 1/4*i**2 - 1/4*i - r.
(i - 2)*(i + 1)/4
Let f(q) be the third derivative of q**5/540 - 11*q**4/108 - 154*q**2. Factor f(c).
c*(c - 22)/9
Let d(r) be the second derivative of -2*r**7/189 + r**6/135 + r**5/45 - r**4/54 + 283*r. Solve d(g) = 0 for g.
-1, 0, 1/2, 1
Let w be -46*(-1 - 1)/4. Let g = w - 21. Suppose -3*k**g + 8*k**4 - 2*k**2 - 3*k**4 = 0. Calculate k.
-1, 0, 1
Factor -39847 + 990*t - 3*t**2 + 16006 - 40662 - 17172.
-3*(t - 165)**2
Let d be (-98)/(-12)*(-225)/(-700). Let l(o) be the first derivative of d*o**2 + 9/4*o**3 + 3/2*o - 10 + 3/20*o**5 + 15/16*o**4. Factor l(i).
3*(i + 1)**3*(i + 2)/4
Let n(d) = -d**3 - 5*d**2. Let x(g) be the first derivative of 2*g**4 + 12*g**3 + 48. Let q(s) = -20*n(s) - 3*x(s). Factor q(f).
-4*f**2*(f + 2)
Let w(q) be the first derivative of -7/9*q**2 + 1/27*q**6 - 8/45*q**5 - 40/27*q**3 - q**4 + 0*q - 15. Let w(r) = 0. Calculate r.
-1, 0, 7
Suppose 0 = 5*v + d - 11, 21*v + 4*d + 6 = 26*v. Determine g, given that -2/11*g**v + 0 + 2/11*g = 0.
0, 1
Let c(q) = 4*q**2 + 105*q - 770. Let a be c(6). What is w in 0 + 2/11*w**5 + 0*w**3 + 0*w - 2/11*w**a + 0*w**2 = 0?
0, 1
Let z(n) be the second derivative of -18*n**7/7 - 384*n**6/5 - 13719*n**5/20 - 5061*n**4/4 - 660*n**3 - 150*n**2 - 17*n + 2. Suppose z(m) = 0. What is m?
-10, -1, -1/6
Let n(p) be the first derivative of p**3/18 + 5*p**2/12 + p + 63. Factor n(y).
(y + 2)*(y + 3)/6
Let y(j) = 19*j**2 - 18*j - 17. Let g be y(11). Let p = -22904/11 + g. Factor -54/11*f**4 + p*f**2 + 36/11*f**3 - 54/11*f**5 - 14/11*f + 2/11.
-2*(f + 1)**2*(3*f - 1)**3/11
Let w = -24 - -28. Solve -2*p**4 + p**2 - 3*p**2 + 0*p**4 + w*p**2 = 0 for p.
-1, 0, 1
Factor -1/11*g**3 + 4/11*g - 40/11 + 10/11*g**2.
-(g - 10)*(g - 2)*(g + 2)/11
Suppose -3*k = f + 4*f, 3*f = 3*k. Let l(b) be the third derivative of 1/120*b**5 + 1/12*b**3 + 6*b**2 + 1/24*b**4 + f*b + 0. Find v, given that l(v) = 0.
-1
Let k(q) be the third derivative of -q**7/630 - q**6/45 - 11*q**5/90 - q**4/3 - q**3/2 - 11*q**2 - 3. Factor k(j).
-(j + 1)**2*(j + 3)**2/3
Suppose -81*x - 3*x**5 + 61*x - 2*x**5 + 7*x**3 + 18*x**3 = 0. Calculate x.
-2, -1, 0, 1, 2
Let v = 1/1235 - -13573/14820. Let z(a) be the second derivative of -9*a + 1/10*a**5 + v*a**3 + 0 - 1/2*a**2 - 13/24*a**4. Factor z(d).
(d - 2)*(d - 1)*(4*d - 1)/2
Let m be 4/(-20) - (44169/105 + -6). Let c = m + 417. Find x such that 6/7*x**2 + c*x**3 + 0 - 9/7*x = 0.
-1, 0, 3/5
Factor -24 - 116/3*x + 12*x**3 - 4*x**2 + 4/3*x**4.
4*(x - 2)*(x + 1)**2*(x + 9)/3
Let t(v) be the second derivative of -2/3*v**3 + 0*v**4 + 5*v + 0*v**2 - 1/1260*v**6 + 1/140*v**5 + 0. Let s(d) be the second derivative of t(d). Factor s(i).
-2*i*(i - 3)/7
Let m(h) be the first derivative of 3*h**5/5 + 3*h**4/4 - 5*h**3 + 9*h**2/2 - 415. Factor m(s).
3*s*(s - 1)**2*(s + 3)
Solve 8/5 + 2/5*t**2 + 8/5*t = 0 for t.
