 Factor -1/6*n**2 + h - 1/6*n.
-n*(n + 1)/6
Let f(g) = -31*g + 205. Let t be f(6). Suppose -4*i = 5*r - 20, 2*r = 27 - t. Let -2/13*z**2 + 10/13*z**3 - 8/13*z**4 + 0*z + i = 0. Calculate z.
0, 1/4, 1
Let g(f) be the third derivative of 8/3*f**3 + 0*f + 0 + 71*f**2 - 2/35*f**7 + 1/84*f**8 - 2*f**4 + 11/15*f**5 - 1/30*f**6. Factor g(a).
4*(a - 2)*(a - 1)**3*(a + 2)
Suppose -33 = -3*o - 4*j, 210*j = -2*o + 214*j - 18. Let -52/5*r**2 - 26/5*r + 12/5 - 14/5*r**o = 0. What is r?
-3, -1, 2/7
Let c(y) be the third derivative of -3*y - 23/120*y**4 + 3/100*y**5 + 1/2*y**3 - 1/600*y**6 + 0 - 29*y**2. Let c(l) = 0. Calculate l.
1, 3, 5
Factor 24 - 6*n**2 - 2*n + 1/2*n**3.
(n - 12)*(n - 2)*(n + 2)/2
Let l(v) = v**5 - 4*v**3 + 3. Let h(f) = 12*f**5 - 108*f**4 - 264*f**3 + 6*f**2 + 207*f + 147. Let a(b) = h(b) - 15*l(b). Factor a(z).
-3*(z - 1)*(z + 1)**3*(z + 34)
Suppose -29 = -33*a + 4. Let u(d) = 0*d**3 - d**2 + 5*d - 5*d + d**3 + d. Let q(w) = -10*w**3 - 5*w. Let g(n) = a*q(n) + 5*u(n). Suppose g(h) = 0. What is h?
-1, 0
Let a be 78/104 + (-67 - -73 - 246/40). Factor 648/5 + a*f**3 + 324/5*f + 54/5*f**2.
3*(f + 6)**3/5
Let b(t) = 48*t - 384. Let k be b(8). Let z(x) be the second derivative of k*x**2 + 1/8*x**4 + 1/4*x**3 + 0 - 3*x. Factor z(d).
3*d*(d + 1)/2
Let v(j) = j**2 + j + 262. Let f be v(0). Let k be f/(-2)*13/(-13). Find l, given that 279*l**4 - 128*l**4 + 23*l + 112*l**2 + 9*l + 88*l**3 - k*l**4 = 0.
-2, -2/5, 0
Let p(z) be the first derivative of z**4/26 - 64*z**3/39 + 61*z**2/13 - 60*z/13 - 249. Factor p(d).
2*(d - 30)*(d - 1)**2/13
Determine f, given that 0 + 4/3*f**2 - 1/9*f**3 - 20/9*f = 0.
0, 2, 10
Let j be (36/(-168))/(360/(-7)) - 0. Let u(y) be the third derivative of -1/48*y**4 + 0*y + 0 + 0*y**3 - 25*y**2 + j*y**5. Find o such that u(o) = 0.
0, 2
Let f be (7 - (-12)/(-8)*2) + 0. Let i be (f - (-125)/(-30))*(-12 + -15). Factor 9/2*a - 1/2 - i*a**3 + 1/2*a**2.
-(a - 1)*(a + 1)*(9*a - 1)/2
Let k(h) = 6*h**2 + 963*h - 1455. Let n be k(-162). Suppose -320*d**n + 0*d - 61/3*d**4 + 0 - 1/3*d**5 - 300*d**2 = 0. What is d?
-30, -1, 0
Let w(i) be the third derivative of 41*i**2 + 1/9*i**4 + 0 - 2/45*i**5 - 1/180*i**6 + 2*i + 0*i**3 + 1/315*i**7. Factor w(r).
2*r*(r - 2)*(r - 1)*(r + 2)/3
Let g be ((-1)/6)/1 - (-23 + 1346/60). Let t be ((-63)/(-90))/(1/4). Determine k, given that -12/5*k**2 - 4/5*k**4 + 4/5 + g*k - t*k**3 = 0.
-2, -1, 1/2
Let l(i) be the first derivative of 41/6*i**2 + 20/3*i + 22/9*i**3 - 70 + 1/12*i**4. Suppose l(k) = 0. What is k?
-20, -1
Let j = 48132 - 144395/3. Suppose -4/3*k + 4/3 - j*k**2 + 1/3*k**3 = 0. Calculate k.
-2, 1, 2
Determine m so that 234/5*m**3 - 16/5 + 484/5*m**2 + 24/5*m = 0.
-2, -2/9, 2/13
Factor 560 + 2/5*a**3 + 68/5*a**2 + 152*a.
