2. Let o(n) be the second derivative of h(n). Factor o(p).
3*(p - 1)*(p + 1)*(3*p + 2)
Let g(o) = 5*o**2 - 31*o + 11. Let r(f) = -f**2 + 6*f - 2. Let l(b) = -4*g(b) - 22*r(b). Factor l(i).
2*i*(i - 4)
Factor -2/5*b - 4/5 + 2/5*b**2.
2*(b - 2)*(b + 1)/5
Suppose -3*f - 5*b = 2*f - 25, -f - 4*b = -20. Factor -3*u**2 + 16*u**3 - 12*u**4 - u**3 + f*u**4.
-3*u**2*(u - 1)*(4*u - 1)
Factor 0*x - 1/4*x**5 + 0 + 13/4*x**4 - 12*x**3 + 9*x**2.
-x**2*(x - 6)**2*(x - 1)/4
Let t(s) be the first derivative of -4*s**5/5 + 2*s**4 - 4*s**2 + 4*s - 54. Factor t(f).
-4*(f - 1)**3*(f + 1)
Let z be (3 - 1) + 0 + 1. Let -8*k**4 + 2*k**z + k**2 + 5*k**4 + 4*k**4 = 0. Calculate k.
-1, 0
Suppose -3*t + 36 = 5*h + t, 2*t + 8 = 4*h. Let o be h/12 - (-2)/6. Solve o + 0*x - 2/3*x**2 = 0.
-1, 1
Factor -37*o**2 + 2*o - 5*o - 9*o + 12 + 40*o**2.
3*(o - 2)**2
Suppose -38*j - 38*j + 4*j - 48 - 27*j**2 - 3*j**3 = 0. What is j?
-4, -1
Let w(y) be the first derivative of y**2 - y - 2. Let o be w(3). Factor 2*l**o + l - 4*l**3 - l + 2*l.
2*l*(l - 1)**2*(l + 1)**2
Suppose 0 = -4*o - 1 + 21. Let s(p) = 8 - 4*p**2 - 7*p - 7*p + o*p. Let v(u) = 2*u**2 + 5*u - 4. Let x(a) = -3*s(a) - 5*v(a). Factor x(d).
2*(d - 1)*(d + 2)
Let w = -6 - -8. Let r be (1/(-3))/(4 + 148/(-36)). Determine j, given that -r*j**2 - 3*j + 4*j + 3*j**4 + 3*j + w*j - 6*j**3 = 0.
-1, 0, 1, 2
Let c(z) be the first derivative of z**3 + 3/2*z**2 - 1 - 3/4*z**4 + 0*z - 3/5*z**5. Let c(k) = 0. What is k?
-1, 0, 1
Factor h**2 + 0*h**2 - 4*h + 3*h + h**2.
h*(2*h - 1)
What is a in -2*a**3 - 4*a - 20 - 2*a**2 + 20 + 8*a = 0?
-2, 0, 1
What is k in 28*k**2 - 9/2*k**5 - 8*k + 21*k**4 + 0 - 73/2*k**3 = 0?
0, 1, 4/3
Let y(f) be the second derivative of f**7/1260 - f**6/360 - f**5/30 - f**4/6 - f. Let v(q) be the third derivative of y(q). Factor v(g).
2*(g - 2)*(g + 1)
Let u(a) = a**2 + a + 4. Let p be u(-3). Let y be 6/p - 14/(-10). Find n, given that -2 + 1 - n**y + 4*n - 2*n = 0.
1
Factor -72/5*m**3 - 8/5*m + 8*m**2 + 0 - 27/10*m**5 + 54/5*m**4.
-m*(m - 2)*(3*m - 2)**3/10
Let d(s) be the second derivative of s**3 - 3/10*s**6 + 0*s**2 + 0 + 3/4*s**4 - 3*s - 3/10*s**5. Solve d(j) = 0.
-1, -2/3, 0, 1
Suppose -2 = 2*w - 4. Let c be w*2*6/4. Factor -3*h**3 - 4*h**5 + h**3 - h**4 - c*h**4 + 2*h**5.
-2*h**3*(h + 1)**2
Let q(w) be the first derivative of 0*w + 2/5*w**3 + 3/10*w**4 + 1 + 2/25*w**5 + 1/5*w**2. Let q(d) = 0. What is d?
-1, 0
Let v(c) = -5*c**2 - 6 + 5 + 0 + 2*c + 2. Let h(f) = f**2. Let j(t) = -6*h(t) - v(t). Solve j(z) = 0.
-1
Find b, given that -5/4*b**3 - 5/2*b**2 - 5 + 35/4*b = 0.
-4, 1
Let b(y) be the first derivative of y**3/4 - 3*y**2/4 - 2. Solve b(q) = 0.
