c**2 + 0.
2*c*(c + 6)*(c + 15)/7
Suppose -616 = -6*k - 38*k. Suppose -9*g = -2*g - k. Factor -2*a**g + 1/2*a**4 + 0 - a**3 + 4*a.
a*(a - 2)**2*(a + 2)/2
Let r be 47/22 + -2 - (-1587)/(-11638). Determine c so that -1/5*c**2 - 1/10*c**4 + 0*c + 3/10*c**3 + r = 0.
0, 1, 2
Let a(u) be the second derivative of -64*u**2 - 4/3*u**6 + 160/3*u**3 + 79*u - 80/3*u**4 + 0 + 2/21*u**7 + 8*u**5. Factor a(g).
4*(g - 2)**5
Let j(n) be the third derivative of n**8/2880 - n**7/280 - n**6/80 + 91*n**5/60 - 105*n**2. Let s(r) be the third derivative of j(r). Factor s(w).
(w - 3)*(7*w + 3)
Let j(n) be the first derivative of -n**4/2 - 46*n**3 - 504*n**2 - 1952*n + 1511. Let j(m) = 0. What is m?
-61, -4
Let p(z) = -6*z + 26. Let i(s) = -s**2 + 39*s + 130. Let u be i(42). Let o be p(u). Factor -9/5*y + 0 - 12/5*y**o - 3/5*y**3.
-3*y*(y + 1)*(y + 3)/5
Let k = 197 - 194. What is w in 2*w - 16*w**2 - 2*w - 81*w**4 + 85*w**4 - 12*w**k = 0?
-1, 0, 4
Let g(b) = 11*b**3 - 9 - 34*b**2 + 106*b**4 - 64*b**4 - 9*b + 43*b - 41*b**4. Let h(z) = -z**4 + z**3 - 1. Let v(s) = -2*g(s) - 6*h(s). Factor v(l).
4*(l - 3)*(l - 2)*(l - 1)**2
Find i such that 2/3*i**4 + 4/3*i + 13/3*i**2 + 0 + 11/3*i**3 = 0.
-4, -1, -1/2, 0
Determine l so that -3*l**3 - 53*l**2 + 2191*l - 4725 - 106*l**2 - 4304*l + 1878*l + 2050*l = 0.
-63, 5
Let o = 14 - 8. Suppose 5*j - 16 = 3*j - 4*s, 0 = -3*s + o. Determine m, given that 4*m**3 + j*m - 7*m**3 - m**3 = 0.
-1, 0, 1
Let u(t) be the first derivative of 4*t**3/15 - 752*t**2/5 + 1258. Factor u(r).
4*r*(r - 376)/5
Solve 4/5*u**3 - 32/5 - 16/5*u - 4/5*u**4 + 24/5*u**2 = 0 for u.
-2, -1, 2
Let g = -76 - -75. Let t(x) = -14*x**2 - 17*x - 3. Let n(c) = c**2 + c. Let o(l) = g*t(l) - 2*n(l). Factor o(u).
3*(u + 1)*(4*u + 1)
Let v = -379 + 374. Let x be 2/4*0/v. Factor 0*i - 2/9*i**5 + 2/3*i**4 + 2/9*i**2 - 2/3*i**3 + x.
-2*i**2*(i - 1)**3/9
Let w be 2/(-27) - (-112)/54 - 2. Suppose -l - 3 = -t - w, -3*l = 0. Factor -1/2 - 1/6*k**2 + 1/6*k**t - 5/6*k.
(k - 3)*(k + 1)**2/6
Let l(h) be the second derivative of h**7/105 - 73*h**6/75 + 1219*h**5/50 + 821*h**4/6 + 4256*h**3/15 + 1444*h**2/5 + 148*h. Factor l(n).
2*(n - 38)**2*(n + 1)**3/5
Suppose -m = 5*g - 73, -5*m - 12*g + 305 = -7*g. Suppose -42*s + m = -26. Factor -42/5*a + 147/5 + 3/5*a**s.
3*(a - 7)**2/5
Let u(r) = r**3 - 5*r**2 - 3*r + 1. Let b(a) = -20*a**3 - 84*a**2 - 912*a + 16112. Let v(c) = b(c) + 16*u(c). Determine w, given that v(w) = 0.
-24, 7
Let f(p) = -31*p**3 - 30*p**2 - 50*p - 17. Let x(a) = 11*a**3 + 10*a**2 + 17*a + 6. Let c = 175 - 181. Let v(w) = c*f(w) - 17*x(w). Factor v(j).
-j*(j - 11)*(j + 1)
Suppose 13*b - 2*b - 22 = 0. Determine k so that 6*k + 29*k - 8*k**b - 3*k**2 + 6*k**2 = 0.
0, 7
Let m be (10/3)/(6/(-9)). Let r(v) = -v**4 - 8*v**3 - 30*v**2 + 3*v + 3. Let t(h) = -15*h**3 - 60*h**2 + 5*h + 5. Let c(u) = m*r(u) + 3*t(u). Factor c(a).