2*(a + 10)**2*(a + 14)/5
Let r(o) be the second derivative of -8*o - 1/66*o**4 - 19/33*o**3 + 0 - 18/11*o**2. Determine l so that r(l) = 0.
-18, -1
Let x(i) = -86 + 219*i**2 + 156 + 6*i**3 - 16*i**3 - 5*i**3 - 318*i. Let t(v) = 3*v**3 - 44*v**2 + 63*v - 14. Let w(j) = -22*t(j) - 4*x(j). Factor w(l).
-2*(l - 14)*(l - 1)*(3*l - 1)
Let o(q) be the first derivative of 1/3*q**4 + 2*q**2 - 4/3*q**3 - 27*q - 17. Let k(f) be the first derivative of o(f). Factor k(d).
4*(d - 1)**2
Determine k so that 2*k**2 - 1959*k**3 + 652*k**3 + 4*k**2 - 187*k + 656*k**3 + 652*k**3 = 0.
-17, 0, 11
Let h be 6 - 13/(13/2). Solve 28*b**3 + 4*b**3 - 28*b**h + 56*b**4 - 64*b**2 + 4*b**5 = 0 for b.
-4, 0, 1
Let y(p) be the first derivative of 2/21*p**3 + 2*p**2 + 37 + 26/7*p. Determine x so that y(x) = 0.
-13, -1
Determine r, given that -13352 - 9660 + 356*r + 13377 - 14081 + 260*r - 4*r**2 = 0.
77
Suppose 616445*n = 616357*n + 176. Determine q so that 0 - 2*q**n - 8/11*q**3 - 14/11*q = 0.
-7/4, -1, 0
Let k(f) be the first derivative of 3*f**4/2 + 88*f**3/3 + 93*f**2 - 72*f + 1662. Suppose k(h) = 0. Calculate h.
-12, -3, 1/3
Let b = 2625 + -10627/4. Let r = -2405/76 - b. Find g such that 0 + 0*g + 2/19*g**3 - r*g**2 = 0.
0, 1
Let n(q) = -17*q**2 - 126*q + 391. Let h(a) = 3*a**2 + 25*a - 78. Let f(c) = -11*h(c) - 2*n(c). Solve f(s) = 0 for s.
4, 19
Factor -3321*x**2 + 11*x**5 + 13*x**5 - 588*x**4 - 1075*x**3 + 3397*x**3 - 68 + 1620*x + 68.
3*x*(x - 20)*(2*x - 3)**3
Let l be -36 + 40 - (3 - 1). Suppose 4 = l*o - 4*y, -5*o + 4*y + 8 = -2. What is x in -3/2 - x + 1/2*x**o = 0?
-1, 3
Let c(g) be the first derivative of 51*g**5 - 95*g**4 - 25*g**3 + 3015. Factor c(z).
5*z**2*(3*z - 5)*(17*z + 3)
Find f such that 1/11*f**2 + 0 + 33*f = 0.
-363, 0
Solve -1/2*s**3 - 15 + 1/2*s**4 - 19/2*s**2 + 49/2*s = 0.
-5, 1, 2, 3
Let y(a) = 6*a**2 + 212*a + 934. Let l(r) = -r**2 - 42*r - 187. Let c(h) = 26*l(h) + 5*y(h). Solve c(d) = 0.
-4, 12
Let x = -1925 - -202127/105. Let q(n) be the second derivative of -n + 0*n**2 + 0 + x*n**6 + 4/35*n**5 + 5/21*n**4 + 4/21*n**3. Solve q(f) = 0.
-2, -1, 0
Let c be (30/24)/((-3)/36). Let f(a) = -a**2 - 16*a - 6. Let y be f(c). Solve -10 + 22*o**2 - y*o**3 + 10 - 12*o**4 - 10*o**2 + 12*o - 3*o**5 = 0.
-2, -1, 0, 1
Find m such that 10 + 107*m**2 + 585*m**2 + 2502*m - 487*m - 22*m**2 + 1335*m**2 = 0.
-1, -2/401
Let p(t) be the first derivative of -t**6/2340 + 19*t**5/780 - t**3/3 + 4*t**2 + 63. Let v(g) be the third derivative of p(g). Suppose v(f) = 0. Calculate f.
0, 19
Let b(t) be the second derivative of t**7/14 + 14*t**6/5 + 159*t**5/20 + 13*t**4/2 + 80*t - 10. Factor b(o).
3*o**2*(o + 1)**2*(o + 26)
Let h(u) be the third derivative of u**5/15 - 245*u**4 + 360150*u**3 - 1800*u**2 - 2*u. Factor h(v).
