**3/3
Let j(h) be the second derivative of -h**5/4 + 5*h**4/4 + 65*h**3/6 - 75*h**2/2 + 10*h + 4. Solve j(u) = 0.
-3, 1, 5
Let h(r) be the first derivative of 5/6*r**6 - 2*r**5 + 0*r**4 + 0*r - 5/2*r**2 - 18 + 10/3*r**3. Factor h(s).
5*s*(s - 1)**3*(s + 1)
Let p(m) = -3*m**2 + 20*m - 27. Let i(q) = -q. Suppose -5*b - 3*h + h + 2 = 0, -20 = 5*h. Let u(v) = b*i(v) + p(v). Let u(n) = 0. What is n?
3
Let x(s) be the second derivative of 0*s**3 + 0 - 1/30*s**6 + 1/10*s**5 - 13*s + 0*s**2 - 1/12*s**4. Determine l so that x(l) = 0.
0, 1
Let y(a) be the third derivative of 0*a + 1/70*a**7 + 1/4*a**6 + 6/5*a**5 - a**2 + 11/4*a**4 + 0 + 7/2*a**3. Factor y(c).
3*(c + 1)**3*(c + 7)
Let i(h) be the second derivative of -h**6/120 - h**5/16 - h**4/8 + 11*h - 9. Suppose i(s) = 0. Calculate s.
-3, -2, 0
Let l(x) be the second derivative of 4*x**2 - 4*x + 7/6*x**4 - 7/3*x**3 + 0. Let c(h) = 5*h**2 - 5*h + 3. Let d(j) = -8*c(j) + 3*l(j). Factor d(a).
2*a*(a - 1)
Let p(s) be the second derivative of -2*s**7/3 + 4*s**6/15 + 7*s**5/5 - 2*s**4/3 - 95*s. Solve p(z) = 0.
-1, 0, 2/7, 1
Factor 2/9*x - 2*x**3 + 0 + 16/9*x**2.
-2*x*(x - 1)*(9*x + 1)/9
Let d be -2 - (-2 + -3 - 1). Suppose -a + d = 1. Factor -y**4 + 2*y**2 + 0*y**4 - y**a + y**2 + 2 + 5*y.
-(y - 2)*(y + 1)**3
Factor -c - 4/7 - 2/7*c**2 + 1/7*c**3.
(c - 4)*(c + 1)**2/7
Suppose -2 = -i + 5*y + 3, 0 = -2*i + 5*y + 10. Let j = 73 - 69. Factor i*g + g + g**2 - j*g**2 - 3 + 0.
-3*(g - 1)**2
Let d = -335 - -11726/35. Let f(s) be the third derivative of 0 + 1/40*s**6 + 2*s**2 + 0*s**4 + 0*s**3 - d*s**7 + 0*s + 1/20*s**5. Determine z so that f(z) = 0.
-1/2, 0, 1
Suppose -4*c - 37 + 49 = 0. Let f be c/(-4)*56/(-189). Factor 0 - 2/9*u**4 + f*u**2 - 2/9*u**5 + 0*u + 2/9*u**3.
-2*u**2*(u - 1)*(u + 1)**2/9
Let j(t) be the first derivative of -5*t**4/36 - 17*t**3/27 - t**2/3 + 6. Factor j(f).
-f*(f + 3)*(5*f + 2)/9
Suppose -3 = 5*a + 77. Let v = 18 + a. Find s, given that 2*s - 7*s**2 - 2*s + 6 + s**3 + 3*s**4 - s**5 - v = 0.
-1, 1, 2
Let k(b) be the third derivative of b**8/28 - 2*b**7/105 - 7*b**6/15 + 4*b**5/15 + 4*b**4/3 + 14*b**2 + 3*b. Suppose k(q) = 0. Calculate q.
-2, -2/3, 0, 1, 2
Let o(h) = -5*h**4 - 6*h**3 + 7*h**2 + 6*h. Let q(t) = 11*t**4 + 12*t**3 - 16*t**2 - 12*t. Let w(j) = -5*o(j) - 2*q(j). Solve w(p) = 0.
-2, -1, 0, 1
Suppose 4*i = -12, 3*i + 9 = l - 3*l. Let u(y) be the first derivative of -3/4*y**4 + 0*y**2 + l*y + 3 - y**3. Suppose u(k) = 0. What is k?
-1, 0
Let x be (-26 + 4046/153)/((-28)/(-18)). Factor 2/3*j + x*j**2 - 4/7.
2*(j + 3)*(3*j - 2)/21
Factor -60 - 72*w - 63/5*w**2 - 3/5*w**3.
-3*(w + 1)*(w + 10)**2/5
Let i(w) = -w**3 - w**2 + w + 1. Let d(y) = -4*y**3 - 12*y**2 + 4*y + 12. Let m(q) = 2*d(q) - 10*i(q). Find x such that m(x) = 0.
