rst derivative of -n**4/2 + 8*n**3/3 + 5*n**2 + 56. Factor w(a).
-2*a*(a - 5)*(a + 1)
Suppose -4*r - k - 7 = -0*k, -10 = r + 3*k. Let t be (3 + -4)/(3/(-2) - r). Factor -2 - 2/9*s**t + 4/3*s.
-2*(s - 3)**2/9
Let c be (-910)/(-273) - (-1)/(-3). Factor 1/9*j**c + 0 - 2/9*j + 1/9*j**2.
j*(j - 1)*(j + 2)/9
Let j(t) be the third derivative of -1 - 11/20*t**5 + 3/2*t**3 + 0*t + 40*t**2 - 5/8*t**4 - 3/40*t**6. Factor j(x).
-3*(x + 1)*(x + 3)*(3*x - 1)
Let x = -41/3 + 124/9. Let r(p) be the second derivative of -1/21*p**7 + 1/6*p**5 + 5*p + x*p**4 - 4/45*p**6 + 0*p**3 + 0 + 0*p**2. Solve r(i) = 0.
-2, -1/3, 0, 1
Let t = 686/17 - 3413/85. Let g(b) be the first derivative of t*b**4 + 2/25*b**5 + 0*b + 0*b**2 + 11 + 2/15*b**3. Factor g(y).
2*y**2*(y + 1)**2/5
Let x(s) be the third derivative of 1/5*s**5 - 8/105*s**7 + 2/3*s**3 + 1/6*s**6 - 37*s - 5/6*s**4 - s**2 + 0. What is g in x(g) = 0?
-1, 1/4, 1
Find s, given that 0 + 1/5*s**2 - 12/5*s = 0.
0, 12
Suppose 2*u = -10, -34*r + 39*r + 2*u = -10. Factor r + 2/7*a**2 - 2/7*a.
2*a*(a - 1)/7
Let d(o) = -7*o**2 + 8*o - 3. Let p(u) = -8*u**2 + 7*u - 2. Suppose 9*x + 11 + 7 = 0. Let c(y) = x*p(y) + 3*d(y). Solve c(q) = 0.
1
Let z(x) be the second derivative of -1/48*x**4 + 0*x**2 + 0*x**3 + 0*x**5 + 0 - 7*x + 1/120*x**6. Factor z(a).
a**2*(a - 1)*(a + 1)/4
Let c(r) = -2*r**2 - 14*r. Let v(b) = -3*b**2 - 29*b. Let w(x) = 5*c(x) - 2*v(x). Factor w(s).
-4*s*(s + 3)
Let g be (-2)/(-13) - 3600/22048. Let p = g - -217/530. Factor 4/5*w + 0 - p*w**2.
-2*w*(w - 2)/5
Let h(c) = -c**2 - 5*c + 17. Let q be h(-7). Factor 2*s**q + 23*s**3 + 2*s**3 - 6*s**2.
3*s**2*(9*s - 2)
Let s(w) = -w**4 - 2*w**3 + w. Let r(y) = -y**4 + 142*y**3 - 480*y**2 + 493*y - 164. Let h(q) = -r(q) + 5*s(q). Factor h(m).
-4*(m - 1)**3*(m + 41)
Determine h, given that 0 - 2/5*h**5 + 12/5*h**4 + 2/5*h**3 - 12/5*h**2 + 0*h = 0.
-1, 0, 1, 6
Suppose 820*z = 881*z. Factor 2/5*d**3 + 2/5*d**4 + z - 16/5*d**2 - 24/5*d.
2*d*(d - 3)*(d + 2)**2/5
Suppose -92/3*u + 4/3*u**2 + 56 = 0. What is u?
2, 21
Let d(c) = -c**3 + 51*c**2 + 67*c - 780. Let f be d(52). Factor 0*g**3 + 0 + f*g + 3/2*g**2 - 3/2*g**4.
-3*g**2*(g - 1)*(g + 1)/2
Let j(s) = -s**3 + 53*s**2 + 55*s - 52. Let x be j(54). Suppose -2/3*a**3 + 2/3*a**5 + 0*a**4 + 0 + 0*a**x + 0*a = 0. Calculate a.
-1, 0, 1
Let f = 14119 + -14115. Solve -4/3*g**f + 0 - 5/3*g**3 - 1/3*g**2 + 0*g = 0.
-1, -1/4, 0
Find w, given that 8 - 4*w + 8*w**3 - 9664*w**5 - 9*w**2 - 7*w**2 + 8*w**4 + 9660*w**5 = 0.
-1, 1, 2
Let n = 4981/10 + -498. Let w(v) be the first derivative of 2/5*v**3 - 8/5*v + n*v**4 + 0*v**2 + 8. Factor w(t).
2*(t - 1)*(t + 2)**2/5
Let a = -29530 + 29532. Factor -8/11*b**a + 10/11*b - 4/11 + 2/11*b**3.
