/2*n.
(n - 2)*(n - 1)/6
Let k(f) be the first derivative of f**6/6 + 19*f**5/5 + 63*f**4/2 + 108*f**3 + 108*f**2 - 258. Factor k(j).
j*(j + 1)*(j + 6)**3
Let l be (-3 + -4)*2/(-7). Determine u, given that u - 36*u**4 + 29*u**3 + 13*u - 64*u**2 + 55*u**3 + l*u = 0.
0, 2/3, 1
Let y(u) be the first derivative of u**3/12 + u**2/2 + 3*u/4 + 274. Factor y(j).
(j + 1)*(j + 3)/4
Let c(f) be the first derivative of 16 + 30*f - 35/2*f**2 + 5/3*f**3. Suppose c(x) = 0. Calculate x.
1, 6
Let y be 86/(-10) - (-16 + 19). Let v = 12 + y. Factor -2/5*k + 2/5 + 4/5*k**3 + v*k**4 - 4/5*k**2 - 2/5*k**5.
-2*(k - 1)**3*(k + 1)**2/5
Determine g, given that 3456 + 3/2*g**4 + 438*g**2 + 2016*g + 42*g**3 = 0.
-8, -6
Let b be 1/(-4) + 5*5/60. Let o(u) be the first derivative of 4 + 0*u + 3/4*u**2 - b*u**3. Factor o(i).
-i*(i - 3)/2
Let 31*y - y**2 + 33*y**2 - 128 - 36*y**2 + 320 + 21*y = 0. Calculate y.
-3, 16
Let r(a) = 4*a**2 + 5*a - 5. Let f(j) = -j**2 + 2*j + 1. Let y(q) = 10*f(q) + 2*r(q). Determine v so that y(v) = 0.
0, 15
Let 4/5*l + 16/5 - 2*l**2 + 2/5*l**3 = 0. Calculate l.
-1, 2, 4
Let c(l) = 6*l**5 + 5*l**4 + 31*l**3 + 19*l**2 - 13*l. Let o(t) = t**5 + t**4 + 5*t**3 + 3*t**2 - 2*t. Let j(k) = 2*c(k) - 13*o(k). Factor j(w).
-w**2*(w + 1)**3
Let i(y) = y**5 + y**4 - 8*y**3 - 8*y**2 - 8*y - 24. Let t(p) = p**5 + p**4 - 5*p**3 - 5*p**2 - 5*p - 15. Let m(j) = 5*i(j) - 8*t(j). Factor m(r).
-3*r**4*(r + 1)
Let y = 97 - 92. Let v(l) be the second derivative of -1/3*l**3 - 1/21*l**7 + 4*l + 0 + 0*l**2 + 0*l**4 + 1/5*l**y + 0*l**6. Factor v(j).
-2*j*(j - 1)**2*(j + 1)**2
Let d(z) = z**3 + 33*z**2 + 22*z + 10. Let w(c) = -c**3 - 33*c**2 - 24*c - 8. Let m(x) = -4*d(x) - 5*w(x). Factor m(o).
o*(o + 1)*(o + 32)
Let l(o) be the first derivative of -o**4/12 - 5*o**3/9 - o**2/2 - o + 12. Let z(y) be the first derivative of l(y). Determine m, given that z(m) = 0.
-3, -1/3
Factor -6*z**2 - 3*z**3 + 156*z**4 + 157*z**4 - 310*z**4.
3*z**2*(z - 2)*(z + 1)
Let i(n) = -n**2 + 27*n + 90. Let w be i(-3). Let k(z) be the second derivative of w*z**3 + 0 - 1/30*z**5 + 0*z**4 - 7*z + 0*z**2. Factor k(q).
-2*q**3/3
Determine g, given that -4/3*g**3 + 4/3 - 4*g - 5*g**2 = 0.
-2, 1/4
Let m(t) be the first derivative of -t**6/5 - 32*t**5/25 - t**4/5 + 32*t**3/15 + t**2 - 192. Suppose m(u) = 0. What is u?
-5, -1, -1/3, 0, 1
Let n(j) be the first derivative of 1/45*j**5 - 1/90*j**6 + 7/2*j**2 + 0*j + 6 + 0*j**3 + 1/9*j**4. Let o(p) be the second derivative of n(p). Factor o(c).
-4*c*(c - 2)*(c + 1)/3
Let q(i) = -i**3 + 25*i**2 - 76*i + 62. Let y(b) = -12*b**3 + 324*b**2 - 990*b + 807. Let k(c) = -27*q(c) + 2*y(c). Solve k(f) = 0.
2, 5
Let h(d) be the second derivative of -d**4/24 - 7*d**3/4 - 56*d. Find f, given that h(f) = 0.
