 n(a) be the third derivative of g(a). Factor n(y).
(y - 1)*(y + 2)*(3*y - 1)/2
Let c(q) be the third derivative of -q**7/70 + q**6/5 - 13*q**5/20 + 3*q**4/4 + 122*q**2 - 2. Let c(v) = 0. Calculate v.
0, 1, 6
Factor 0*d**4 + 50*d**2 - 4*d**4 + 5*d**4 - d**3 + 10*d**3 + 18*d**3.
d**2*(d + 2)*(d + 25)
Suppose -3*f + 211 = 61. Let u be 4/(-6) + f/30. Let b(t) = -t**2 - t + 4. Let m(w) = 1. Let a(n) = u*b(n) - 4*m(n). Suppose a(s) = 0. What is s?
-1, 0
Let j(u) be the second derivative of u**5/210 + u**4/18 + 8*u**3/63 - 16*u**2/21 + 3*u + 111. Factor j(n).
2*(n - 1)*(n + 4)**2/21
Suppose -5*g + 30 = -5*z, -12*g + z = -8*g - 36. Let o(p) = -5*p + 50. Let h be o(g). Suppose 8/9*l**3 + 2/9*l**4 - 32/9*l + h*l**2 - 32/9 = 0. What is l?
-2, 2
Suppose 11*h - 5*h = 24. Let i(d) be the third derivative of 1/210*d**5 + 0*d + 0 + 1/42*d**h + 2*d**2 + 1/21*d**3. Factor i(u).
2*(u + 1)**2/7
Let -15*b**4 - 24*b**3 + b**5 + b**3 + 5*b**3 + 2*b**5 = 0. Calculate b.
-1, 0, 6
Let a(t) = 41*t - 2583. Let l be a(63). Let 0*j - 2/13*j**5 + l + 0*j**3 + 0*j**2 + 4/13*j**4 = 0. What is j?
0, 2
Let b(h) be the third derivative of 0 - 2/9*h**3 + 2*h**2 + 7/90*h**5 + 0*h + 1/60*h**6 - 1/63*h**7 - 1/12*h**4. Find u, given that b(u) = 0.
-1, -2/5, 1
Let b(t) be the first derivative of -500*t - 5/3*t**3 + 50*t**2 - 17. Find c, given that b(c) = 0.
10
Find x such that -108*x**3 - 3*x**4 - 301*x**3 + 387 + 19*x**3 - 165*x**2 + 390*x - 208*x**2 - 11*x**2 = 0.
-129, -1, 1
Suppose -3*r = 2*w - 6, -5*r - w + 15 - 5 = 0. Let a(t) be the second derivative of -1/12*t**4 + 1/60*t**5 + 1/9*t**3 + 0*t**r + 3*t + 0. Factor a(z).
z*(z - 2)*(z - 1)/3
Suppose 85*a - 408 = -51*a. Let f(w) be the third derivative of -1/150*w**5 + 1/20*w**4 + 9*w**2 + 0*w + 0 + 0*w**a. Factor f(u).
-2*u*(u - 3)/5
Suppose 67*l = 58*l. Let v(m) be the first derivative of -2*m**3 + 2*m**2 + l*m**4 + 0*m + 2/5*m**5 - 10. Let v(u) = 0. Calculate u.
-2, 0, 1
Let t(q) be the second derivative of q**8/560 + q**7/175 - q**6/200 - q**5/50 + 5*q**2 + 9*q. Let v(n) be the first derivative of t(n). What is z in v(z) = 0?
-2, -1, 0, 1
Factor -5/4*o**3 + 45*o - 50 - 15/2*o**2.
-5*(o - 2)**2*(o + 10)/4
Suppose 5*z = 7*s - 3*s - 786, -4*s = -4*z - 788. Let q = s + -1392/7. Factor q*k**3 + 0 - 3/7*k**2 + 0*k.
k**2*(k - 3)/7
Let g(u) = -4*u. Let j(v) = -3*v - 1. Let n(l) = -5*g(l) + 6*j(l). Let a be n(4). Solve -a*t**5 - 1 + 3*t + 4*t**3 - 5*t + 1 = 0.
-1, 0, 1
Let s = -52213/3 - -17421. What is m in 32/3*m - 8/3 - s*m**2 + 2/3*m**5 + 38/3*m**3 - 14/3*m**4 = 0?
1, 2
Let d(z) be the third derivative of -z**6/1440 - z**5/240 + z**4/32 + 2*z**3 + 7*z**2. Let x(m) be the first derivative of d(m). Factor x(i).
-(i - 1)*(i + 3)/4
Let n(p) be the first derivative of -3 - 1/2*p**2 + 1/3*p**3 - 1/16*p**4 + 0*p. Factor n(z).