-1, 1, 7
Let z(i) = i**3 - i - 1. Let k(o) = -63*o**3 + 54*o**2 + 9*o + 6. Suppose -36 = -8*m + 2*m. Let s(c) = m*z(c) + k(c). Factor s(b).
-3*b*(b - 1)*(19*b + 1)
Let l(t) be the second derivative of -t**10/6720 - t**9/2016 - t**8/2240 - 2*t**4/3 + 10*t. Let a(w) be the third derivative of l(w). Factor a(x).
-3*x**3*(x + 1)*(3*x + 2)/2
Let p(w) be the second derivative of 0*w**2 + 1/10*w**5 + 0 - 12*w + 1/15*w**6 + 0*w**3 - 1/3*w**4. What is u in p(u) = 0?
-2, 0, 1
Let n(t) be the second derivative of t**5/20 + t**4/2 + 4*t**3/3 + t + 3. Factor n(f).
f*(f + 2)*(f + 4)
Let u = -641/24 - -219/8. Let r(f) be the second derivative of u*f**4 + 2/3*f**2 - 3/10*f**5 + 11/9*f**3 + 0 + 5*f. Factor r(z).
-2*(z - 2)*(3*z + 1)**2/3
Determine k, given that 4*k**3 - 4*k + 0 + 2/5*k**2 - 2/5*k**4 = 0.
-1, 0, 1, 10
Suppose 20*h**2 - 4/5*h**5 + 44/5*h**4 + 0*h + 0 - 28*h**3 = 0. Calculate h.
0, 1, 5
Let n = -107 - -111. Let s(z) = z - 2. Let m be s(5). Solve -34*p**2 + 12*p + 16*p**n + 5*p**4 - 2*p**2 - 27*p**m = 0 for p.
-1, 0, 2/7, 2
Let m(n) be the first derivative of 0*n**3 + 0*n**2 + 1 - 1/10*n**5 - 1/3*n**4 - n. Let c(r) be the first derivative of m(r). Suppose c(g) = 0. Calculate g.
-2, 0
Suppose c + 3*f - 12 = 0, 2*c + 2*f = 10 - 6. Let g be ((-36)/(-30))/(-2*c/15). Solve 2/3 + 22/3*p**g + 2/3*p - 8/3*p**4 - 6*p**2 = 0 for p.
-1/4, 1
Let p(z) be the second derivative of z**6/105 + z**5/70 - z**4/14 - z**3/21 + 2*z**2/7 + 18*z - 5. Factor p(m).
2*(m - 1)**2*(m + 1)*(m + 2)/7
Let y be 18/((-2)/4*-2). Let d be ((-24)/4)/2 + y. Determine k so that 21*k + 16*k**2 + 3*k**4 + 27*k**2 - 16*k**2 + 6 + d*k**3 + 0*k**4 = 0.
-2, -1
Let k(c) be the first derivative of c**5/15 - 5*c**4/2 + 325*c**3/9 - 250*c**2 + 2500*c/3 + 409. Factor k(o).
(o - 10)**2*(o - 5)**2/3
Let f(b) be the second derivative of b**4/54 - 13*b**3/9 - 40*b**2/9 + 720*b. Suppose f(h) = 0. Calculate h.
-1, 40
Let p(x) = -x**3 - 2*x**2 - 2*x + 2. Let v be p(0). Determine z, given that -z**3 + 2*z**v - 2*z + 7*z - 8 + 3*z - 4*z = 0.
-2, 2
Let t(g) = -g**2 - 25*g + 6. Let m(b) = 20*b - 5. Let s(u) = -6*m(u) - 5*t(u). Factor s(i).
5*i*(i + 1)
Let c(t) be the second derivative of -5/2*t**2 + 1/20*t**6 - t + 1/8*t**4 + 3/20*t**5 + 0 + 0*t**3. Let v(n) be the first derivative of c(n). Solve v(j) = 0.
-1, -1/2, 0
Let r(n) be the second derivative of -2/27*n**3 + 1/9*n**2 + 1/54*n**4 - 2*n - 6. Factor r(p).
2*(p - 1)**2/9
Let c(w) = -w**2 + 4*w + 6. Let t be 238/63 + (-4)/(-18). Let n be c(t). Factor g**4 + 9*g**3 - n*g**4 - 4 + 3*g**2 - 9*g - 2 + 8*g**4.
3*(g - 1)*(g + 1)**2*(g + 2)
Let -1/6*n**4 + 4 - 3*n**2 - 3/2*n**3 + 2/3*n = 0. Calculate n.
-6, -2, 1
Let c(g) be the first derivative of 5*g**3/3 + 185*g**2/2 + 510*g + 174. Factor c(l).
