st derivative of -z**6/1080 - z**5/120 - z**4/36 + 4*z**3 + 27. Let c(g) be the third derivative of x(g). Factor c(u).
-(u + 1)*(u + 2)/3
Solve -4*v**5 - 64*v - 16 - 182*v**2 - 135*v**2 - 76*v**3 + 217*v**2 - 28*v**4 = 0 for v.
-2, -1
Let l(i) be the first derivative of 18 + 4/15*i**3 + 2/5*i**2 + 0*i. Determine f, given that l(f) = 0.
-1, 0
Let n(x) = -15*x**3 - 31*x**2 + 270*x + 319. Let t(l) = 8*l**3 + 16*l**2 - 134*l - 160. Let y(f) = -6*n(f) - 11*t(f). Factor y(i).
2*(i - 7)*(i + 1)*(i + 11)
Let o be (-4)/(-5)*(278/496 - (-32)/496). Let u(f) = f + 1. Let t be u(1). Let -o*y**t - 1/4*y + 0 = 0. What is y?
-1/2, 0
Let r(d) be the second derivative of d**4/4 - d**3/2 - 3*d**2 + 213*d. Factor r(g).
3*(g - 2)*(g + 1)
Let a(o) be the first derivative of o**6/3 - 14*o**5/5 + 15*o**4/2 - 26*o**3/3 + 4*o**2 - 53. Let a(s) = 0. Calculate s.
0, 1, 4
Let r be ((-192)/(-27))/((-320)/(-240)). Factor 16/3*t**3 - r*t + 4/3*t**4 - 16/3 + 4*t**2.
4*(t - 1)*(t + 1)*(t + 2)**2/3
Let g be 3 + (-4)/2 + 2. Suppose -d = -g*d + 4. Factor -2*z**4 + d*z**3 + 0*z**4 - 4*z**3 + 8*z**4.
2*z**3*(3*z - 1)
Suppose 4 + 0 = l. Let z(x) be the first derivative of 0*x**3 - 3/4*x**l + 5 + 0*x + 3/2*x**2. Solve z(q) = 0 for q.
-1, 0, 1
Let b = 422 + -17725/42. Let a = b - -1/6. Factor -3/7*z - 2/7 - a*z**2.
-(z + 1)*(z + 2)/7
Let p(z) be the second derivative of -1/24*z**4 + 0 - 1/12*z**3 + 9*z + 1/2*z**2. Factor p(c).
-(c - 1)*(c + 2)/2
Determine g so that 103*g**2 + 144 + 104*g**2 - 211*g**2 = 0.
-6, 6
Let i(f) be the second derivative of 0*f**2 + 1/36*f**4 + 36*f - 1/30*f**5 + 0 + 1/9*f**3 - 1/90*f**6. Factor i(l).
-l*(l - 1)*(l + 1)*(l + 2)/3
Factor 12881*n - 2145*n**2 - 5*n**4 - 5780 - 3520*n + 190*n**3 - 2901*n.
-5*(n - 17)**2*(n - 2)**2
Suppose -2*i + g - 14 + 21 = 0, -3*i + 5 = 4*g. Factor 4/9*a**i + 0 + 4*a - 8/3*a**2.
4*a*(a - 3)**2/9
Solve 183/5*n**2 + 108/5 + 42/5*n**3 + 252/5*n + 3/5*n**4 = 0.
-6, -1
Let d(z) be the third derivative of z**8/21 - 22*z**7/105 - 19*z**6/30 - 4*z**5/15 - 102*z**2. Suppose d(u) = 0. What is u?
-1, -1/4, 0, 4
Let n be ((-18)/(-12))/((-1)/(-2)). Suppose 2*y + n*c - 17 = 0, 3*y + 0*y = -3*c + 24. Solve 23*s + y*s**2 - 13*s - 15 - 2*s**2 = 0.
-3, 1
Let y(r) be the first derivative of r**7/4620 + r**6/1980 - r**5/660 - r**4/132 + 4*r**3 - 12. Let o(h) be the third derivative of y(h). Factor o(n).
2*(n - 1)*(n + 1)**2/11
Let n(x) be the first derivative of 5*x**3 + 5/6*x**6 - 5*x**2 - 3*x**5 + 5/4*x**4 - 9 + 0*x. Solve n(o) = 0 for o.
-1, 0, 1, 2
Solve 9/4*x - 9/2*x**4 + 0 - 15/2*x**2 + 3/4*x**5 + 9*x**3 = 0 for x.
0, 1, 3
Let s(l) be the first derivative of l**5 + 15*l**4/4 + 10*l**3/3 + 51. Factor s(m).
5*m**2*(m + 1)*(m + 2)
Let n be 40/6*7/((-42)/(-45)). Let x be ((-16)/(-30))/(20/n). Factor -x + 2/3*y + 2/3*y**2.
