(n). Factor i(v).
-3*v*(v + 1)*(7*v + 2)
Solve 2/5*x**3 + 0 - 6*x**2 + 28/5*x = 0.
0, 1, 14
Let r = 46 - 43. Suppose 0 = r*b + 2*d - 1, b + 9 = -2*d - d. Let 0 - 2/11*o**2 - 2/11*o**b + 4/11*o = 0. What is o?
-2, 0, 1
Let y = -349 + 354. Let u(k) be the second derivative of 2*k - 2/15*k**4 + 0 - 27/35*k**7 - 39/25*k**6 - 4/5*k**y + 0*k**3 + 0*k**2. Factor u(c).
-2*c**2*(c + 1)*(9*c + 2)**2/5
Suppose -136*s = -43*s. Factor -2/7*y**5 - 2/7*y**4 + 2/7*y**2 + s*y + 0 + 2/7*y**3.
-2*y**2*(y - 1)*(y + 1)**2/7
Let p(l) be the third derivative of 0 - 1/60*l**5 - 43*l**2 + 0*l - 121/6*l**3 + 11/12*l**4. What is y in p(y) = 0?
11
Suppose 24 - 3*c**3 - 17*c - 5*c - 10*c**2 + 12*c**2 + 16*c**2 - 14*c = 0. What is c?
2
Let d = 141 - 81. Let u = d - 38. What is g in 10 - u - 48*g**2 + 8 + 32*g**3 + 0 + 24*g = 0?
1/2
Solve 67*s**3 + 43*s**3 - 106*s**3 + 28*s**2 + 40*s = 0.
-5, -2, 0
Let h(f) be the first derivative of f**5/5 - 19*f**4/4 - 20*f**3/3 + 19. Solve h(i) = 0 for i.
-1, 0, 20
Suppose -33*q + 21*q + 1140 = 0. Let y = q + -189/2. Find f, given that 1/6*f**2 - 2/3 + y*f = 0.
-4, 1
Let j(c) be the second derivative of 3*c**5/140 - 39*c**4/28 + 57*c**3/2 - 1083*c**2/14 - 18*c + 4. Let j(s) = 0. Calculate s.
1, 19
Let k be 1 + -42*6/(-81) + -3. Let h = -16 + 18. Factor k*g**h + 2/9*g**5 - 4/9*g - 2/3*g**3 + 0 - 2/9*g**4.
2*g*(g - 1)**3*(g + 2)/9
Let z(v) be the first derivative of -v**6/90 + 10*v**3/3 + 14. Let l(k) be the third derivative of z(k). Find s, given that l(s) = 0.
0
Let a(b) be the second derivative of -27/20*b**5 + 0 + 3/5*b**6 - 1/14*b**7 - b**4 + 0*b**2 + 33*b + 6*b**3. Find n such that a(n) = 0.
-1, 0, 2, 3
Factor 4/13*z**2 - 14/13*z + 2/13*z**3 + 8/13.
2*(z - 1)**2*(z + 4)/13
Let x(t) be the third derivative of -24*t**3 + 6*t**2 + 0*t - 1/15*t**5 + 2*t**4 + 0. What is i in x(i) = 0?
6
Let a(m) be the first derivative of 0*m**2 + 2/33*m**3 + 1/22*m**4 + 0*m + 7. Factor a(p).
2*p**2*(p + 1)/11
Let n(z) be the first derivative of z**7/420 + z**6/30 + z**5/5 + 2*z**4/3 + 7*z**3/3 - 2. Let a(c) be the third derivative of n(c). Factor a(o).
2*(o + 2)**3
Suppose 12 = 3*q - 2*y, 4*y + 7 + 5 = 0. Let h = -5 + 8. Factor -6*f**3 + 2*f**h - q*f**4 - 4 + 4.
-2*f**3*(f + 2)
Determine k, given that -11/2*k**2 - 1/2*k**4 - 5/2*k + 0 - 7/2*k**3 = 0.
-5, -1, 0
Factor -2/7*h**2 + 2*h - 12/7.
-2*(h - 6)*(h - 1)/7
Factor -27/4 + 13/2*h + 1/4*h**2.
(h - 1)*(h + 27)/4
Let j be (-1)/(-105)*(-154)/(-132). Let i(h) be the third derivative of 0*h + j*h**5 - 4*h**2 + 0*h**3 + 0 + 1/36*h**4. Suppose i(b) = 0. Calculate b.
-1, 0
Let h = -43 - -46. Factor -2 - 6*r**2 + 18*r**4 - 3*r**5 - 3 + 27*r - 8*r**h - 16*r**3 - 7.
-3*(r - 4)*(r - 1)**3*(r + 1)
Determine y, given that 192*y**2 + 87*y**3 - 148*y - 121*y**5 + 100*y**5 + 48 - 80*y - 78*y**4 = 0.