5*(l + 3)*(l + 34)
Let p(f) be the third derivative of 0 + 0*f - 1/30*f**5 + 1/24*f**4 + 1/120*f**6 + 0*f**3 - 6*f**2. Factor p(g).
g*(g - 1)**2
Let l(o) = -7 + 9 - o + o**3 - 3. Let k(i) = -i**4 + 3*i**3 - 8*i**2 - 12*i - 8. Let z(c) = -5*k(c) + 40*l(c). Let z(h) = 0. What is h?
-2, -1, 0
Suppose -5*o - 25 = -3*s, -2*o - 127 = 3*s - 117. Solve 0*q**2 + s - 1/2*q**3 + 2*q = 0.
-2, 0, 2
Let k(o) be the second derivative of 16/3*o**2 + 3/5*o**6 + 8*o**4 + 17*o + 18/5*o**5 + 80/9*o**3 + 0. Suppose k(t) = 0. What is t?
-2, -2/3
Let z(f) be the third derivative of 2/315*f**7 + 0*f - 1/9*f**4 + 0*f**3 - 1/45*f**5 + 1/45*f**6 + 0 + 8*f**2. Suppose z(b) = 0. Calculate b.
-2, -1, 0, 1
Let w(l) be the first derivative of l**3/9 + l**2 + 3*l + 156. Factor w(h).
(h + 3)**2/3
Let f(a) be the third derivative of 1/10*a**6 + 0*a**4 + 0*a + 0*a**3 - 1/42*a**8 + 0 - 2/15*a**5 + 2/35*a**7 - 35*a**2. Let f(l) = 0. Calculate l.
-1, 0, 1/2, 2
Factor -6*a**4 + 20*a**4 - 15*a**2 + 5*a**5 - 30*a**3 - 25*a**2 + a**4.
5*a**2*(a - 2)*(a + 1)*(a + 4)
Let a(d) be the first derivative of 5*d**3/3 + 19*d**2/6 + 4*d/3 - 55. Solve a(i) = 0 for i.
-1, -4/15
Suppose 5 = 5*a - 10. Factor 4*z**2 - 5*z**a - 17*z**2 + 3*z**2.
-5*z**2*(z + 2)
Let i(g) be the second derivative of 7*g + 2/3*g**3 - 1/2*g**2 + 0 - 1/4*g**4 - 1/5*g**5 + 2/15*g**6. Factor i(h).
(h - 1)*(h + 1)*(2*h - 1)**2
Determine g, given that -4*g**5 + 180*g**3 - 4200 + 188*g**2 - 17*g + 81*g + 52*g**4 + 4200 = 0.
-1, 0, 16
Let u(i) be the third derivative of -1/330*i**5 - 2/33*i**4 + 0 + 0*i - 2*i**2 - 16/33*i**3. Determine p, given that u(p) = 0.
-4
Let o(z) be the third derivative of z**6/1080 - z**5/540 - z**4/216 + z**3/54 + 61*z**2. Factor o(q).
(q - 1)**2*(q + 1)/9
Suppose 4*p = -20, -a - 249*p = -253*p - 22. Suppose 8/5 - 4/5*d - 3*d**3 - 34/5*d**a = 0. What is d?
-2, -2/3, 2/5
Let y(c) be the first derivative of -c**6/6 + 12*c**5/5 - 47*c**4/4 + 52*c**3/3 + 24*c**2 - 64*c + 17. Factor y(l).
-(l - 4)**3*(l - 1)*(l + 1)
Let d(p) be the third derivative of 0*p**6 + 0*p**3 + 0 - 2/1155*p**7 - 1/1848*p**8 + 1/132*p**4 + 1/165*p**5 + 0*p - 3*p**2. Determine m so that d(m) = 0.
-1, 0, 1
Let y(g) = g**2 - 4. Let b be y(-4). Let i be 4/(48/5) + 3/b. Factor -2*u**2 + 4/3 + 2/3*u**4 + 2/3*u**3 - i*u.
2*(u - 1)**2*(u + 1)*(u + 2)/3
Let j(t) = 1. Let x(z) be the first derivative of -z**3/3 - z**2/2 + 5*z - 5. Let q(o) = 6*j(o) - 2*x(o). Suppose q(v) = 0. What is v?
-2, 1
Let o be (-4)/(-9) - 23/(3312/(-32)). Factor -2/3*h + 0 + o*h**2.
2*h*(h - 1)/3
Let c(j) = 4*j**2 - 1. Let r(n) = n**2 - n - 1. Let q = 1 - -2. Let g(t) = q*r(t) - c(t). Factor g(u).
-(u + 1)*(u + 2)
Let c = -23019/5 + 92081/20. Factor 3/4 - 7/4*m + 5/4*m**2 - c*m**3.
-(m - 3)*(m - 1)**2/4
Sup