
Let t(n) be the first derivative of n**7/420 - n**5/120 - 4*n**2 - 4. Let l(k) be the second derivative of t(k). Factor l(p).
p**2*(p - 1)*(p + 1)/2
Factor -24*h**2 - 2*h**2 - 281 - 1916 - 13*h**2 - h**3 - 507*h.
-(h + 13)**3
Let x(u) be the second derivative of -1/6*u**3 + 3/4*u**2 + 13*u + 1/20*u**5 + 0 - 1/9*u**4 - 1/180*u**6. Factor x(k).
-(k - 3)**2*(k - 1)*(k + 1)/6
Let j(h) be the third derivative of h**5/30 - h**4/2 + 8*h**3/3 - 227*h**2 - 1. Find a such that j(a) = 0.
2, 4
Let w(h) be the second derivative of h**10/15120 + h**9/7560 - h**8/1680 - 11*h**4/12 + 10*h. Let o(p) be the third derivative of w(p). Factor o(y).
2*y**3*(y - 1)*(y + 2)
Let q(k) be the first derivative of 2*k**5/5 - 2*k**4 - 4*k**3 + 4*k**2 + 10*k + 97. What is g in q(g) = 0?
-1, 1, 5
Solve -28/5*m**3 + 0 - 47/5*m**4 + 12/5*m**2 - 7/5*m**5 + 0*m = 0.
-6, -1, 0, 2/7
Let o(w) be the first derivative of 1/5*w**2 + 1/15*w**3 - 5*w + 1/120*w**4 + 11. Let t(y) be the first derivative of o(y). Factor t(m).
(m + 2)**2/10
Let r(m) be the third derivative of -m**8/1176 + m**6/105 + 235*m**2. Suppose r(z) = 0. Calculate z.
-2, 0, 2
Suppose 3*a = 5*q - 5 - 4, 4*q - a - 10 = 0. Let i(o) = 5*o - 2. Let z be i(q). Let -36*c - z + 1 + 3*c**2 + 36*c = 0. What is c?
-2, 2
Let p(k) = -k - 15. Let o be p(-15). Suppose o = -j - j + 22. Factor 9*h + 7*h**3 + 33*h**2 - 8*h**3 - j*h**3.
-3*h*(h - 3)*(4*h + 1)
Let j(r) = r**2 - 10*r - 16. Let a(t) = -3*t**2 + 28*t + 46. Let s(u) = -4*a(u) - 11*j(u). Let s(w) = 0. What is w?
-2, 4
Let o(m) be the first derivative of m**6/6 + 3*m**5 + 13*m**4/4 - 5*m**3 - 7*m**2 - 42. Determine j so that o(j) = 0.
-14, -1, 0, 1
Suppose f + l - 5 = 0, -13 + 2 = -f - 3*l. Let 8/9 + 10*w**f - 56/9*w**3 - 98/9*w**4 + 56/9*w = 0. Calculate w.
-1, -2/7, 1
Let m(q) = 2*q**5 + q**4 - 3*q**3 + 2*q**2 + q + 6. Let z(o) = -o**5 - o**4 + o**3 - 2. Let v(j) = -m(j) - 3*z(j). Factor v(k).
k*(k - 1)*(k + 1)**3
Let g(o) be the third derivative of 23*o**5/60 + 15*o**4/4 - 4*o**3/3 - 442*o**2. Factor g(h).
(h + 4)*(23*h - 2)
Let o(f) = 6*f**3 + 40*f**2 + 72*f + 12. Let i(u) = -5*u**3 - 39*u**2 - 70*u - 9. Let n(b) = 4*i(b) + 3*o(b). Factor n(m).
-2*m*(m + 2)*(m + 16)
Let j be (-66)/6 + 12 + 2. Factor 1/2*n**2 + 1/2*n + 1/6 + 1/6*n**j.
(n + 1)**3/6
Let u(t) be the second derivative of 1/4*t**3 + t**2 - 1/24*t**4 + 0 - 31*t. Find q such that u(q) = 0.
-1, 4
Let r(k) = k**2 - 9*k - 6. Let o be r(10). Solve -9*v + 5*v**4 - 9*v**5 - 5*v**2 - 17*v**2 + 25*v**o + 37*v - 8 - 19*v**3 = 0.
-1, 2/3, 1, 2
Solve 94*g**2 + 44/3*g**3 + 200/3 + 440/3*g + 2/3*g**4 = 0 for g.
-10, -1
Let j(d) be the first derivative of 3*d**6/16 - 33*d**5/20 + 71*d**4/16 - 11*d**3/6 - 87*d**2/16 - 9*d/4 - 582. What is f in j(f) = 0?