0, 2
Solve 10/9*i**3 + 0 - 8/9*i + 16/9*i**2 = 0 for i.
-2, 0, 2/5
Let t(g) be the second derivative of g**6/300 - g**5/50 + g**4/20 - g**3/15 - g**2/2 - 4*g. Let c(z) be the first derivative of t(z). Factor c(j).
2*(j - 1)**3/5
Let m = -6 + 12. Let k(o) = o. Let x(r) be the second derivative of -r**5/10 + r**3 + r. Let l(h) = m*k(h) - x(h). Factor l(c).
2*c**3
Let v(t) be the second derivative of -t**5/150 + t**4/10 - t**3/3 - 5*t**2/3 + t - 8. Let v(u) = 0. Calculate u.
-1, 5
Let z = 1511/4 - 376. Let 11/4*p**2 + 0 + z*p**4 + 1/2*p + 4*p**3 = 0. Calculate p.
-1, -2/7, 0
Let i(h) = -9*h**2 + 18*h - 48. Let b(v) = -v**2 - v. Let c(d) = -6*b(d) + i(d). Find y such that c(y) = 0.
4
Let z(w) = -2*w**3 + 6*w**2 + 4*w - 10. Let k(c) = c**3 - c**2 - 1. Let b(t) = -2*k(t) + z(t). Factor b(i).
-4*(i - 2)*(i - 1)*(i + 1)
Let l = 138 - 356/3. Let u = 293/69 + 25/23. Suppose -2/3 - l*h**2 - 20/3*h + 32*h**4 - u*h**3 = 0. Calculate h.
-1/3, -1/4, 1
Let f(v) be the first derivative of 1/6*v**3 + 0*v**2 + v - 1 + 0*v**4 - 1/20*v**5. Let g(n) be the first derivative of f(n). Factor g(i).
-i*(i - 1)*(i + 1)
Let n(y) be the second derivative of -y**5/20 + y**4/3 - 2*y**3/3 - 11*y. Factor n(h).
-h*(h - 2)**2
Let j(k) be the first derivative of 3*k**4/8 + k**3/2 + 20. Let j(x) = 0. What is x?
-1, 0
Factor -3*k**2 + k + 2*k + 2 + 4*k**2.
(k + 1)*(k + 2)
Let l(v) be the second derivative of 3*v**5/80 - v**3/8 - 3*v. Factor l(j).
3*j*(j - 1)*(j + 1)/4
Let i(u) be the second derivative of -u**6/195 + u**5/26 - 4*u**4/39 + 4*u**3/39 + 9*u. Factor i(m).
-2*m*(m - 2)**2*(m - 1)/13
Let b(m) = 0*m**2 + 0*m**2 + 2*m**2. Let u be -7 + 1 - (-1 + 1). Let p(x) = 5*x**2. Let i(v) = u*p(v) + 14*b(v). Suppose i(a) = 0. Calculate a.
0
Let p(b) be the third derivative of b**7/140 + b**6/40 - b**5/40 - b**4/8 + 31*b**2. What is q in p(q) = 0?
-2, -1, 0, 1
Let t(o) be the second derivative of o**6/360 + o**5/60 + o**3/2 + 5*o. Let k(a) be the second derivative of t(a). Find c such that k(c) = 0.
-2, 0
Suppose 3*o + o**3 - 5*o**2 + 16*o**2 - 7*o**2 + 1 - o**2 = 0. Calculate o.
-1
Determine g so that -3/4*g**2 + 9/2*g + 21/4 = 0.
-1, 7
Let v(f) = -f**3 - 3 + 0 - 3*f + 2*f**4 - f**4. Let x be (-1)/4 - 52/(-16). Let a(z) = 4*z**4 - 4*z**3 - 10*z - 10. Let h(b) = x*a(b) - 10*v(b). Factor h(o).
2*o**3*(o - 1)
Let r = 20 - 8. Let g be (-1 + 2)/(6/r). Factor 0*i**g + i + 1/2*i**4 - 1/2 - i**3.
(i - 1)**3*(i + 1)/2
Let z(s) = -s**2 + 10*s - 1. Let d be z(9). Let y = d - 5. Find g, given that 0*g**2 - 2/3*g**4 + 2/3*g**y + 0*g + 0 = 0.
0, 1
Suppose -3*s = -s - 8. Factor 0*u**2 + 7*u**s - u**2 - 6*u**4 + u**3 - u**5.
-u**2*(u - 1)**2*(u + 1)
Let t(u) be the first derivative of 0*u + 5 + 0*u**4 + 2/5*u**5 - 2/3*u**3 + 1/2*u**2 - 1/6*u**6. Solve t(o) = 0.
-1, 0, 1
Let t(b) = -4*b - 1. Let v be t(-1). Suppose -8*u = -v*u. Factor u*z - 1/5*z**3 + 0*z**2 + 0.