-2
Suppose -4*u + 25 + 11 = 0. Suppose -5 = u*h - 32. Factor -4/11*v**2 + 6/11*v - 2/11*v**h + 0.
-2*v*(v - 1)*(v + 3)/11
Let u(q) be the second derivative of 2/15*q**4 + 0 - 11/15*q**3 + 6/5*q**2 - 22*q + 1/50*q**5. Factor u(l).
2*(l - 1)**2*(l + 6)/5
Factor 78*k**2 - 12*k**4 - 36*k**2 - 2*k**5 + 14*k**3 - 42*k**2.
-2*k**3*(k - 1)*(k + 7)
Let u be (-182)/(-35)*(-45)/(-6). Solve -u*c**3 + 5*c**4 + 45*c**2 - 19*c - c + 9*c**3 = 0.
0, 1, 4
Let k be 914/18 + (-12)/(-54). Let a = k + -49. Suppose 1/3*s**a + 3 + 2*s = 0. What is s?
-3
Let h = -32 + 45. Suppose 99*k + 15*k**3 + h - 56*k**2 + 41 - 74*k**2 + 46*k**2 = 0. What is k?
-2/5, 3
Suppose 0 = -3*g - 2*d + 21, 3*g - 3*d - 6 + 0 = 0. Let c(v) = -v**2 + 7*v - 3. Let z be c(g). What is t in t - 3*t - 2*t**2 - 4 + z + 1 = 0?
-2, 1
Solve -3 + 1/4*o**2 - 11/4*o = 0.
-1, 12
Let g(o) = -2*o**2 - 10*o + 2. Let d be g(-5). Factor -j - 45*j**2 + 3*j**3 + 41*j**d + 4 - j - j**3.
2*(j - 2)*(j - 1)*(j + 1)
Let l(k) = -k**3 + 15*k**2 - 14*k + 2. Let j = -17 + 31. Let x be l(j). Suppose 1/4*p**4 + 0 + 1/2*p**3 + 1/4*p**x + 0*p = 0. What is p?
-1, 0
Suppose 0 = 3*r - 0*r - 4*f - 6, 0 = 5*f. Suppose -15 = -n - 4*v, -r*n - 7 = -v - 10. Factor 1/4*a**4 + 0 - 3/4*a - 1/4*a**n - 5/4*a**2.
a*(a - 3)*(a + 1)**2/4
Suppose 2*p = 18 - 2. Suppose -u - p*u = -18. Factor -1/2*x + 1/2*x**3 + 0*x**u - 1/4*x**4 + 1/4.
-(x - 1)**3*(x + 1)/4
Factor 375/4*h**3 + 100*h**2 + 4 + 35*h.
(5*h + 2)**2*(15*h + 4)/4
Let y(i) = 8*i**3 + 12*i**2 - i + 5. Let c(n) = -4*n**3 - 6*n**2 + n - 3. Suppose 0 = -5*u - 5 + 30. Let x(f) = u*c(f) + 3*y(f). Find b, given that x(b) = 0.
-1, -1/2, 0
Let c(q) be the second derivative of -q**4/9 + 14*q**3/9 - 20*q**2/3 - 16*q - 4. Factor c(o).
-4*(o - 5)*(o - 2)/3
What is z in -43/6*z + 15/2*z**2 + 7/3 - 17/6*z**3 + 1/6*z**4 = 0?
1, 14
Let a(l) be the third derivative of -l**10/302400 + l**8/40320 - l**5/30 + 3*l**2. Let p(n) be the third derivative of a(n). Solve p(g) = 0.
-1, 0, 1
Factor 15/4*t - 3*t**2 - 3/2 + 3/4*t**3.
3*(t - 2)*(t - 1)**2/4
Let f = 3163/6 + -526. Let x(a) be the second derivative of -a**2 + 1/6*a**6 + 0 + f*a**3 + a - 7/20*a**5 - 1/4*a**4. Factor x(l).
(l - 1)**2*(l + 1)*(5*l - 2)
Let w(z) be the first derivative of z**8/6720 + z**7/480 + z**6/80 + z**5/24 + z**4/12 + 5*z**3/3 - 9. Let s(m) be the third derivative of w(m). Solve s(c) = 0.
-2, -1
Let k = 1306/1793 - 2/1793. Determine v so that 8/11 + 2/11*v**2 - k*v = 0.
2
Suppose 18 = -5*q - 4*h - 17, -h = q + 8. Let y be 0*(-2)/(-8) - q. Find n, given that -3*n - y*n - 3*n**2 + 6 - 6 = 0.
-2, 0
Suppose -8 - 4 = -2*f. Solve -y**2 - 36 - 10*y + f*y - 8*y = 0 for y.
-6
Let f(p) be the third derivative of 19*p**2 + 0*p**4 + 0 + 0*p**3 - 3/200*p**6 - 1/100*p**5 - 3/350*p**7 - 1/560*p**8 + 0*p. Factor f(w).