-21, 0
Let o be (-2)/(-8) + 6/(-24). Determine k, given that 4*k + 6 - 17 + 3 + o + 8*k**2 - 4*k**3 = 0.
-1, 1, 2
Let o(d) = -16*d**4 - 132*d**3 + 144*d**2 - 64*d + 12. Let r(u) = u**3 - u**2 - 2*u + 1. Let b(w) = o(w) - 12*r(w). Factor b(m).
-4*m*(m + 10)*(2*m - 1)**2
Factor -8*v**3 + 33/2*v + 1/4*v**4 + 0 - 35/4*v**2.
v*(v - 33)*(v - 1)*(v + 2)/4
Let x = -12601/5 + 2521. Determine c, given that 16/5*c + c**4 - 3*c**2 - x - 2/5*c**3 = 0.
-2, 2/5, 1
Factor 5 + 20*x**2 + 4*x - 21*x**2 - 23*x**2 + 23.
-4*(x + 1)*(6*x - 7)
Let i be 10/(-55) - (-4)/((-704)/738). Let l = 261/56 + i. Suppose 2/7*j + l*j**2 + 0 = 0. Calculate j.
-1, 0
Let n(k) be the first derivative of k**4/46 - 44*k**3/23 - 135*k**2/23 - 136*k/23 - 312. Factor n(s).
2*(s - 68)*(s + 1)**2/23
Suppose 3 + 12 = 5*p. Let u = -26/33 + 38/11. Factor 2/3*l**4 + 4*l**2 + u*l + 2/3 + 8/3*l**p.
2*(l + 1)**4/3
Let q(f) be the second derivative of f**7/5880 - f**6/504 + f**5/105 - f**4/42 + 5*f**3/2 + 18*f. Let o(v) be the second derivative of q(v). Solve o(b) = 0.
1, 2
Let s(u) = 59*u**3 - 2*u**2 + 2*u - 1. Let r be s(1). Suppose -5*z = -158 + r. Factor 14*k + 7*k + z*k**2 + 8 - k + 8*k.
4*(k + 1)*(5*k + 2)
Let q be ((-320)/(-1024))/(135/12). Let i(n) be the second derivative of 0 + 12*n - 5/18*n**3 + q*n**4 + 1/30*n**5 + 1/3*n**2. Factor i(a).
(a - 1)*(a + 2)*(2*a - 1)/3
Let t(w) be the third derivative of -w**7/1680 - 13*w**6/960 + 7*w**5/240 + 4*w**2 + 111. What is z in t(z) = 0?
-14, 0, 1
Suppose -2*n = n + 5*j - 8, -n + 4 = 3*j. Solve -6*u**4 + 1 - n + 14*u**5 - 11*u**5 = 0 for u.
0, 2
Factor 98 - 14*c + 1/2*c**2.
(c - 14)**2/2
Suppose -369*m + 339*m + 60 = 0. Suppose -d + 1 + 1/4*d**m = 0. Calculate d.
2
Suppose 0 = 2*u + 5*i + 6 + 111, -3*i + 75 = -u. Let f = u - -135/2. Factor -f - 1/6*k**2 - k.
-(k + 3)**2/6
Solve -33/5*d - 14/5 - 3/5*d**3 - 23/5*d**2 + 1/5*d**4 = 0 for d.
-2, -1, 7
Let k = -6/181 + 1466/543. Solve 4/3*i**2 + 0 + 1/3*i**5 + 0*i + k*i**3 + 5/3*i**4 = 0.
-2, -1, 0
Let s = -816 + 826. Let b(l) be the first derivative of 1/3*l**3 + 0*l - s - 1/2*l**2. Determine v, given that b(v) = 0.
0, 1
Suppose 13 = -r - 4*n, -4*n + 2 = 2*r + 12. Suppose -7*j = -r + 3. Suppose -3/4*p**4 + j*p - 3/4 + 3/2*p**2 + 0*p**3 = 0. What is p?
-1, 1
Let s(g) = g + 2. Let t = 8 + -8. Let x be s(t). Factor 18*z**2 - 17*z**2 - 3*z**4 - x*z**3 + 4*z**4.
z**2*(z - 1)**2
What is q in 0 + 3/4*q**5 + 3*q**4 + 0*q + 9/4*q**3 + 0*q**2 = 0?
-3, -1, 0
Let x = -169/11 + 6253/44. Find j such that -x - 3/4*j**2 + 39/2*j = 0.
13
Let k(q) be the first derivative of q**5/5 - 3*q**4 - 17*q**3/3 + 24*q**2 + 52*q + 786. Solve k(a) = 0 for a.
-2, -1, 2, 13
Suppose 13*a - 37 = 6*y - 8*y, 14 = 5*a + y. Factor 2/5 + 1/5*w**a - 2/5*w**2 - 1/5*w.