2*(b - 2)*(b - 1)**2/11
Factor -6/17*x**4 + 0*x + 4/17*x**2 + 10/17*x**3 + 0.
-2*x**2*(x - 2)*(3*x + 1)/17
Suppose -n = 8*n - 45. Let t(u) be the first derivative of 4 + 0*u + u**2 + 1/5*u**n + 0*u**4 - u**3. What is h in t(h) = 0?
-2, 0, 1
Let i be 936/27 + 2/6. Let a = -26 + i. Let r(c) = -2*c**3 - 4*c**2 - 2*c + 2. Let x(b) = 8*b**3 + 15*b**2 + 7*b - 9. Let p(y) = a*r(y) + 2*x(y). Factor p(m).
-2*m*(m + 1)*(m + 2)
Let u(l) = l**3 + 26*l**2 + 51*l + 75. Let a be u(-24). Factor 0*v + 32/15*v**4 + 16/15*v**a + 0 + 2/15*v**2.
2*v**2*(4*v + 1)**2/15
Suppose 0 = -5*o + 10. Let r(l) = -l**3 + 2*l**2 + 2*l. Let z be r(o). Solve 2*c**2 + z + 2*c + 1 - 5 = 0.
-1, 0
Let j(w) = -w**3 + 3*w**2 + 4*w + 3. Let i be j(4). Let o be 1/2*(i - 4)*-6. Factor -3/5*s + s**4 + 3/5*s**o + 2/5 - 7/5*s**2.
(s - 1)*(s + 1)**2*(5*s - 2)/5
Suppose -38*l - 195 = 6*l - 371. What is v in 9/2*v**l + 3/4*v**5 + 0 + 9*v**2 + 39/4*v**3 + 3*v = 0?
-2, -1, 0
Let n(f) = 2*f + 3. Let z be n(-3). Let l be (-7)/(28/(-3))*(-2)/z. Factor -1/2*m**4 + m**2 - l + 0*m + 0*m**3.
-(m - 1)**2*(m + 1)**2/2
Let l(w) = 12*w**4 - 4*w**3 + 16*w**2 - 4*w. Let k(x) = 10*x**4 - 6*x**3 + 15*x**2 - 4*x. Let f(v) = 4*k(v) - 3*l(v). Solve f(h) = 0 for h.
0, 1
Let o(u) be the third derivative of -u**6/420 - 13*u**5/30 + 185*u**4/84 - 31*u**3/7 - 3*u**2 + 22*u. Factor o(w).
-2*(w - 1)**2*(w + 93)/7
Solve 0*k + 0 - 2/17*k**3 + 16/17*k**2 = 0.
0, 8
Let g = 16705 - 16703. Let u be 1/(-21) + 2/6. Factor u*m**g + 12/7*m + 18/7.
2*(m + 3)**2/7
Let o(f) be the first derivative of -f**4/54 - 2*f**3/27 - f**2/9 + 8*f + 13. Let b(s) be the first derivative of o(s). What is y in b(y) = 0?
-1
Let q(n) be the second derivative of n**6/270 - 43*n**5/180 - 89*n**4/108 - 5*n**3/6 + 9*n + 38. Suppose q(i) = 0. Calculate i.
-1, 0, 45
Suppose -4*p - 2*h + 28 = 0, 3*h + 13 = p + 4*p. Let -51*o**2 + 81*o**2 + 48*o - p*o**4 + 15 - 8*o = 0. Calculate o.
-1, 3
Let l(m) be the first derivative of 2*m**3/57 - 5*m**2/19 + 8*m/19 + 81. Determine a, given that l(a) = 0.
1, 4
Let y(m) be the second derivative of 0 - 36/5*m**5 + 5*m**2 - 16/15*m**6 + 12*m**3 + 47/6*m**4 - 9*m. Suppose y(o) = 0. What is o?
-5, -1/4, 1
Factor 400 - 26*o**2 - 21*o**2 - 16*o**2 + 92*o**2 + 404*o - 25*o**2.
4*(o + 1)*(o + 100)
Let u be (333/(-81))/(4/(-6)). Let l = -247/42 + u. Find h such that l - 4/7*h**3 + 2/7*h + 2/7*h**4 + 2/7*h**5 - 4/7*h**2 = 0.
-1, 1
Find m such that -16/9 + 4*m - 20/9*m**2 = 0.
4/5, 1
Let f = 6684 + -46780/7. Factor 0 - f*p + 2/7*p**3 - 6/7*p**2.
2*p*(p - 4)*(p + 1)/7
Let w(m) be the third derivative of 5*m**5/4 + 195*m**4/2 + 3042*m**3 + 243*m**2. Factor w(o).
3*(5*o + 78)**2
Let v(d) be the third derivative of d**7/42 - 3*d**6/8 + 7*d**5/3 - 15*d**4/2 + 40*d**3/3 + 8*d**2 + 6*d. Find k, given that v(k) = 0.