4*(v - 735)**2
Let c(i) = i**2 - i + 1. Let o(y) = -4*y**4 - 4*y**3 + 52*y**2 - 44*y + 12. Suppose -h - 4 = -4*u, 5*u - 10 = 4*h + 28. Let m(r) = h*c(r) + o(r). Factor m(s).
-4*s*(s - 2)*(s - 1)*(s + 4)
Let a be (((0/2)/(-2))/((91 - 44) + -48))/5. Factor 0*c**2 + 0*c**3 + a - 1/3*c**5 + 2/3*c**4 + 0*c.
-c**4*(c - 2)/3
Suppose -1942*x = -1934*x - 2592. Factor x - 24*d + 4/9*d**2.
4*(d - 27)**2/9
Let h be 2 + -4*1/8. Let a be 5 - (6 - -1*(0 - 3)). Factor -3/2 - 21/4*l**a - 21/4*l - h*l**3.
-3*(l + 1)*(l + 2)*(2*l + 1)/4
Let v(q) = 9*q**2 - 12*q + 28. Let z be v(-14). Factor 33*h**4 + 6*h**5 + 0*h**5 + z*h**2 + 2794*h + 2000 + 392*h**3 + 806*h - 5*h**5.
(h + 1)*(h + 2)*(h + 10)**3
Let q(d) be the first derivative of -6/13*d**2 + 2/39*d**3 + 18/13*d + 68. Factor q(u).
2*(u - 3)**2/13
Let j(n) be the first derivative of -3*n**4/20 - 76*n**3/5 - 222*n**2/5 - 593. Factor j(s).
-3*s*(s + 2)*(s + 74)/5
Let f(w) be the third derivative of -1/20*w**5 + 27*w**2 + 0 + 1/80*w**6 + 1/280*w**7 - 1/16*w**4 + 0*w + 3/8*w**3. Factor f(k).
3*(k - 1)**2*(k + 1)*(k + 3)/4
Let o(i) be the second derivative of i**7/252 + 19*i**6/90 + 23*i**5/5 + 472*i**4/9 + 2944*i**3/9 + 1024*i**2 - 155*i + 10. What is s in o(s) = 0?
-12, -8, -2
Let d be ((-11)/(-22))/(2/24) - 4. Find q, given that 4*q**4 - 48*q**d + 52*q + 7*q**4 - 2 - 9*q**4 - 16 + 12*q**3 = 0.
-9, 1
Suppose -30*t + 7 = -29*t - 5*a, 0 = -2*t - 4*a. Let h(f) be the second derivative of -f + 0 - 2*f**3 + 7/3*f**4 + 0*f**t - f**5 + 2/15*f**6. Factor h(x).
4*x*(x - 3)*(x - 1)**2
Let 216*s - 57 - 33*s**2 + 45 - 78 - 18 = 0. What is s?
6/11, 6
Factor -6*p - 88/15 - 2/15*p**2.
-2*(p + 1)*(p + 44)/15
Let r(k) be the second derivative of -34*k**7/105 + 676*k**6/75 - 2204*k**5/25 + 5176*k**4/15 - 7424*k**3/15 - 1024*k**2/5 + 322*k. Suppose r(u) = 0. What is u?
-2/17, 2, 8
Determine u, given that -1/2*u**3 + 4/3*u**4 + 0 - 1/2*u**5 + 0*u - 1/3*u**2 = 0.
-1/3, 0, 1, 2
Let z be (-272)/187*561/(-34) + -24. Factor z + 4/3*k**3 - 1/3*k**4 + 0*k - 4/3*k**2.
-k**2*(k - 2)**2/3
Let d(j) = 776*j**2 + 204090*j + 528. Let r be d(-263). Find g, given that -1/5 + 11/10*g**r + 7/10*g**3 - 7/10*g - 9/10*g**4 = 0.
-1, -2/9, 1
Let a(d) be the first derivative of -5*d**4/24 - 115*d**3/18 - 355*d**2/6 - 100*d - 1112. Find v, given that a(v) = 0.
-12, -10, -1
Let w(t) = -t**2 - 49*t + 14. Suppose -5*l - 5*f = -15, -5*l - 4*f + 5 = -9. Let d(n) = -12*n + 4. Let j(o) = l*w(o) - 9*d(o). Factor j(h).
-2*(h - 4)*(h - 1)
Let t(f) be the second derivative of -f**5/4 + 85*f**4/4 - 1125*f**3/2 + 13365*f**2/2 + 4*f - 23. Factor t(o).
-5*(o - 33)*(o - 9)**2
Let s be ((-12)/22)/(3468/(-3179)). Solve -10*g**2 + 19/2*g + g**4 - s*g**5 + 3*g**3 - 3 = 0 for g.
-3, 1, 2
Let p = 410952/5 + -82184. What is o