*k + 5. Let p(g) = -g**4 - g**3 + g**2 + 9*g + 8. Let o(b) = 5*p(b) - 8*y(b). Find q, given that o(q) = 0.
-1, 0, 1
Let m be (-10 + 0)*(-5)/10. Factor -5*x**3 + m*x**3 - 4*x**3 + 2*x**3 + 2*x**4.
2*x**3*(x - 1)
Factor 2 + 12*r - 8*r - 4*r**2 + 6 + 0*r**2.
-4*(r - 2)*(r + 1)
Suppose -4*v + 21 - 13 = 0. Let t(d) be the first derivative of -3*d**3 + 1/2*d**4 + 2 - 4*d + 6*d**v. Determine g, given that t(g) = 0.
1/2, 2
Suppose 4*d - 1 = 3*b + 24, -4*d + b + 19 = 0. Suppose d*x = x + 6. Determine u, given that 0*u + 0 - 1/2*u**3 - u**x = 0.
-2, 0
Let j(m) be the third derivative of m**6/600 + m**5/100 + m**4/60 + 2*m**2. Solve j(i) = 0.
-2, -1, 0
Factor 3368 - 3*x**2 - 3368 - 3*x**3.
-3*x**2*(x + 1)
Suppose 4*b - b - 52 = -4*u, -77 = -5*b + 3*u. Factor g**2 + 17*g**4 - 2*g**3 - b*g**4 + 4*g**3.
g**2*(g + 1)**2
Let a(o) be the third derivative of -o**8/1680 - o**7/840 + 2*o**3/3 - o**2. Let p(j) be the first derivative of a(j). Factor p(g).
-g**3*(g + 1)
Let a(u) be the second derivative of 9*u**5/20 + u**4/6 + 4*u. Find b such that a(b) = 0.
-2/9, 0
Let m(o) be the first derivative of -5*o**6/6 + o**5 + 15*o**4/2 - 70*o**3/3 + 55*o**2/2 - 15*o - 30. Find k such that m(k) = 0.
-3, 1
Let i(v) = -2*v. Let g be i(-1). Factor 9*s - 10*s - s**g + 0 + 2.
-(s - 1)*(s + 2)
Let n(v) = -v**3 - 7*v**2 - 6*v + 2. Let z be n(-6). Let h = 121 - 603/5. Find r such that 6/5*r + 6/5*r**z + 2/5 + h*r**3 = 0.
-1
Let f(q) be the third derivative of q**10/15120 + q**9/7560 - q**8/3360 - q**7/1260 + q**4/8 - 3*q**2. Let a(g) be the second derivative of f(g). Factor a(s).
2*s**2*(s - 1)*(s + 1)**2
Let d(o) be the third derivative of o**5/180 + o**4/72 + o**2. Suppose d(v) = 0. Calculate v.
-1, 0
Let k = 95 + -183/2. Factor r**2 + k*r - 7/2*r**3 - 1.
-(r - 1)*(r + 1)*(7*r - 2)/2
Let s(g) be the second derivative of -g**4/6 - g**3/3 + 6*g. Factor s(r).
-2*r*(r + 1)
Let x(w) be the second derivative of -5*w**4/12 + 5*w**3/3 - 5*w**2/2 - 7*w. Factor x(c).
-5*(c - 1)**2
Suppose 4*s - 21 = -4*h - s, -h = -4*s. Let c(b) be the second derivative of 0*b**2 + 0 - 2*b + 1/9*b**3 - 1/9*b**h + 1/30*b**5. Find f, given that c(f) = 0.
0, 1
Let c(l) = -3*l**2 - 11*l - 27. Let u(v) = -2*v**2 - 7*v - 18. Suppose 4*r = 2*r - 14. Let b(x) = r*u(x) + 5*c(x). Suppose b(g) = 0. Calculate g.
-3
Suppose -3*z + 8*z - 30 = 0. Find r, given that -r**2 + 0*r + 9/2*r**3 - z*r**4 + 5/2*r**5 + 0 = 0.
0, 2/5, 1
Let x(u) = -u**2 + 6*u + 7. Let t be x(7). Let f(g) be the first derivative of 1/2*g**2 - 2 - 1/10*g**5 + 1/6*g**3 - 1/4*g**4 + t*g. Factor f(l).
-l*(l - 1)*(l + 1)*(l + 2)/2
Factor 3*u**3 + 235*u - 33*u**3 - 75*u - 5*u**4.