-z*(z - 2)**2/4
Let m(t) = t + 5. Let h be (-1)/(-3) + (-156)/(-18). Let b be m(h). Determine w, given that w - 6*w**3 - 14*w**2 + b*w**3 - 5*w = 0.
-1/4, 0, 2
Let q(v) = v**2 - v + 4. Let m be q(0). Find a, given that 8*a**2 - m*a**2 + 0*a**2 - a**2 + 24 + 18*a = 0.
-4, -2
Let o(c) be the second derivative of 0 + 13*c + 1/6*c**3 + 0*c**2 - 1/12*c**4. Factor o(n).
-n*(n - 1)
Let p = -713 - -1427/2. Let k be 2 + -1 + -1 + 2. Factor 1/2*l**k + p - l.
(l - 1)**2/2
Let i(a) = -a**2 - 110*a - 174. Let u(w) = 7*w. Let j(o) = i(o) + 3*u(o). Find g, given that j(g) = 0.
-87, -2
Let b(i) = -i**2 - 4*i + 1. Suppose 5*s = -5*o - 25, 5*o + 0*s = 5*s - 5. Let j be b(o). Factor -4*t**j - 3*t**2 + 4*t**3 - 5*t**2 + 8*t**3.
-4*t**2*(t - 2)*(t - 1)
Let h(p) be the third derivative of 2*p**7/21 - 29*p**6/24 + 47*p**5/12 - 25*p**4/12 + 4*p**2 + 12*p. Factor h(c).
5*c*(c - 5)*(c - 2)*(4*c - 1)
Let s(z) be the second derivative of -4/3*z**2 + 11/6*z**4 + 0 - 6*z + 21/20*z**5 + 2/9*z**3. Factor s(a).
(3*a + 2)**2*(7*a - 2)/3
Let z(n) = -n**2 - 5*n - 6. Let q = -51 + 46. Let w(u) = 5*u + 5. Let b(d) = q*z(d) - 6*w(d). Solve b(f) = 0 for f.
0, 1
Let r(m) = m**3 + 11*m**2 + 4*m - 20. Let t(p) = -2*p**3 - 12*p**2 - 3*p + 20. Let n(l) = -3*r(l) - 4*t(l). Solve n(a) = 0 for a.
-2, 1
Let q(w) be the second derivative of 0 + 5/12*w**4 - 4/3*w**3 - 1/20*w**5 + 2*w**2 - 28*w. Suppose q(a) = 0. What is a?
1, 2
Let c(o) be the third derivative of -o**7/15120 - o**6/1080 - o**5/240 - 3*o**4/8 - 32*o**2. Let m(q) be the second derivative of c(q). Let m(h) = 0. What is h?
-3, -1
Let t(m) be the first derivative of m**3/6 + 2*m**2 + 8*m + 171. Suppose t(s) = 0. Calculate s.
-4
Let r(h) be the third derivative of 1/35*h**7 + 0*h**4 + 3/10*h**5 + 0*h + 0 + 0*h**3 + 1/504*h**8 + 14*h**2 + 3/20*h**6. Let r(u) = 0. What is u?
-3, 0
Determine x so that 0 - 3/8*x**4 + 9/8*x**3 + 9/4*x**2 - 3*x = 0.
-2, 0, 1, 4
Let w(y) be the third derivative of 0 - 4/15*y**5 - 1/3*y**6 + 4/105*y**7 + 0*y + 5/84*y**8 + 5/6*y**4 + 4/3*y**3 + 7*y**2. Determine s so that w(s) = 0.
-1, -2/5, 1
Factor -4*j**4 - 57*j**3 - 65*j**3 + 146*j**3 - 16*j - 36*j**2 + 58 - 10.
-4*(j - 3)*(j - 2)**2*(j + 1)
Let f(b) be the first derivative of b**7/140 - b**6/90 - b**5/20 + b**4/6 + 5*b**3/3 + 9. Let x(q) be the third derivative of f(q). Factor x(g).
2*(g - 1)*(g + 1)*(3*g - 2)
Factor -19/2*z**2 - 1/2*z**3 + 21*z + 0.
-z*(z - 2)*(z + 21)/2
Let l(k) = 515*k**3 + 660*k**2 + 120*k - 25. Let w = -50 - -48. Let f(i) = 43*i**3 + 55*i**2 + 10*i - 2. Let p(q) = w*l(q) + 25*f(q). Factor p(c).
5*c*(c + 1)*(9*c + 2)
Let a(d) = d - 1. Let n(u) = -2*u**2 + 4*u - 6. Let k(h) = -6*a(h) - n(h). Factor k(s).