(w - 2)*(w - 1)*(w + 1)/5
Suppose 0 = -5*l + 2*s + 15, -7*l + 3*l = 5*s - 12. Suppose -2*r + l + 3 = 0. Let r*d - 3/4*d**2 - 3 = 0. Calculate d.
2
Let a(r) = 2*r**5 - 2*r**2 - r - 1. Let t(b) = 15*b**5 - b**4 + 12*b**3 + 12*b**2 + 8*b - 8. Let u(s) = 40*a(s) - 5*t(s). Factor u(p).
5*p*(p - 4)*(p + 1)*(p + 2)**2
Find c such that 27/2*c**2 - 25/2*c**3 - 5*c + 0 - 1/2*c**5 + 9/2*c**4 = 0.
0, 1, 2, 5
Let h(i) be the third derivative of -i**8/30240 - i**7/3780 - 19*i**5/60 - 6*i**2. Let v(k) be the third derivative of h(k). Let v(m) = 0. Calculate m.
-2, 0
Factor -2*l**4 + 5*l**4 + 4*l**4 + 45*l**2 + 45*l - 12*l**4 - 5*l**3.
-5*l*(l - 3)*(l + 1)*(l + 3)
Let s be (-6 - 9)/(1*-1). Suppose 0 = -5*b - 5*f - s, -5*b + 40 = -5*f + 5. Factor 14*a**2 + 5*a**3 - 5*a + 5*a**4 - 34*a**2 + 15*a**b.
5*a*(a - 1)*(a + 1)**2
Let t(o) be the second derivative of o**7/210 - 7*o**6/120 + o**5/4 - 3*o**4/8 - 4*o**2 + 9*o - 2. Let h(s) be the first derivative of t(s). Factor h(q).
q*(q - 3)**2*(q - 1)
Let r = 1927 - 5780/3. Let d(h) be the second derivative of 0*h**3 - r*h**4 + 0*h**2 - 2*h + 2/21*h**7 + 3/5*h**5 - 2/5*h**6 + 0. Factor d(f).
4*f**2*(f - 1)**3
Let f = 14 + -10. Suppose -3*i = 4*d + 16, -3*i + f*d = 2*i - 16. Factor -16/5*g**4 - 14/5*g**3 + i*g + 0 - 4/5*g**2 - 6/5*g**5.
-2*g**2*(g + 1)**2*(3*g + 2)/5
Let z(g) be the first derivative of -3*g**5/80 + g**4/16 + g**3/4 + 17*g + 12. Let t(k) be the first derivative of z(k). Factor t(q).
-3*q*(q - 2)*(q + 1)/4
Suppose z + 2 + 0 = 0. Let i be 2 - 1 - (z + 1). Factor 0 - 4 - 2*f**3 + 3 + 3*f**i.
-(f - 1)**2*(2*f + 1)
Let h(i) be the first derivative of 3/8*i**4 + 0*i**3 - 9/4*i**2 + 31 - 3*i. Factor h(f).
3*(f - 2)*(f + 1)**2/2
Factor -7*d**3 + 3*d**4 - 19*d**3 + 14*d + 4*d**2 + 10*d**3 - 8 + d**4 + 2*d**5.
2*(d - 1)**3*(d + 1)*(d + 4)
Let a(v) be the second derivative of -v**7/1470 - v**6/630 + v**5/105 - v**3/6 - 15*v. Let j(x) be the second derivative of a(x). Determine q so that j(q) = 0.
-2, 0, 1
Let x be (-1*1/(-1))/((-1)/(-61)). What is z in -x*z - 84*z**2 - 16 + 128*z**4 + 80*z**3 - 12*z - 7*z - 28*z**4 = 0?
-1, -2/5, 1
Let a(u) be the third derivative of -u**6/120 - u**4/8 - 13*u**2. Let c(b) = -b**2 - b. Let g(s) = a(s) - 2*c(s). Factor g(k).
-k*(k - 1)**2
Let l(w) be the third derivative of 0*w + 11/156*w**4 + 7 - 3*w**2 + 1/780*w**6 + 5/39*w**3 + 7/390*w**5. Suppose l(x) = 0. Calculate x.
-5, -1
Let d(t) = t**3 + 9*t**2 + 5*t - 3. Let i(k) be the second derivative of -k**5/20 - 2*k**4/3 - 5*k**3/6 + k**2 + 2*k. Let y(p) = 4*d(p) + 5*i(p). Factor y(s).
-(s + 1)**2*(s + 2)
Suppose 4 = -2*y + 2*b, -5*y = 4*b - 11 - 15. Let r = 613/1365 + -4/195. Factor 12/7 + 0*i - r*i**y.
-3*(i - 2)*(i + 2)/7
Let b(u) be the second derivative of u**6/105 + 8*u**5/7 + 800*u**4/