 0*k - 2*k**2 + 2*k**f - 2 + k**4 - 6/5*k**5. Factor p(n).
-2*n*(n - 1)*(n + 1)*(3*n - 2)
Let m(p) be the first derivative of p**8/280 + p**7/210 - p**6/45 - p**5/30 + p**4/12 + 2*p**3/3 + 4. Let x(a) be the third derivative of m(a). Factor x(k).
2*(k - 1)*(k + 1)**2*(3*k - 1)
Suppose 4*i = i. Let y(v) be the third derivative of 7/540*v**6 + i - 1/54*v**5 + 0*v**3 + 0*v + v**2 - 1/54*v**4. Factor y(n).
2*n*(n - 1)*(7*n + 2)/9
Let 227*d**4 - d**5 - 2*d**5 - 230*d**4 = 0. Calculate d.
-1, 0
Factor 0*p**3 + 2/11*p**5 - 2/11*p + 0 - 4/11*p**4 + 4/11*p**2.
2*p*(p - 1)**3*(p + 1)/11
Let l be (-1)/(-4) - (-30)/8. Suppose -l*c**3 - 2*c + 2*c**3 - 6*c**2 - 4*c**3 - 2*c**4 + 0*c**4 = 0. Calculate c.
-1, 0
Let d(s) be the second derivative of 0 - 1/18*s**4 - 2/3*s**2 + 2*s + 1/3*s**3. Factor d(t).
-2*(t - 2)*(t - 1)/3
Let l = 15855/17 - 933. Let g = 16/51 - l. Let 2/3*m - g*m**5 + 4/3*m**2 + 0*m**3 - 4/3*m**4 + 0 = 0. What is m?
-1, 0, 1
Let a(p) be the second derivative of -1/4*p**2 + 1/40*p**5 - 1/8*p**4 + 1/4*p**3 + p + 0. Factor a(i).
(i - 1)**3/2
Let y = -8 - -8. Suppose -8*g = -9*g. Solve g + y*c - 1/3*c**2 = 0 for c.
0
Let c be 1/8*4*24. Let l be 0/(4/((-16)/c)). Factor 2/5*f**5 - 2/5*f**2 + l + 6/5*f**3 + 0*f - 6/5*f**4.
2*f**2*(f - 1)**3/5
Let f(p) be the second derivative of p**7/5040 + p**6/1440 + 5*p**4/12 + 2*p. Let m(n) be the third derivative of f(n). Factor m(x).
x*(x + 1)/2
Factor -1 + 35*o - 5 - 40*o**2 - 4 + 15*o**3 + 0*o.
5*(o - 1)**2*(3*o - 2)
Suppose -3*f + t + 113 = 0, f + 6*t - 2*t - 16 = 0. Factor 3/2*r**3 + f*r + 24 + 27/2*r**2.
3*(r + 1)*(r + 4)**2/2
Let p(y) = 24*y**4 - 54*y**3 + 68*y**2 - 34*y + 2. Let v(t) = -t**4 - t**3 + t**2 - t + 1. Let o(m) = p(m) + 6*v(m). Factor o(k).
2*(k - 1)**2*(3*k - 2)**2
Suppose -4*k + 2*g = -18, 2*k + 0 - 18 = 4*g. Let h(c) be the second derivative of 0 - 1/9*c**4 + 1/3*c**2 + 1/9*c**k - 3*c. Suppose h(z) = 0. What is z?
-1/2, 1
Let x(w) be the third derivative of -w**9/5040 - 3*w**8/2240 - w**7/280 - w**6/240 - 7*w**4/24 + 9*w**2. Let s(u) be the second derivative of x(u). Factor s(k).
-3*k*(k + 1)**3
Let u(v) be the first derivative of -5*v**4/4 - 35*v**3/3 - 75*v**2/2 - 45*v - 10. Factor u(z).
-5*(z + 1)*(z + 3)**2
Let i be 126/480 - (-3)/(-12). Let d(y) be the second derivative of 0 - 1/8*y**2 + i*y**5 - 1/24*y**3 + 1/48*y**4 - 2*y. Solve d(o) = 0.
-1, 1
Let m(s) be the third derivative of -s**6/200 - s**5/25 + s**4/8 - 4*s**2. Let m(l) = 0. Calculate l.
-5, 0, 1
Let q(v) be the first derivative of v**5/5 - v**4/2 + v**2 - v - 4. Suppose q(y) = 0. What is y?
-1, 1
Let a(f) be the first derivative of -f**5/60 - f**4/24 + f**3/3 + 3*f**2/2 + 2. Let p(r) be the second derivative of a(r). Factor p(z).