-4, -2, 2/7, 1
Let b(r) = 10*r**2 + 100*r + 90. Let t(o) = 2*o**2 + 20*o + 18. Let y(g) = 2*b(g) - 11*t(g). Determine u, given that y(u) = 0.
-9, -1
Let w(t) be the first derivative of t**5/100 + t**4/15 - t**3/10 - 9*t**2/5 + 22*t + 24. Let c(p) be the first derivative of w(p). Suppose c(n) = 0. What is n?
-3, 2
Let b(p) be the second derivative of -5*p**4/12 + 55*p**3/2 + 3*p + 65. Factor b(f).
-5*f*(f - 33)
Let n(v) be the first derivative of -7*v**5/25 + 3*v**4/2 - 29*v**3/15 + 3*v**2/5 + 264. Factor n(y).
-y*(y - 3)*(y - 1)*(7*y - 2)/5
Factor 0*z**2 + 105 - 43*z - 45*z - 2*z**2 - 15.
-2*(z - 1)*(z + 45)
Let w(d) be the first derivative of 2*d**2 + 8/5*d - 30 + 8/15*d**3. Factor w(n).
4*(n + 2)*(2*n + 1)/5
Factor -272*s + 38*s**2 - 12*s**2 - 2*s**3 + 20*s**2 + 480.
-2*(s - 15)*(s - 4)**2
Solve -12/5*v**4 + 0*v - 16/5 + 4/5*v**3 - 4/5*v**5 + 28/5*v**2 = 0 for v.
-2, -1, 1
Let l = -4049/27 - -150. Let t(k) be the second derivative of 0*k**2 + 5*k - 1/54*k**4 - l*k**3 + 0. Factor t(r).
-2*r*(r + 1)/9
Let h be (-2 - 8/12*-12) + -3. Suppose 18 = 3*r + h*x, -r - 2 = 3*x - 4*x. What is a in 0*a**r + 0 + 4/11*a**3 + 0*a + 2/11*a**4 = 0?
-2, 0
Let s(b) = 11*b**5 - b**4 + 5*b**3 + 3*b**2 + 6*b - 6. Let u(n) = -20*n**5 + 2*n**4 - 10*n**3 - 5*n**2 - 11*n + 11. Let g(r) = 11*s(r) + 6*u(r). Solve g(p) = 0.
-3, 0, 1
Factor 0*a**2 + 8 - 8*a**3 - 2*a**3 - 2*a**4 + 16*a + 2*a**5 - 4*a**2 - 2*a**2 + 8*a**2.
2*(a - 2)**2*(a + 1)**3
Let z(t) be the third derivative of t**8/1008 - t**7/126 - 11*t**6/360 + 11*t**5/60 - t**4/4 - 4*t**2 + 30. Find r, given that z(r) = 0.
-3, 0, 1, 6
Let h(t) = 4*t**4 - 4*t**3 - 6*t**2 - 5*t + 5. Let c(i) = 11*i**4 - 12*i**3 - 18*i**2 - 12*i + 15. Let s(f) = 3*c(f) - 8*h(f). Suppose s(m) = 0. Calculate m.
-1, 1, 5
Let q be (-168)/(-585)*18 + 135/585. Solve q*x + 0 + 8/5*x**4 - 18/5*x**3 - 1/5*x**5 + 0*x**2 = 0.
-1, 0, 3
Suppose 0 = 4*c - c. Determine m so that 3*m**2 + 1 - m**2 + c - 9 - 6*m = 0.
-1, 4
Factor 2*h**4 + 50 - 90*h - 18*h**3 + 121/2*h**2.
(h - 2)**2*(2*h - 5)**2/2
Let j be 3/(-4) + (-3)/12. Let t be 0 + 1 - (j - 2). Factor -8*g**2 + 4*g**3 - t*g**4 - 5*g**3 - 9*g**3 - 2*g.
-2*g*(g + 1)**2*(2*g + 1)
Solve 297/2*x - 243/2 + 3/2*x**3 - 57/2*x**2 = 0 for x.
1, 9
Let c = -16327/4 - -4085. Factor -1 - c*y**2 - 1/4*y**4 + 3/2*y**3 + 3*y.
-(y - 2)**2*(y - 1)**2/4
Factor -53*y**2 - 13*y**3 + 92*y - 14*y**3 + 21*y**3 - 16 - 30*y**3 - 67*y**2.
-4*(y + 4)*(3*y - 1)**2
Let t(g) be the first derivative of -4*g**3/9 - 12*g**2 - 34. Solve t(j) = 0 for j.
-18, 0
Let s(l) be the first derivative of l**8/168 - l**7/70 + l**6/180 - l**3 - 19. Let f(h) be the third derivative of s(h). Suppose f(n) = 0. What is n?