1, 2, 4
Let h be (1/(0 + 4))/(72/216). Suppose 0 - h*k + 15/8*k**2 = 0. Calculate k.
0, 2/5
Let n(p) = 3*p**4 + 12*p**3 - 18*p**2 + 13*p + 5. Let t(b) = -b**4 - 6*b**3 + 9*b**2 - 6*b - 2. Let r(q) = -2*n(q) - 5*t(q). Factor r(u).
-u*(u - 4)*(u - 1)**2
Suppose k - 3*i - 2*i = -13, 2*k + 3*i = 13. Let 67/3*z**3 + 0 + 3*z**5 + 17*z**4 + 4/3*z + 29/3*z**k = 0. Calculate z.
-4, -1, -1/3, 0
Let p(a) = -11*a**2 - 81*a + 270. Let y(d) = 5*d**2 + 40*d - 133. Let q(k) = 4*p(k) + 9*y(k). Factor q(n).
(n - 3)*(n + 39)
Let n(k) = 9*k**4 - 23*k**3 - 20*k**2 + 3*k - 3. Let p(z) = -19*z**4 + 45*z**3 + 40*z**2 - 7*z + 7. Let f(c) = 14*n(c) + 6*p(c). Let f(x) = 0. Calculate x.
-2/3, 0, 5
Let b = -4 + 7. Factor -12*d + 14 + 700*d**3 - 2 - 9*d**2 - b*d**4 - 688*d**3.
-3*(d - 2)**2*(d - 1)*(d + 1)
Factor -4/3*q - 1/3*q**2 - 1.
-(q + 1)*(q + 3)/3
Suppose 0 = q + 9 - 13. Determine u, given that 30*u**2 - 6*u**2 + 100*u**q - 19*u**2 + 10*u - 115*u**3 = 0.
-1/4, 0, 2/5, 1
Let q(s) = s + 3. Let m be q(2). Suppose n = -5*n + m*n. Factor 2/15*r**3 + 8/15 - 2/5*r**2 + n*r.
2*(r - 2)**2*(r + 1)/15
Let f(a) be the first derivative of a**5/15 - 7*a**4/12 + 11*a**3/9 - 5*a**2/6 - 19. Factor f(v).
v*(v - 5)*(v - 1)**2/3
Let z(w) be the third derivative of 1/192*w**8 - 1/420*w**7 - 7/480*w**6 + 0*w + 20*w**2 + 0 + 0*w**3 + 0*w**4 + 1/120*w**5. Solve z(q) = 0 for q.
-1, 0, 2/7, 1
Let w(f) be the second derivative of 1/14*f**7 + 22*f - 3/10*f**6 - 3/10*f**5 + 0 + 0*f**2 + 3*f**4 - 4*f**3. Factor w(h).
3*h*(h - 2)**2*(h - 1)*(h + 2)
Let v(t) be the third derivative of -t**9/6048 + t**8/1344 - t**6/144 - 7*t**5/60 - 22*t**2. Let q(r) be the third derivative of v(r). Factor q(h).
-5*(h - 1)**2*(2*h + 1)
Let c = 2415 - 2413. Solve -28/3*p + 8/3 - 16/3*p**c = 0.
-2, 1/4
Suppose 384/7*w + 18432/7 + 2/7*w**2 = 0. What is w?
-96
Suppose 4*d + 2 = 6*d. Let p = 4 + d. Factor 15*q + p*q**3 + 60*q + 0*q**2 + 45 + 31*q**2 + 4*q**2.
5*(q + 1)*(q + 3)**2
Let r = 9277 + -9275. Determine x so that 3/7*x**3 + 0 - 6/7*x + 3/7*x**r = 0.
-2, 0, 1
Let v(r) be the first derivative of r**3/15 - 59*r**2/5 + 3481*r/5 - 234. Determine n, given that v(n) = 0.
59
Let p(x) = -2*x**3 - x**2 + 10*x - 6. Let v be p(2). Let o be -14*v/48*(-2)/(-14). Factor -1/4*q**4 - 1/4*q + o*q**2 + 0 + 1/4*q**3.
-q*(q - 1)**2*(q + 1)/4
Solve -3/7*x + 12/7*x**2 - 6/7 - 3/7*x**5 + 6/7*x**3 - 6/7*x**4 = 0.
-2, -1, 1
Suppose 2*j = s + 6, 4*j - 16 = s - 0*j. Suppose 4*f + 6 = -r, 5*r - f - 4*f = 20. Factor -3*i**2 + s*i**r - i**4 + 0*i**4.
-i**2*(i - 1)*(i + 1)
Let w(z) be the second derivative of z**7/63 + 5*z**6/3 + 1441*z**5/30 + 407*z**4/6 - 2738*z**3/9 - z - 49. Suppose w(m) = 0. Calculate m.
-37, -2, 0, 1
Solve -18/5*h**3 - 3/5*h**4 - 12/5 - 39/5*h**2 - 36/5*h = 0.
-2, 