-z**3/5
Let y(i) be the third derivative of i**5/180 - i**4/72 + 4*i**2. What is z in y(z) = 0?
0, 1
Let f(x) be the first derivative of -x**4/3 + 2*x**3/3 - x - 3. Let h(l) be the first derivative of f(l). Factor h(z).
-4*z*(z - 1)
Let d(k) = -k**3 - 8*k**2 - k - 6. Let t be d(-8). Factor -j + 2*j**2 - 3*j**t - 3*j + 2*j**3 - j**2.
2*j*(j - 2)*(j + 1)
Suppose -4*l = -4*h - 32, 9*h = 4*h + 10. Let g be (-2 - l/(-4))*14. What is t in 0 - 16*t - 1 - g*t**2 - 3 = 0?
-2, -2/7
Let d(c) = 2*c**2 - c + 1. Let n be d(1). Factor -3/4*g**3 + 0*g + 1/4*g**4 + 0 + 1/2*g**n.
g**2*(g - 2)*(g - 1)/4
Let c be 92/80 - (-3 + (-75)/(-20)). Factor -c*k**2 + 0*k + 0 - 4/5*k**3.
-2*k**2*(2*k + 1)/5
Let d(t) be the first derivative of -2*t**3/51 + 2*t/17 + 30. Factor d(g).
-2*(g - 1)*(g + 1)/17
Let t(s) be the first derivative of -s**3 - 2*s**2 + 5*s - 1. Let u(x) = -3*x**2 - 3*x + 4. Let l(m) = 4*t(m) - 5*u(m). Find z such that l(z) = 0.
0, 1/3
Let y be 0*(28/8 + -3). Let r(q) be the third derivative of y*q**5 - 1/90*q**6 + 0*q**4 + 0 + 1/315*q**7 - 2*q**2 + 0*q**3 + 0*q. Let r(x) = 0. What is x?
0, 2
Let s(q) be the second derivative of -q**8/23520 - q**7/4410 - q**6/2520 + q**4/6 + 3*q. Let g(h) be the third derivative of s(h). Factor g(d).
-2*d*(d + 1)**2/7
Let i(y) = 2*y**3 - 3*y**2 + 2. Let r be i(2). Factor -9*x**2 - r*x**3 + 3*x - 2*x - 2*x**4 - 3*x + 3*x**2.
-2*x*(x + 1)**3
Let x = 248/105 + -8/105. Factor -2/7*k**5 - 12/7*k**4 + 0*k - x*k**2 + 0 - 24/7*k**3.
-2*k**2*(k + 2)**3/7
Let w = 38/55 + 6/55. Determine f so that -w*f + 4/5 + 1/5*f**2 = 0.
2
Let x(i) = -37*i**2 - 21*i - 7. Let c(t) = 10*t**2 + 10*t + 4*t**2 + 4*t**2 + 3. Let z be (-3)/(-3) - 1/(-1). Let s(w) = z*x(w) + 5*c(w). Factor s(a).
(4*a + 1)**2
Suppose -4*u - 44 = -3*y + 17, y - 47 = 3*u. Let b be u/(-396) - (-6)/33. Suppose 0 + 2/9*w**4 + 4/9*w**3 + 0*w + b*w**2 = 0. What is w?
-1, 0
Let w(c) be the third derivative of c**8/1344 - 3*c**6/160 + c**5/60 + c**4/8 + 9*c**2. Determine q so that w(q) = 0.
-3, -1, 0, 2
Let h(l) = 44*l**2 - 52*l + 8. Let f be (-99)/21 + 10/(-35). Let z(g) = 22*g**2 - 26*g + 4. Let b(o) = f*z(o) + 2*h(o). Determine a, given that b(a) = 0.
2/11, 1
Let f(b) be the first derivative of 4*b**4/3 + 4*b**3/9 - 8*b**2/3 - 4*b/3 + 12. Factor f(l).
4*(l - 1)*(l + 1)*(4*l + 1)/3
Let m(b) = 3*b**4 - 15*b**3 + 9*b**2 + 25*b. Let p(c) = -c. Let v(a) = m(a) - 2*p(a). Let v(s) = 0. Calculate s.
-1, 0, 3
Let p(g) be the third derivative of -g**8/840 - 2*g**7/525 + g**5/75 + g**4/60 + 8*g**2. Factor p(m).
-2*m*(m - 1)*(m + 1)**3/5
Let q(n) be the third derivative of n**3/6 + 8*n**2. Let k(w) = 4*w**2 + 8*w + 1. Let i(r) = k(r) + 3*q(r). Factor i(a).
4*(a + 1)**2
Let a be ((-8)/14)/((-2)/7). Let h b