-5*u*(u - 2)*(u + 4)**2
Let z be ((-12)/(-3))/(0 - -10). Factor 0*q + z*q**2 - 2/5.
2*(q - 1)*(q + 1)/5
Suppose -3*r - 28 = -r. Let z(w) = -4 + 6*w**2 + 20*w + 4. Let b(l) = -2*l**2 - 7*l. Let y(j) = r*b(j) - 5*z(j). Factor y(o).
-2*o*(o + 1)
Factor -5*b**3 - 2 + 2 - 15*b**2 - 5 - 15*b.
-5*(b + 1)**3
Let i(w) be the second derivative of w**4/3 + 2*w**3/3 - 12*w**2 + 6*w. Suppose i(r) = 0. Calculate r.
-3, 2
Let k(p) be the first derivative of -p**7/5040 + p**5/720 + 3*p**3 + 2. Let l(f) be the third derivative of k(f). Factor l(m).
-m*(m - 1)*(m + 1)/6
Let o(a) = a**4 + a - 1. Let f(x) = 12*x**5 + 26*x**4 - 4*x**3 - 8*x**2 + 10*x - 10. Let h(s) = f(s) - 10*o(s). Factor h(p).
4*p**2*(p + 1)**2*(3*p - 2)
Let v(t) be the first derivative of -t**6/69 - 12*t**5/115 - 11*t**4/46 - 4*t**3/69 + 12*t**2/23 + 16*t/23 - 27. Suppose v(n) = 0. Calculate n.
-2, -1, 1
Determine t so that 10/13*t**2 - 4/13*t - 6/13*t**4 + 0 + 8/13*t**3 = 0.
-1, 0, 1/3, 2
Let -27*f**3 + 102*f**3 + 495*f - 342 + 165*f - 18 - 5*f**4 - 370*f**2 = 0. What is f?
1, 2, 6
Let l = 463 - 175. Let o be l/(-40)*1/(-3). Suppose 243/5*d**2 + 108/5*d + o = 0. Calculate d.
-2/9
Let y(k) be the first derivative of -2*k**5/45 + 2*k**4/9 - 8*k**3/27 - 27. Find q, given that y(q) = 0.
0, 2
Suppose 38*s - 56 = 10*s. Let 0*c - 1/2*c**s + 1/2 = 0. What is c?
-1, 1
Find u, given that 6*u + 5*u**5 - 6*u**3 - 2*u**5 - 3*u = 0.
-1, 0, 1
Let u(d) be the second derivative of 3*d**7/112 - 11*d**6/240 + d**5/80 - 15*d. Suppose u(m) = 0. Calculate m.
0, 2/9, 1
Factor -2/9*t**3 - 14/9*t - 10/9*t**2 - 2/3.
-2*(t + 1)**2*(t + 3)/9
Let c = 19 - 21. Let l(t) = -t**3 + t**2 + t + 1. Let p(j) = -2*j**5 + 6*j**3 + 6*j**2 - 4*j - 2. Let o(v) = c*l(v) + p(v). Factor o(m).
-2*(m - 2)*(m - 1)*(m + 1)**3
Let f(z) be the second derivative of -5*z**7/84 - z**6/6 + 5*z**4/12 + 5*z**3/12 + z. Factor f(s).
-5*s*(s - 1)*(s + 1)**3/2
Suppose 2*s - 5*s + 105 = 0. Let q(l) = 16 + l + 2*l - s*l**2 - 3. Let d(h) = 17*h**2 - 2*h - 6. Let k(r) = 10*d(r) + 4*q(r). Factor k(j).
2*(3*j - 2)*(5*j + 2)
Suppose d - 9 = -3*p + 39, -5*d = p - 30. Let o = 31 - p. Factor -y**5 + y**3 - o + 16.
-y**3*(y - 1)*(y + 1)
Let z = 2 + 2. Find j, given that 3*j - 3*j**3 + 2*j**3 - 4*j**3 - z*j**3 - 6*j**2 = 0.
-1, 0, 1/3
Let q(v) be the first derivative of v**8/336 - v**7/210 - v**6/120 + v**5/60 - v**2/2 - 4. Let a(y) be the second derivative of q(y). Factor a(s).
s**2*(s - 1)**2*(s + 1)
Suppose 111*c = 98*c + 26. Factor 0 + 3/2*k - 3/2*k**4 + 9/2*k**3 - 9/2*k**c.
-3*k*(k - 1)**3/2
Let c = 1 + 15. Let r = 19 - c. Factor 0 - 2/3*i**r + 2/9*i**4 - 2/9*i + 2/3