-1/3, 2, 3
Let a(b) be the third derivative of -b**7/168 - 5*b**6/72 - b**5/6 - 5*b**3 + 4*b**2. Let i(n) be the first derivative of a(n). Solve i(h) = 0.
-4, -1, 0
Let w(a) be the second derivative of a**4/60 - 38*a**3/5 + 6498*a**2/5 - 3*a + 21. Let w(f) = 0. What is f?
114
Let a(y) be the second derivative of -y**6/60 + 3*y**5/20 - y**4/3 - y**3/2 + 9*y**2/4 - 3*y - 6. Factor a(r).
-(r - 3)**2*(r - 1)*(r + 1)/2
Let c be (-90 + (-1 - -1))/(4/(-8)). Let k be (-6)/2 + (c/(-8))/(-5). Factor -k*q**2 - 9/2 + 3/2*q**3 - 15/2*q.
3*(q - 3)*(q + 1)**2/2
Let g be 2/76*54 + -1. What is s in -6/19 + g*s - 2/19*s**2 = 0?
1, 3
Factor 15/7*o - 3/7*o**2 - 3/7*o**3 - 9/7.
-3*(o - 1)**2*(o + 3)/7
Let n(j) be the second derivative of -j**3/6 - 3*j. Let w be n(0). Let 5 + w*i + 5*i**3 + 1 - 2*i**3 - 9*i = 0. What is i?
-2, 1
Let w = 106 - 105. Suppose q + 0*q - 4 = 0. Factor -q*p**4 + 5*p**4 - 2*p**2 + 0*p**2 - w + 2.
(p - 1)**2*(p + 1)**2
Suppose -3*h + 3*n + 0*n = 0, -h = -2*n. Let d = 122 - 120. Factor -3*m - m**d + 2*m + h*m + 2*m**2.
m*(m - 1)
Let p(a) be the second derivative of 0 - 27/5*a**6 + 0*a**2 - 5/3*a**7 - 1/5*a**5 + 6*a**4 - 8/3*a**3 - 40*a. Suppose p(z) = 0. Calculate z.
-2, -1, 0, 2/7, 2/5
Factor -18/23*v**2 + 2/23 - 10/23*v**3 - 6/23*v.
-2*(v + 1)**2*(5*v - 1)/23
Suppose 0 - 140*l**4 + 848/3*l**3 + 8/3*l - 436/3*l**2 = 0. Calculate l.
0, 2/105, 1
Let n(s) = -2*s**3 - 4*s**2 + 2*s + 2. Let f(r) = r**2 - r - 1. Let c(j) = -j**3 + 3*j**2 - 2*j + 5. Let v be c(3). Let x(q) = v*n(q) - 2*f(q). Factor x(o).
2*o**2*(o + 1)
Let f(x) be the third derivative of -11*x**6/240 + 23*x**5/240 + 5*x**4/96 - x**3/4 - 105*x**2. Determine c, given that f(c) = 0.
-1/2, 6/11, 1
Let k be 1/(-5 - -4) - -6. Find g, given that 3*g**4 - 7*g**5 + 7*g**3 - 2*g - 3*g**2 + 2*g**k + 0*g**5 = 0.
-1, -2/5, 0, 1
Suppose -98/13 + 28/13*n - 2/13*n**2 = 0. Calculate n.
7
Let x be 4628/180 - 22/(-330). Factor x*s + 28/9*s**2 + 64/9.
4*(s + 8)*(7*s + 2)/9
Suppose -13*r + 27 + 15 = 16. Factor -2/17*o**r + 8/17*o - 8/17.
-2*(o - 2)**2/17
Suppose m + m = -3*o + 7, 3*m = -3*o + 6. Let b(a) be the second derivative of 2*a**o + 3/4*a**4 - 4*a + 0 + 2*a**2. Factor b(z).
(3*z + 2)**2
Let x = 27619 + -27616. Factor 0 + 1/3*d**x + d - 4/3*d**2.
d*(d - 3)*(d - 1)/3
Let c(o) be the second derivative of -13*o**6/30 + 3*o**5/10 - 5*o**4/4 - 11*o. Let x(j) = 7*j**4 - 3*j**3 + 8*j**2. Let h(a) = -6*c(a) - 11*x(a). Factor h(z).
z**2*(z - 2)*(z - 1)
Let j(k) be the first derivative of k**6/60 - k**5/15 - 5*k**4/12 + 2*k**3 - 6*k**2 + 37. Let b(s) be the second derivative of j(s). Find v such that b(v) = 0.
-2, 1, 3
Factor 22*r**4 + 6*r**5 - 355*r**3 - 4*r**5 + 56*r**2 + 419*r**3.
2*r**2*(r + 2)**2*(r + 7)
Suppose -34*r + 20 = -30*r. Factor -10 + 17*z**2 - 2*z - 5*z**4 + 3*z**2 + 5*z**3 - 3*z - r*z**2.