2*(y - 1)*(y + 2)/3
Let v(f) = 3*f + 20. Let u be v(-5). Suppose 2*i - 2*a + 0*a = 4, -u*a = -3*i + 6. Suppose 2/9*q**i + 2/3 + 8/9*q = 0. Calculate q.
-3, -1
Factor 0*t**3 - 8*t**3 - t**2 + 7*t**3.
-t**2*(t + 1)
Let a(q) = -q - 11. Let g be a(7). Let y be 178/42 - 0 - g/54. Factor y*f**2 + 4/7*f**4 - 20/7*f**3 + 0 - 16/7*f.
4*f*(f - 2)**2*(f - 1)/7
Let v = 86 + -90. Let x be 2/28 - 2/v. Solve -10/7*r**3 + 6/7*r - 24/7*r**4 + 16/7*r**2 - x - 8/7*r**5 = 0.
-2, -1, 1/2
Factor -20/9*y**3 + 52/9*y**2 + 104/9*y + 32/9.
-4*(y - 4)*(y + 1)*(5*y + 2)/9
Let f(u) = 9*u - 42. Let g be f(5). Let h(d) be the second derivative of -3*d + 4/45*d**g + 1/150*d**5 + 0*d**2 + 0 - 2/45*d**4. Factor h(z).
2*z*(z - 2)**2/15
Suppose 10*h + 4 = 4*x + 11*h, 0 = 3*h - 12. Let o(t) be the third derivative of 0*t**4 + 0*t**3 + 0 + x*t - 4*t**2 - 1/60*t**6 - 1/15*t**5. Factor o(r).
-2*r**2*(r + 2)
Let c = 59 + -59. Let u = -134 + 406/3. Suppose -u*o**3 + c + 2/3*o**2 + 2/3*o**4 + 0*o = 0. What is o?
0, 1
Let h(z) be the third derivative of z**7/168 + z**6/120 - z**5/60 + z**3/2 - 12*z**2. Let o(b) be the first derivative of h(b). Factor o(q).
q*(q + 1)*(5*q - 2)
Let b(y) be the second derivative of y**4/28 - 5*y**3/14 + 9*y**2/7 + 2*y + 14. Solve b(h) = 0 for h.
2, 3
Suppose x - 11*x**2 + 17*x**2 - 6 - 5*x**2 = 0. Calculate x.
-3, 2
Let n(a) = 5*a**2 - 12*a + 37. Let f(w) = 2*w**2 + w + 1. Let j(g) = 6*f(g) - 2*n(g). Factor j(c).
2*(c - 2)*(c + 17)
Let d be 1 + 8/(-10) + (-84)/(-5). Factor 2*l**3 + 2*l**4 - d*l**2 - 18*l**2 - 22*l**2 - 2*l + 55*l**2.
2*l*(l - 1)*(l + 1)**2
Let y be (-20)/(-3)*161/(-336). Let o = y + 40/9. Factor 0*k + 0 - 1/2*k**2 + o*k**3.
k**2*(5*k - 2)/4
Let s(t) = 25*t**2 + 13*t - 11. Let v(k) = 11*k**2 + 8*k - 5. Let w(q) = -6*s(q) + 15*v(q). What is o in w(o) = 0?
-3, 1/5
Let n(w) = -w**2 - 9*w + 24. Let m be n(-11). Factor -3*g**m + 86*g - 2*g**2 + 71*g - 142*g.
-5*g*(g - 3)
Let q(f) = -3*f**2 - 15*f. Let c = 20 + -19. Let t(m) = m**2. Let b(v) = c*q(v) - 2*t(v). Determine n, given that b(n) = 0.
-3, 0
Let p(b) = -2*b**3 - 5*b**2 - 3. Let t(y) = y**3 + y**2 + 1. Let n(u) = -p(u) - 3*t(u). Factor n(r).
-r**2*(r - 2)
Solve -70*x**2 + 489819 + 2*x**4 - 489819 - 32*x**3 - 36*x = 0 for x.
-1, 0, 18
Suppose 4*a - 4*y = 0, 134*y - 6 = -3*a + 135*y. Solve 2/11*d - 2/11 + 6/11*d**2 - 2/11*d**a - 4/11*d**4 = 0.
-1, 1/2, 1
Suppose -2*f = 5*t - 9, -f + t + 2*t = 23. Let n = f + 13. Factor -2*v**4 - 8*v**4 - 3*v**n + 9*v + 2 - 4*v - 10*v**3.
-(v + 1)**4*(3*v - 2)
Let m(d) be the first derivative of -6/5*d**5 + 2*d**3 + 3/2*d**2 + 0*d**4 - 1/2*d**6 + 11 + 0*d. Determine w so that m(w) = 0.
-1, 0, 1
Let f = 1484 - 1484. Factor -3/5*r**4 + 3/5*r**2 + f - 3/5*r**3 + 0*r + 3/5*r**5.
