et v(g) be the first derivative of -3 + 1/120*g**6 + 0*g + 0*g**4 + 2/3*g**3 + 1/40*g**5 + 0*g**2. Let u(y) be the third derivative of v(y). Factor u(j).
3*j*(j + 1)
Let n(r) be the third derivative of -1/448*r**8 + 1/6*r**4 + 2/15*r**5 + 0 - 1/105*r**7 + 0*r**3 + 0*r + 1/60*r**6 - 33*r**2. Let n(s) = 0. What is s?
-2, -2/3, 0, 2
Let r(c) be the third derivative of -1/12*c**6 + 0*c**5 + 1/42*c**7 + 0*c - 5/6*c**3 + 5/12*c**4 + 2*c**2 + 32. Find g, given that r(g) = 0.
-1, 1
Let x(j) be the third derivative of 2*j**3 - j**2 - 23/20*j**5 - j**4 + 11/14*j**7 + 0 + 19/40*j**6 + 0*j + 25/112*j**8. Let x(o) = 0. What is o?
-1, 2/5
Let l(v) be the first derivative of 0*v + 5 + 1/7*v**4 - 4/35*v**5 + 0*v**2 - 1/14*v**6 + 0*v**3. Suppose l(d) = 0. What is d?
-2, 0, 2/3
Suppose 0 = 2*t + 4*p - 20, -29 = -7*t + 2*t - 3*p. Suppose t*s + 6 = -3*o, 4*o + 13 = -4*s + 5. Factor 1/4*y**2 + s - 1/2*y.
y*(y - 2)/4
Factor 24*x**2 + 25/9*x**3 + 512/9 + 704/9*x + 1/9*x**4.
(x + 1)*(x + 8)**3/9
Let m(p) be the second derivative of p**7/14 + 3*p**6/10 + 3*p**5/10 - p**4/2 - 3*p**3/2 - 3*p**2/2 - 6*p + 9. Solve m(i) = 0 for i.
-1, 1
Let a be (40/24)/((-10)/(-12)). Let j = 29/3 + -9. Suppose a*d - 2/3*d**5 + j - 4/3*d**3 - 2*d**4 + 4/3*d**2 = 0. What is d?
-1, 1
Determine f, given that -2/9*f + 0 + 1/3*f**2 - 1/9*f**3 = 0.
0, 1, 2
Let a be 8*(-10)/400*(-3)/3. Factor -4/5 - a*c**2 - c.
-(c + 1)*(c + 4)/5
Let i(b) = -200*b + 34. Let u be i(-6). Suppose 108*o**2 + 2*o**4 + u - 24*o**3 + 18*o - 234*o - 1072 = 0. What is o?
3
Let p be (0 + 0 + 4)*(2553/(-184))/(-37). Solve -3*a**2 + 3/4*a**3 - p + 15/4*a = 0 for a.
1, 2
Let v(z) be the first derivative of 1/8*z**3 - 3/40*z**5 + 3/32*z**4 + 0*z**2 - 1/16*z**6 + 1 + 0*z. Determine i so that v(i) = 0.
-1, 0, 1
Let w be 0 - (1 - (3 - 1)) - -1. Factor -2/5*i**3 + 2/5 + 6/5*i**w - 6/5*i.
-2*(i - 1)**3/5
Let c(h) be the third derivative of -h**7/1365 + 4*h**6/195 + 7*h**5/78 + 3*h**4/26 + h**2 - 585*h. Factor c(q).
-2*q*(q - 18)*(q + 1)**2/13
Determine t, given that -36 + 15/2*t**3 + 5*t**2 - 1/2*t**5 - 30*t + 0*t**4 = 0.
-2, 3
Solve 0 + 15*w**2 - 12*w**3 + 3*w**4 + 8327*w + 0 - 8333*w = 0.
0, 1, 2
Let r = 26519/2 - 13256. Factor 15/2*l - r*l**2 - 9/2 + 1/2*l**3.
(l - 3)**2*(l - 1)/2
Let q(m) be the first derivative of -m**5 + 15*m**4/2 - 65*m**3/3 + 30*m**2 - 20*m + 362. Determine k so that q(k) = 0.
1, 2
Let s = -1 + 10. Factor 9*w**2 - s*w**4 + 4*w**4 + w**2 - 5.
-5*(w - 1)**2*(w + 1)**2
Let k = -68657/3 - -22891. Let -1/3*r**4 + 8/3*r**3 - k + 32/3*r - 8*r**2 = 0. Calculate r.
2
What is s in 39*s**3 + 29*s**2 + 3*s**4 + 5*s**2 + 108*s + 11*s**2 + 19*s**2 + 56*s**2 = 0?
-9, -2, 0
Factor 18*p**3 + 5*p**4 - 57*p**3 - 2*p**4.