-(z - 1)*(z + 2)
Suppose 5*q + 4*v - 18 = 0, 7 + 2 = 2*q + v. Suppose 0 = 4*g - q - 2. Factor -p**g + 5*p - 2 - p**2 - p.
-2*(p - 1)**2
Let p(l) be the second derivative of l**7/42 + l**6/6 - 3*l**5/10 - 49*l. Find m, given that p(m) = 0.
-6, 0, 1
Let t = 4 - 2. Suppose -t = 2*m - 14. Suppose 4*n + 8*n**2 + m*n**3 - 14*n**4 + 6*n**2 - 13*n**5 + 3*n**5 = 0. Calculate n.
-1, -2/5, 0, 1
Let r(g) be the third derivative of -g**8/840 + g**6/90 - g**4/12 + g**3/6 + g**2. Let w(z) be the first derivative of r(z). Solve w(o) = 0.
-1, 1
Let y(j) be the first derivative of -j**4/18 + 4*j**3/27 + 4*j**2/9 - 16*j/9 - 9. Solve y(r) = 0 for r.
-2, 2
Suppose 0 = -3*h + 5*i + 29, 0*h - 26 = -2*h + 5*i. Let j(r) be the second derivative of -1/24*r**4 + 0*r**2 + 0 - 1/12*r**h - 2*r. Factor j(k).
-k*(k + 1)/2
Let l(o) be the first derivative of -7*o**6/120 + 9*o**5/80 - o**4/24 + 2*o - 9. Let d(q) be the first derivative of l(q). Determine z so that d(z) = 0.
0, 2/7, 1
Let w(o) be the first derivative of -2/5*o**2 - 7 + 0*o + 1/10*o**4 - 2/15*o**3. Solve w(r) = 0 for r.
-1, 0, 2
Let s = -969/5 + 194. Factor 0 + 2/5*j**2 + 0*j + s*j**3.
j**2*(j + 2)/5
Let o(r) be the first derivative of -r**6/120 + r**4/24 - r**2 - 3. Let z(w) be the second derivative of o(w). Factor z(t).
-t*(t - 1)*(t + 1)
Let g(k) = -8405*k**2 - 1155*k - 35. Let x(n) = 12607*n**2 + 1732*n + 52. Let o(z) = -8*g(z) - 5*x(z). Factor o(s).
5*(29*s + 2)**2
Let c(j) be the first derivative of 2*j**6 + 4*j**5 - 2*j**4/3 - 56*j**3/9 - 14*j**2/3 - 4*j/3 + 16. Determine k, given that c(k) = 0.
-1, -1/3, 1
Let x(f) be the second derivative of 0*f**3 - 1/70*f**5 - f + 0 + 0*f**2 + 1/42*f**4. Solve x(y) = 0.
0, 1
Let d(j) be the third derivative of j**9/21168 + j**8/3920 + j**7/1960 + j**6/2520 + j**3 - 8*j**2. Let m(z) be the first derivative of d(z). Factor m(a).
a**2*(a + 1)**3/7
Suppose -4*l - 2*u = -0*l + 2, 5 = -u. Suppose 0 = -l*k - k. Factor -6*t**2 - 11*t + 10*t**3 + 8*t**4 - 2 + t + k*t.
2*(t - 1)*(t + 1)**2*(4*t + 1)
Let v be (15/240)/(((-3)/1)/(-12)). Solve y + v*y**2 + 1 = 0 for y.
-2
Let g(a) be the second derivative of 2*a**6/15 - 8*a. Factor g(d).
4*d**4
Let j be (-12)/16 + 91/84. Factor 1/3*l + 2/3*l**2 + j*l**3 + 0.
l*(l + 1)**2/3
Let j(q) = -q + 7. Let l = -8 - -12. Let i be j(l). Solve y**3 - 3*y**2 + 8*y + y**i - 5*y**2 = 0 for y.
0, 2
Let -15*j**3 + 7 + j**2 - 7 + 17*j**3 + j**4 = 0. What is j?
-1, 0
Let l(u) be the second derivative of u**4/4 - 3*u**2/2 + 4*u. Solve l(n) = 0 for n.
-1, 1
Suppose -4*j + 9*j = 0. Let n(f) be the first derivative of 2 + 0*f**2 + j*f**3 + 1/12*f**6 + 0*f**5 - 1/8*f**4 + 0*f. Let n(r) = 0. Calculate r.
-1, 0, 1
Let q(m) = -4*m - 1. Let i be q(-1). Factor 3*z**5 + 12*z**3 + 6*z**i + 12*z**2 + 6*z**4 + 6*z**4 + 3*z.