0, 1/5, 1
Let f(u) be the first derivative of -5*u**7/21 - 4*u**6/5 - 2*u**5/5 + 12*u + 4. Let d(x) be the first derivative of f(x). Solve d(g) = 0 for g.
-2, -2/5, 0
Let k = -184 - -183. Let q be 1*(k - 34)/(-7). Factor 0*o + 4/3*o**3 + 8/3*o**4 + 0 + 4/3*o**q + 0*o**2.
4*o**3*(o + 1)**2/3
Let q(d) be the first derivative of d**4/4 + 4*d**3/3 + d**2/2 - 6*d - 48. Factor q(i).
(i - 1)*(i + 2)*(i + 3)
Let q(c) be the first derivative of -5*c**7/392 + c**6/168 + 2*c**5/35 + c**4/14 + 4*c**3 + 6. Let j(h) be the third derivative of q(h). Factor j(s).
-3*(s - 1)*(5*s + 2)**2/7
Let n(c) = -21*c + 5 + 6 + 21*c**3 - 33*c**2 + 22. Let o(r) = 5*r**3 - r - r - 8*r**2 - 3*r + 8. Let z(m) = 2*n(m) - 9*o(m). Factor z(v).
-3*(v - 2)*(v - 1)*(v + 1)
Let w(h) be the second derivative of 3*h**5/20 - 2*h**4 - h**3/2 + 12*h**2 + 27*h - 1. Factor w(o).
3*(o - 8)*(o - 1)*(o + 1)
Let k(a) be the first derivative of a**5/25 + a**4/10 - 19*a**3/15 - 34*a**2/5 - 12*a + 303. Factor k(q).
(q - 5)*(q + 2)**2*(q + 3)/5
Let p(b) be the second derivative of 2*b**6/15 - 11*b**5/5 + 26*b**4/3 - 32*b**3/3 + 191*b. Factor p(l).
4*l*(l - 8)*(l - 2)*(l - 1)
Let t(p) be the first derivative of -p**4/12 - 2*p**3 - 10*p**2 + 200*p/3 + 435. Suppose t(s) = 0. What is s?
-10, 2
Let q(c) be the second derivative of c**7/378 + c**6/27 + 2*c**5/15 + 11*c**4/54 + 7*c**3/54 + 2*c + 21. Factor q(x).
x*(x + 1)**3*(x + 7)/9
Let r = 33 - 31. Find n such that -n + 0*n**2 + 3*n + 5*n**2 - 3*n**r = 0.
-1, 0
Let x = 3/655 - -646/1965. Factor -x*m**3 - m**2 - 2/3*m + 0.
-m*(m + 1)*(m + 2)/3
Let z(s) be the first derivative of -49*s**6/10 - 693*s**5/25 - 717*s**4/20 + 123*s**3/5 + 432*s**2/5 + 324*s/5 + 839. What is j in z(j) = 0?
-3, -1, -6/7, 1
Let c be (-2 - -23)*24/(-28). Let i be (-2 + (-25)/(-15))*c/4. Factor 3/4*b**3 - 3/4*b - i*b**2 + 3/2.
3*(b - 2)*(b - 1)*(b + 1)/4
Let p(v) be the second derivative of 9/20*v**5 - 1/60*v**6 + 18*v**3 - 11*v + 0*v**2 - 9/2*v**4 + 0. Solve p(r) = 0.
0, 6
Suppose 5*z = -a + 1 - 11, -5*a = 3*z - 38. Suppose -20*t + 15*t + a = 0. Factor 2/3*f**t + 0 - 2/3*f.
2*f*(f - 1)/3
Let o(a) be the first derivative of -2/33*a**3 + 0*a**2 + 8/11*a - 45. Factor o(u).
-2*(u - 2)*(u + 2)/11
Let d(u) = u**2 - 5*u + 2. Let y be d(5). Solve -c**2 - 72 + y*c**3 + 72 - c**4 = 0.
0, 1
Let g = 1723 + -1723. Let k(h) be the second derivative of -1/18*h**4 - 1/9*h**3 + g*h**2 - 9*h + 0. Solve k(s) = 0 for s.
-1, 0
Let r(g) be the third derivative of g**8/4032 + 5*g**7/1008 + g**6/24 + 2*g**5/15 + 24*g**2. Let u(x) be the third derivative of r(x). Factor u(y).
5*(y + 2)*(y + 3)
Let n(r) be the third derivative of 3*r**8/448 + r**7/280 - 9*r**6/80 + 9*r**5/40 - r**4/32 - 3*r**3/8 + 775*r**2. What is w in n(w) = 0?
-3, -1/3, 1
Let u(l) be the third der