3*p**3*(p - 13)
Let n = -185/2 - -1303/14. Factor -4/7 + 2/7*g - 2/7*g**3 + n*g**2.
-2*(g - 2)*(g - 1)*(g + 1)/7
Let c(m) be the third derivative of 5*m**7/168 - m**6/8 + 23*m**5/120 - m**4/8 + m**3/24 - 484*m**2. Suppose c(v) = 0. What is v?
1/5, 1
Determine i so that -88*i**2 + 25*i - 439*i**3 - 715*i + 435*i**3 - 800 + 130*i = 0.
-10, -2
Factor 6*a**2 + 1/5*a**3 + 45*a + 0.
a*(a + 15)**2/5
What is x in -48/7*x**2 - 132/7*x**4 - 4*x**5 - 184/7*x**3 + 0 + 32/7*x = 0?
-2, -1, 0, 2/7
Let j be 2/(-5) - (-1044)/10. Let l = -6 + 8. Factor -j*n - l*n**3 + 3*n**3 + 103*n.
n*(n - 1)*(n + 1)
Let f = -1555 + 1555. Let x(c) be the second derivative of 1/21*c**7 + 0*c**2 - 9*c - 1/3*c**4 - 1/3*c**3 + 2/15*c**6 + f*c**5 + 0. Factor x(p).
2*p*(p - 1)*(p + 1)**3
Determine s, given that -12/5 + 24/5*s**3 - 51/5*s**2 - 51/5*s + 36/5*s**4 = 0.
-1, -1/2, 4/3
Let j = 109/54 + -14/27. Let z(r) be the first derivative of -2 - j*r**2 - 2*r**3 + 9*r. Find p, given that z(p) = 0.
-3/2, 1
Let s(l) be the first derivative of 5*l**3/3 + 15*l**2 - 455*l - 647. Factor s(y).
5*(y - 7)*(y + 13)
Suppose 4514*v - 734/5*v**2 + 6/5*v**3 - 7442/5 = 0. Calculate v.
1/3, 61
Let i = 767/4 - 2537/12. Let q = -286/15 - i. Determine a, given that q*a**3 + 0 + 3/5*a**2 + 1/5*a + 1/5*a**4 = 0.
-1, 0
Let b(a) = a**3 + 4*a**2 + 4*a + 3. Let x be b(-3). Suppose x = 2*n - 5 + 1. Let 16/3*y**n + 8/3 - 20/3*y - 4/3*y**3 = 0. Calculate y.
1, 2
Let d = 28/45 - -8/45. Let c(a) be the first derivative of 11/2*a**2 - 2*a - 5 + d*a**5 - 1/4*a**4 - 4*a**3. Factor c(l).
(l - 1)**2*(l + 2)*(4*l - 1)
Let j(q) be the second derivative of q**6/24 + 5*q**5/8 + 55*q**4/16 + 25*q**3/3 + 10*q**2 + 71*q. Factor j(s).
5*(s + 1)**2*(s + 4)**2/4
Let m be 240/693 + (-14)/49. Let l(t) be the second derivative of -m*t**3 + t + 0 + 0*t**2 + 1/66*t**4. Factor l(d).
2*d*(d - 2)/11
Let u = -79/3 + 239/9. Let i be (-18)/108 - 5/(-6). Determine z, given that i*z**3 + 0 + 2/9*z**4 + 2/3*z**2 + u*z = 0.
-1, 0
Let b(t) be the first derivative of 4/35*t**5 - 8/7*t**2 - 5/7*t**4 + 32/21*t**3 + 0*t - 3. Suppose b(d) = 0. Calculate d.
0, 1, 2
Let t(l) be the first derivative of -l**3/24 - 9*l**2/2 - 331. Factor t(w).
-w*(w + 72)/8
Let d(t) = -21*t - 62. Let l be d(-3). Let x(g) be the first derivative of 0*g + 1/9*g**6 + 0*g**5 - 1/3*g**4 + 0*g**3 + 1/3*g**2 - l. Factor x(c).
2*c*(c - 1)**2*(c + 1)**2/3
Let q(m) be the third derivative of 0*m - 1/60*m**5 + 25*m**2 - 1/6*m**3 - 1/12*m**4 + 0. What is b in q(b) = 0?
-1
Let c(d) be the first derivative of d**6/2 + 22*d**5/5 + 31*d**4/4 - 40*d**3/3 - 8*d**2 - 15. Factor c(g).
g*(g - 1)*(g + 4)**2*(3*g + 1)
Let g(v) be the first derivative of -2*v**3/9 + 7*v**2 + 108*v + 121. Find f, given that g(f) = 0.