3*z*(z + 1)**4
Let o(h) be the third derivative of -1/150*h**6 - 1/75*h**5 - 1/15*h**3 + 1/20*h**4 + 1/175*h**7 - h**2 + 0 + 0*h - 1/840*h**8. Factor o(v).
-2*(v - 1)**4*(v + 1)/5
Suppose -1860 = -0*a - 6*a. Let t be 1/(-6) + a/60. Factor 2/9*d**t + 0 + 0*d**2 + 2/9*d**3 + 4/9*d**4 + 0*d.
2*d**3*(d + 1)**2/9
Let j(t) = 10*t**3 - 18*t**2 + 14*t - 2. Let r(g) = g**4 + 1. Let w(q) = j(q) - 2*r(q). Find u such that w(u) = 0.
1, 2
Let v(k) be the first derivative of -k**6/105 + k**5/210 + k**4/21 - k**3/21 + k**2/2 - 2. Let a(r) be the second derivative of v(r). Factor a(i).
-2*(i - 1)*(i + 1)*(4*i - 1)/7
Let i be (-3 + -2)*1*10/(-25). Suppose -1/3 + 2/3*g**3 - 1/3*g**i + 1/6*g**5 + 2/3*g**4 - 5/6*g = 0. What is g?
-2, -1, 1
Let y be 8 + -4 - 54/15. Let x(p) be the first derivative of 2/15*p**3 - 1/5*p**2 + 1/10*p**4 - y*p + 1. Find v, given that x(v) = 0.
-1, 1
Let g(n) be the second derivative of 1/12*n**4 - 1/180*n**6 + 0*n**2 + 0*n**5 + 1/3*n**3 + 0 + n. Let l(r) be the second derivative of g(r). Factor l(h).
-2*(h - 1)*(h + 1)
Find z such that -3 - 12*z**2 - 20*z + 7*z**4 + 4*z**3 - 5 - 3*z**4 = 0.
-1, 2
Let v(c) be the second derivative of -9*c - 1/18*c**3 + 0*c**2 + 0 - 1/36*c**4. Factor v(s).
-s*(s + 1)/3
Let c be 24/(-330)*(-25)/10. Determine d so that -2/11*d**2 + 0 + c*d**4 - 2/11*d + 2/11*d**3 = 0.
-1, 0, 1
Let r be (2/3)/((-1)/(-6)). Suppose -12 = m - g + 4*g, -5*m = r*g + 5. Factor -2*n + n**4 + 0 + m*n**3 - 1 - n**3.
(n - 1)*(n + 1)**3
Let u = -24 + 24. Let t(l) be the second derivative of -1/3*l**2 + u + l - 1/18*l**4 - 2/9*l**3. Factor t(i).
-2*(i + 1)**2/3
Let v be (4/(-3))/(20/(-30)). Solve 9*o**5 + v*o**2 + 23*o + 148*o**2 + 8 + 145*o**3 + 37*o + 26*o**4 + 34*o**4 = 0 for o.
-2, -1/3
Suppose 9*u + 30 = 66. Suppose 3/2*t**3 + 0 - 3*t**2 + 0*t + 3/2*t**u = 0. Calculate t.
-2, 0, 1
Let d(z) be the third derivative of z**8/2352 - z**6/420 + z**4/168 + 10*z**2. Factor d(o).
o*(o - 1)**2*(o + 1)**2/7
Let h(p) be the third derivative of p**9/1008 - p**8/560 - p**7/140 - p**3/2 - 8*p**2. Let n(m) be the first derivative of h(m). Factor n(c).
3*c**3*(c - 2)*(c + 1)
Let j be 20/6*144/40. Let d be (-4)/(2 - 0) + 8. Factor j + d*i**2 - 4 - 4*i**2 - 8*i.
2*(i - 2)**2
Let c(v) = -11*v**2 + 16*v + 21. Let d(y) = -10*y**2 + 15*y + 20. Let z(p) = 5*c(p) - 6*d(p). Determine q so that z(q) = 0.
-1, 3
Suppose -6 + 0 = -2*q. Let g(s) be the second derivative of 0*s**2 + 0 + 1/90*s**6 - s + 0*s**5 + 0*s**4 + 0*s**q. Factor g(j).
j**4/3
Suppose 3*h**5 - 5*h**5 + h**4 + 7*h**5 - 4*h**5 = 0. Calculate h.
-1, 0
Let o be ((-3)/(15/(-34)))/(-2). Let h = -41/15 - o. Factor 2/3*p**2 + h*p**3 + 0*p + 0.
2*p**2*(p + 1)/3
Let 5*w - 16 - 37*w - 4*w**3 + 8*w**2 - 28*w**2 = 0. Calculate w.
-2, -1
Let f(h) be the th