2*(s - 3)*(s - 2)
Suppose 5*q - 8 = g - 1, 2*g - 8 = -q. Factor -h**3 - h**3 - 8*h**g - 5*h**4 + 5*h**2 + 10*h.
-5*h*(h - 1)*(h + 1)*(h + 2)
Let u be ((-50)/(-20))/(5/4). Suppose u*f - f - 4 = 0. Factor 16*w**3 - 4*w**f - 2*w**2 - 293*w + 293*w - 10*w**2.
-4*w**2*(w - 3)*(w - 1)
Factor 6300 + 1/7*t**2 + 60*t.
(t + 210)**2/7
Let r(d) = 61*d + 3507. Let l be r(-57). Determine w, given that 2250 - 2/3*w**3 + l*w**2 - 450*w = 0.
15
Let h(k) = 7*k**3. Let z be h(1). Factor -2 - 2 - z*t + 3*t - t**2.
-(t + 2)**2
Let c(k) be the second derivative of -k**6/10 - 7*k**5/20 + k**4/4 - 4*k**2 + 7*k. Let p(z) be the first derivative of c(z). Let p(w) = 0. Calculate w.
-2, 0, 1/4
Let s(t) = t**2 - 3*t + 2. Let x be s(5). Find k such that -8 - 14*k**4 + 78*k**3 + 60*k - 46*k**2 - 52*k**2 - x*k - 6*k**4 = 0.
2/5, 1/2, 1, 2
Let l(f) be the third derivative of 0 - 1/4*f**4 + 0*f + 12*f**2 + 1/70*f**7 + 0*f**3 + 0*f**6 - 3/20*f**5. Factor l(n).
3*n*(n - 2)*(n + 1)**2
Let o(m) be the second derivative of 3*m**5/160 - 19*m**4/32 - 5*m**3/4 - 2*m - 32. Factor o(b).
3*b*(b - 20)*(b + 1)/8
Let m(s) be the second derivative of -7/60*s**5 + 17*s + 0*s**2 + 4/9*s**3 + 0 + 13/18*s**4. Factor m(f).
-f*(f - 4)*(7*f + 2)/3
Let j(t) be the third derivative of -121*t**8/588 - 22*t**7/49 - 8*t**6/35 - 4*t**5/105 + 132*t**2. Suppose j(l) = 0. What is l?
-1, -2/11, 0
Factor -8/11*p**4 - 10/11*p**3 - 2/11*p**5 + 0 + 0*p - 4/11*p**2.
-2*p**2*(p + 1)**2*(p + 2)/11
Let r(p) be the first derivative of -49*p**6/12 - 7*p**5 + 3*p**4/8 + 10*p**3/3 - p**2 - 61. Suppose r(q) = 0. What is q?
-1, 0, 2/7
Suppose -4*v + 6*w = 2*w, 0 = 4*v - 5*w + 3. Let s(h) = 2*h - 4. Let l be s(v). Suppose -6/5*k - 2/5*k**3 + l*k**2 - 18/5 = 0. Calculate k.
-1, 3
Let a be -2 - 2*5 - 10471/(-566). Factor 1/2*f + 0 - 3*f**2 + 2*f**5 - 6*f**4 + a*f**3.
f*(f - 1)**2*(2*f - 1)**2/2
Let s(r) be the second derivative of r**5/26 - 7*r**4/13 - 29*r**3/39 + 18*r**2/13 - 7*r + 1. Determine h, given that s(h) = 0.
-1, 2/5, 9
Let m(u) be the first derivative of u**4/38 + 52*u**3/19 - 159*u**2/19 + 160*u/19 - 481. Factor m(g).
2*(g - 1)**2*(g + 80)/19
Factor 2*q**2 - 1019*q - 1058*q + 200 + 2117*q.
2*(q + 10)**2
Let k = -17 + 19. Factor 4*t**4 - 3*t**4 - k*t**2 - 9 + 10.
(t - 1)**2*(t + 1)**2
Let -124/5*r - 16*r**2 + 12/5*r**3 - 32/5 = 0. What is r?
-1, -1/3, 8
Let u be 9/18*36/54. Let 3 + u*i**2 + 2*i = 0. What is i?
-3
Let c(n) be the first derivative of 169*n**6/14 - 429*n**5/5 + 1119*n**4/7 - 804*n**3/7 + 216*n**2/7 - 340. Suppose c(g) = 0. What is g?
0, 6/13, 1, 4
Let u(p) be the second derivative of -p**4/24 + 5*p**3/3 - 2*p - 3. Factor u(t).
-t*(t - 20)/2
Let u(z) be the third derivative of z**9/45360 + z**8/20160 - z**7/7560 - z**6/2160 - z**4/8 - 10*z**2. Let q(y) be the