-6, 27
Let g(h) = -9*h**2 - 6*h + 11. Let y(n) = 5*n**2 + 3*n - 6. Suppose 0 = -13*c + 18*c - 55. Let o(z) = c*y(z) + 6*g(z). Suppose o(v) = 0. Calculate v.
0, 3
Let l(s) be the first derivative of s**8/168 + s**7/175 - s**6/150 + s**2 + 17. Let m(p) be the second derivative of l(p). Factor m(t).
2*t**3*(t + 1)*(5*t - 2)/5
Let f(h) = -11*h**2 - h + 70. Let t(c) = 5*c**2 + c - 30. Let g(a) = -3*f(a) - 7*t(a). Let g(r) = 0. Calculate r.
-2, 0
Suppose -3/2*t**4 - 2/5*t - 19/5*t**2 + 49/10*t**3 + 4/5 = 0. What is t?
-2/5, 2/3, 1, 2
Let n(a) = 27*a - 105. Let f be n(4). Suppose 3*g - 2*g = 0. What is d in g + 0*d + 8*d**4 + 0*d**2 - 7/2*d**5 - 2*d**f = 0?
0, 2/7, 2
Let b(o) be the first derivative of 5*o**7/42 - o**6/3 - o**5 + 5*o**4/6 + 5*o**3/2 - 7*o + 42. Let k(c) be the first derivative of b(c). Factor k(y).
5*y*(y - 3)*(y - 1)*(y + 1)**2
Let w(u) be the third derivative of u**6/270 + u**5/15 + u**4/2 - u**3/6 + 7*u**2. Let j(d) be the first derivative of w(d). Factor j(r).
4*(r + 3)**2/3
Let b(z) be the first derivative of 1/36*z**4 - 4 + 1/12*z**3 + 4*z - 1/120*z**5 + 0*z**2. Let d(u) be the first derivative of b(u). Solve d(s) = 0.
-1, 0, 3
Let k be (-551)/1140 + 1 + (-2)/(-24). Find c such that -9/5*c + 9/5*c**2 + k - 3/5*c**3 = 0.
1
Suppose -9 = -4*h + h. Let j be (9 - 8)*(-1 + h). Factor 3*w**j - 3*w - 4*w - 2*w.
3*w*(w - 3)
Find j such that 31*j + 2*j**2 - 33*j + 35*j + 768 + j**2 + 63*j = 0.
-16
Let o(p) = 7*p**2 + 416*p - 8816. Let g(u) = -10*u**2 - 415*u + 8815. Let a(z) = 4*g(z) + 5*o(z). Suppose a(n) = 0. Calculate n.
42
Factor 2*u - 62*u - 54 + 47*u**2 + 28*u**2 - 86 - 5*u**3.
-5*(u - 14)*(u - 2)*(u + 1)
Let f = 595/6246 + 11/694. Factor -2/9*g + 1/9 + f*g**2.
(g - 1)**2/9
Let m be 10/50 + (-24)/(-5). Let -5 - 25*l + m*l**2 + 25*l = 0. What is l?
-1, 1
Let k be ((-11908)/(-364) - 35)*(-2 - 7/(-4)). Solve -16/7*h**2 + 8/7*h + 12/7 - 8/7*h**3 + k*h**4 = 0 for h.
-1, 1, 3
Suppose -7*m = s - 6*m + 2, 4*s + 5*m = -12. Let g(t) be the first derivative of -2/5*t**5 - 2*t**4 + 0*t - 10/3*t**3 + 1 - s*t**2. Let g(o) = 0. Calculate o.
-2, -1, 0
Find x, given that x**4 - 8*x**2 - 6*x**3 + 12*x**2 + 6*x + 76 - 81 = 0.
-1, 1, 5
Let l(y) = -9*y**2 - 9*y + 3. Let n(v) = v. Let o(j) = -j - 4. Let t be (-1)/((-1)/(9/(-3))). Let c be o(t). Let a(b) = c*l(b) - 3*n(b). Factor a(d).
3*(d + 1)*(3*d - 1)
Factor -32*s + 64/3 + 8*s**3 + 4/3*s**4 + 4/3*s**2.
4*(s - 1)**2*(s + 4)**2/3
Suppose 0*m - 3*m + 21 = 5*n, -4*n - 2*m + 16 = 0. Let a(o) = 2*o**3 + 28*o**2 + 26*o. Let g be a(-13). Factor g*w**4 - 1/4*w**n + 0*w**2 + 0 + 1/4*w**5 + 0*w.
w**3*(w - 1)*(w + 1)/4
Let z(f) be the third derivative of f**6/30 - 44*f**5/15 + 173*f**4/24 - 43*f**3/6 + 4*f**2 - 7*f. Factor z(w).
(w - 43)*(2*w - 1)**2
Let u(t) = 2*t**2 + 11*t. Let z(w) be the second derivative of