-3*w**2*(w + 1)**3/5
Let j(m) be the second derivative of 1/10*m**5 + 0*m**3 + 22*m + 0*m**2 + 1/30*m**6 + 1/12*m**4 + 0. Factor j(c).
c**2*(c + 1)**2
Suppose -5*i + 36 = -3*t + 13, 0 = 4*i - 16. Let b be (37/370)/(t/(-5)). Solve 0*p**2 + 0 - b*p**3 + 0*p**4 + 0*p + 1/2*p**5 = 0 for p.
-1, 0, 1
Suppose 590*k - 635*k - k**2 + 82 + 6*k**2 + 18 = 0. Calculate k.
4, 5
Let y(s) be the first derivative of 2/13*s**2 + 0*s - 3/26*s**4 + 14 - 2/39*s**3. Factor y(t).
-2*t*(t + 1)*(3*t - 2)/13
Find j, given that 6*j + 30*j**3 + 2*j + 7*j**2 - 37*j**2 + 14*j**4 + 2*j**5 + 56*j**2 = 0.
-4, -1, 0
Let c be ((-2)/9)/(1230/(-108) + 11). Find n, given that 4/7 + 12/7*n**2 + c*n**3 + 12/7*n = 0.
-1
Suppose -3 = -u - 4, 4*u = j - 78. Let t = 593/8 - j. What is b in -3/8*b**2 + t*b**3 + 0 + 1/8*b**5 + 3/8*b**4 - 1/4*b = 0?
-2, -1, 0, 1
Let o(p) be the first derivative of -p**4/10 + 8*p**3/15 + 7*p**2/5 - 4*p + 181. Factor o(g).
-2*(g - 5)*(g - 1)*(g + 2)/5
Suppose 9*i - 76 = -58. Let p(r) be the second derivative of 0 + 49/3*r**4 - 4*r - 40/3*r**3 + 13*r**5 - 8*r**i. Find s, given that p(s) = 0.
-1, -2/13, 2/5
Let z(g) be the second derivative of -g**5/5 + 116*g**4/3 + 78*g**3 - 3*g + 53. Factor z(d).
-4*d*(d - 117)*(d + 1)
Let r(v) = v**3 - 12*v**2 - 14*v + 489. Let u be r(19). Factor -2500/3 - 5600/3*i**2 - 68*i**4 - 1580/3*i**3 - u*i - 10/3*i**5.
-2*(i + 5)**4*(5*i + 2)/3
What is p in -2/5*p**3 + 0*p**2 + 2/5*p + 0 = 0?
-1, 0, 1
Let i(z) = -z + 8. Suppose 3*y - u = -12 + 1, -4*y = -5*u + 33. Let n be i(y). Factor n*h + 2*h**3 + 2 + 17/2*h**2.
(h + 2)**2*(4*h + 1)/2
Let y(p) be the second derivative of -2*p**7/35 + 22*p**6/75 - 14*p**5/25 + 2*p**4/5 + 2*p**3/15 - 2*p**2/5 + 73*p. Let y(a) = 0. What is a?
-1/3, 1
Let q be (-14)/(-21)*(-6)/(-1). Factor 4/7*c**2 - 2/7 - 2/7*c**q + 0*c**3 + 0*c.
-2*(c - 1)**2*(c + 1)**2/7
Let f be (-293923)/(-6963) + (-6)/11. Factor -f + 50/3*j - 5/3*j**2.
-5*(j - 5)**2/3
Suppose -8 = -u - 3*u. Solve -8*o - 5*o**4 + 17*o**4 + 0*o**2 + 4*o**5 + 3*o**3 + o**3 - 12*o**u = 0 for o.
-2, -1, 0, 1
Let w be (-63)/42*(-6)/(-21) - (-17)/7. Solve 2/5*n**3 + 6/5*n - 18/5 + 2*n**w = 0 for n.
-3, 1
Let a(j) = -52*j**5 - 26*j**3 - 9*j**3 - 60*j**4 + 15*j**3 + 7. Let d(q) = 51*q**5 + 60*q**4 + 20*q**3 - 6. Let l(b) = 6*a(b) + 7*d(b). Factor l(u).
5*u**3*(3*u + 2)**2
Let c(m) be the first derivative of -m**5/30 - m**4/18 - 27*m - 23. Let l(d) be the first derivative of c(d). Factor l(w).
-2*w**2*(w + 1)/3
Let -19/5*d**4 - 68/5*d - 2/5*d**5 + 16/5*d**3 + 53/5*d**2 + 4 = 0. What is d?
-10, -2, 1/2, 1
Suppose 4*x = -5*p + 5, -x + 5*p + 12 = -8. Suppose -3*v - h + 6 = 0, x*h + 10 = -