-5*(z - 2)*(z - 1)*(z + 1)**2
Let c = 14 - 8. Suppose -c*v - 6 = -8*v. Suppose -3 - 12*q**2 - 4*q**3 + 5*q - q**4 - 8*q - 2*q**v - 7*q = 0. Calculate q.
-3, -1
Let t = -11 + 15. Factor h**2 + 2*h**2 + 2*h**2 - h**3 + 0*h**2 - t*h.
-h*(h - 4)*(h - 1)
Let p(q) be the first derivative of -q**4/4 + q**3 + q**2/2 - q - 8. Let w be p(2). Solve 3*u**2 + 0*u**2 + w*u + 3*u + u**2 = 0.
-2, 0
Let a(k) be the first derivative of -k**4/7 - 16*k**3/21 + 2*k**2/7 + 16*k/7 + 64. Factor a(g).
-4*(g - 1)*(g + 1)*(g + 4)/7
Let l(u) = 2*u + 8. Let f be l(-2). Suppose 5*w + 4*w = f*w. Factor 1/2*x**2 + w*x + 0.
x**2/2
Let p(u) = -3*u**2 + 96*u - 717. Let h be p(20). Determine b, given that -45/11*b**5 + 75/11*b**h - 118/11*b**4 + 76/11*b**2 + 12/11*b + 0 = 0.
-3, -2/5, -2/9, 0, 1
Factor 64/7*t + 24/7*t**2 + 0 - 4/7*t**3.
-4*t*(t - 8)*(t + 2)/7
Let p(c) be the second derivative of -c**5/80 + 161*c**4/16 - 25921*c**3/8 + 4173281*c**2/8 - c + 211. Suppose p(i) = 0. Calculate i.
161
Let k(p) be the second derivative of -1/18*p**4 + 6*p - p**3 + 0 - 8/3*p**2. Suppose k(o) = 0. What is o?
-8, -1
Let z(l) be the third derivative of l**5/30 - 2*l**4/3 + 16*l**3/3 + 4*l**2 - 16*l. Factor z(w).
2*(w - 4)**2
Let c(n) be the first derivative of -n**6/30 + n**5/20 + 28*n - 29. Let g(t) be the first derivative of c(t). What is v in g(v) = 0?
0, 1
Let f(p) = 8*p**4 + 18*p**3 + 47*p**2 + 30*p. Let o(x) = -x**4 + x**3 - x. Let s(a) = 3*f(a) + 21*o(a). Factor s(g).
3*g*(g + 1)**2*(g + 23)
Let x(j) be the second derivative of 0 + 4/3*j**3 - 2*j + 6*j**2 - 1/3*j**4. Solve x(w) = 0.
-1, 3
Let g(m) be the third derivative of 4*m**7/735 - m**6/420 - m**5/70 + 100*m**2. Factor g(o).
2*o**2*(o - 1)*(4*o + 3)/7
Find d, given that -8*d**3 + 14/13*d**4 + 252/13*d**2 + 54/13 - 216/13*d = 0.
3/7, 1, 3
Let i(j) = 41*j**3 - 80*j**2 + 26*j + 6. Let g(h) = -575*h**3 + 1120*h**2 - 365*h - 85. Suppose 0 = 6*w - 9*w + 255. Let k(m) = w*i(m) + 6*g(m). Factor k(y).
5*y*(y - 2)*(7*y - 2)
Find r, given that 5*r**2 + 27/5*r + 9/5*r**3 + 2 + 1/5*r**4 = 0.
-5, -2, -1
Let t(j) = 1 + 2 + 127*j**3 - 3*j**2 - j - 126*j**3 + 4. Let x be t(3). Factor 0*b + 1/3*b**3 + 1/3*b**x + 0 + 0*b**2.
b**3*(b + 1)/3
Let u be 6790/2425 - 8/10. Solve 5/3*x - 3*x**u - 1/3 - 2/3*x**4 + 7/3*x**3 = 0.
1/2, 1
Let f(a) = a**4 - a**3 - a + 1. Let g(q) = 4*q**4 - 11*q**3 - 12*q**2 - 13*q + 5. Suppose -8*w - 16 + 0 = 0. Let j(z) = w*g(z) + 10*f(z). Factor j(c).
2*c*(c + 2)**3
Let u(b) = -b**3 - b**2 + b + 1. Let i be u(-2). Let j = -3 - -5. Factor -3*m**i - 4*m**j + 2*m + 0*m**3 + 5*m**3.
2*m*(m - 1)**2
Let y(k) = -k**2 + k - 1. Let g(n) = -n**2 + n + 4. Let f(c) = 3*c**2 - 2*c - 9. Let w(m) = -2*f(m) - 5*g(m). Let l(u) = 3*