3*r**2*(r - 1)**2*(r + 1)/5
Let z(f) = f**5 + f**4 + 2*f**3 + f. Let d(b) = 15*b**5 - 42*b**4 + 207*b**3 + 540*b**2 + 312*b. Let o(w) = d(w) - 12*z(w). Solve o(n) = 0.
-1, 0, 10
Let q = 3727/4476 + 1/1492. Factor -q*f - 1/3 + 1/6*f**4 - 1/2*f**2 + 1/6*f**3.
(f - 2)*(f + 1)**3/6
Let h(u) = 24*u**4 + 67*u**3 - 37*u**2 - 207*u - 106. Let c(q) = -11*q**4 - 33*q**3 + 18*q**2 + 103*q + 54. Let o(p) = 7*c(p) + 3*h(p). Factor o(g).
-5*(g - 2)*(g + 1)**2*(g + 6)
Factor 1/8*d**5 + d - 11/4*d**2 - d**4 + 0 + 21/8*d**3.
d*(d - 4)*(d - 2)*(d - 1)**2/8
Let l(a) be the first derivative of a**5/420 - 2*a**3/21 + 13*a**2/2 - 5. Let s(z) be the second derivative of l(z). What is r in s(r) = 0?
-2, 2
Let w = 27420 + -27416. Let 10/3*a - 2/3*a**2 - w = 0. Calculate a.
2, 3
Let s = -21 + 25. Solve -s*f**2 - 120 - 4*f**4 + 8*f**3 + 120 = 0.
0, 1
Let n be (9 + -3)/(5 + 12/(-3)). Let z(y) be the second derivative of 0*y**3 + 0*y**5 + 0 + 0*y**4 + n*y + 1/45*y**6 + 0*y**2. Let z(m) = 0. What is m?
0
Factor 0 + 38/3*u**3 + 0*u - 4*u**2 - 64/9*u**4 + 10/9*u**5.
2*u**2*(u - 3)**2*(5*u - 2)/9
Suppose -12*k + 8*k - 8 = 0. Let p be 0*(3/(-3) - k). What is l in 1/3*l - 1/3*l**2 + p = 0?
0, 1
Let s(h) = 9*h**5 - 3*h**4 - 49*h**3 - 46*h**2 - 16*h + 7. Let m(x) = -x**5 - x**4 + x**3 - 1. Let b(j) = -14*m(j) - 2*s(j). Let b(l) = 0. Calculate l.
-1, 0, 8
Let a = 10754 - 376456/35. Let y = 16/7 + a. Factor 1/5 + 1/5*p**2 + y*p.
(p + 1)**2/5
Factor -20 + 15*k**4 - 4455*k + k**3 + 4515*k - 9*k**3 - 2*k**3 - 45*k**2.
5*(k - 1)**2*(k + 2)*(3*k - 2)
Let x = -303 - -303. Let w(i) be the third derivative of -1/45*i**6 - 7*i**2 + 0*i**5 + 0*i**3 + 2/315*i**7 + 1/252*i**8 + x*i**4 + 0 + 0*i. Factor w(m).
4*m**3*(m - 1)*(m + 2)/3
Let f(u) = -5*u**2 - 2*u + 4. Let q(a) = -2 - 11 + 6*a + 14*a**2 + 2. Let i(o) = -11*f(o) - 4*q(o). Let z(w) = w. Let j(g) = -i(g) - 3*z(g). Factor j(c).
c*(c - 1)
Let t = -48441 + 629735/13. Suppose -t*w**2 + 24/13*w + 0 = 0. Calculate w.
0, 12
Solve -3*h**3 + 4*h**2 - 20*h**4 + 39*h**4 + 10*h + 2*h**5 - 6 - 9*h**3 - 17*h**4 = 0.
-3, -1, 1
Let u(z) be the second derivative of 3*z**5/20 + z**4/4 - 2*z**3 - 6*z**2 - 37*z. Factor u(k).
3*(k - 2)*(k + 1)*(k + 2)
Let r = -9640 - -48204/5. Let -r*h + 3/5 + 1/5*h**2 = 0. What is h?
1, 3
Let d(u) be the third derivative of -u**7/1260 + u**6/135 + u**5/60 - u**4/2 - 16*u**3/3 - 10*u**2. Let h(a) be the first derivative of d(a). Factor h(n).
-2*(n - 3)**2*(n + 2)/3
Let n(h) be the second derivative of -15/16*h**4 - 53*h + 1/24*h**6 - 55/24*h**3 - 1/16*h**5 - 5/2*h**2 + 0. Factor n(c).
5*(c - 4)*(c + 1)**3/4
Let 0 + 0*j + 3/2*j**3 + 3*j**2 = 0. What is j?
-2, 0
Let l be 2/3*(-8853)/(-286). Let z = 21 - l. Solve -z*f - 2/11 - 2/11*f**2 = 0 for f.
-1