5*a**2*(a - 3)*(a + 2)
Let r(z) be the first derivative of -4*z**6/3 - 114*z**5/5 - 155*z**4/2 + 100*z**3 - 2400. Determine g so that r(g) = 0.
-10, -5, 0, 3/4
Let z(j) = -2*j**2 + 58*j + 52. Let k(d) = -3*d**2 + 115*d + 104. Let c(i) = -4*k(i) + 7*z(i). Factor c(f).
-2*(f + 1)*(f + 26)
Let g(f) be the second derivative of 2*f**6/135 + 2*f**5/45 - 7*f**4/27 - 40*f**3/27 - 8*f**2/3 + 710*f. Solve g(d) = 0 for d.
-2, -1, 3
Let o = -741404/9 + 3707074/45. Factor -o*a - 4 + 2/5*a**2.
2*(a - 5)*(a + 2)/5
Let d(x) = -19*x**3 - 1303*x**2 - 2437*x - 1297. Let s(j) = j**3 + j**2 - 8*j + 1. Let g(y) = d(y) + 16*s(y). Suppose g(h) = 0. What is h?
-427, -1
Let -3636/13*a + 1652562/13 + 2/13*a**2 = 0. What is a?
909
Let v(k) be the first derivative of k**6/6 - 3*k**5 + 3*k**4 + 28*k**3/3 + 2490. Suppose v(n) = 0. Calculate n.
-1, 0, 2, 14
Suppose -1816*u + 7610 - 2162 = 0. Factor -1/6*g**4 + 1/6*g**5 + 5/6*g**2 + 0 - 1/3*g - 1/2*g**u.
g*(g - 1)**3*(g + 2)/6
Factor -11*b**4 + 551*b**2 - 257*b**2 - 3*b**5 - 231*b**3 + 37*b**4 + 22*b**4.
-3*b**2*(b - 7)**2*(b - 2)
Suppose 5*i + 2*z = -30, 201*z - 203*z = 13*i + 14. Suppose 7688/5 + 2/5*p**i + 248/5*p = 0. Calculate p.
-62
Let m(i) be the second derivative of 0*i**2 + 0*i**3 - 1/2*i**4 - 3/140*i**5 - 6*i + 20. Factor m(n).
-3*n**2*(n + 14)/7
Let q = 21398/25 + -20358/25. Factor -q - 192/5*z + 4/5*z**3 - 36/5*z**2.
4*(z - 13)*(z + 2)**2/5
Let z(y) be the second derivative of -y**4/6 - 5*y**3 - 56*y**2 - 482*y. Factor z(u).
-2*(u + 7)*(u + 8)
Suppose 50 - 17 = 11*t. Factor -83 + 8*q**t - 27*q**2 - 4*q**5 + 8*q**4 + 28*q + 17*q**2 + 75 - 22*q**2.
-4*(q - 1)**4*(q + 2)
Let b(v) be the first derivative of -v**6/6 - 17*v**5/5 - 55*v**4/2 - 334*v**3/3 - 465*v**2/2 - 225*v - 2036. Factor b(t).
-(t + 1)*(t + 3)**2*(t + 5)**2
Let q = 1183/36 + -343/36. Solve -15*z**3 + 0*z - q*z**2 - 5/3*z**4 + 0 = 0 for z.
-7, -2, 0
Suppose 5*p + 23 = -m - 124, -2*p = 2*m + 54. Let z be ((-207)/p - 5) + 4/8. Factor 6/5*n**2 + 8/5 + z*n + 1/5*n**3.
(n + 2)**3/5
Let m(t) be the third derivative of -t**6/780 - 467*t**5/390 + 946*t**4/39 - 7600*t**3/39 - 7154*t**2. Determine f so that m(f) = 0.
-475, 4
Suppose -2*z - 3*z + 844 = v, z = -3*v + 166. Solve -66 + 16*m - 104*m**2 - 73 + 139 + z*m**3 = 0 for m.
0, 4/13
Let o(y) = -1882*y + 7533. Let b be o(4). Let -b + 5/2*d**2 - 5/2*d = 0. Calculate d.
-1, 2
Let f(x) = -637*x**3 + 4226*x**2 - 3016*x + 612. Let s(z) = 3440*z**3 - 22820*z**2 + 16285*z - 3305. Let w(g) = -65*f(g) - 12*s(g). Factor w(r).
5*(r - 6)*(5*r - 2)**2
Let x(f) be the second derivative of -f - 4/15*f**5 + 15/2*f**2 + 1/6*f**4 + 0*f**3 + 0. Let z(b) be the first derivative of x(b). Solve z(w) = 0.
0, 1/4
Suppose 2*v = -45*v + 74*v. Factor -57/2*d**2 - 3*d**3 - 27/2*d + v.
-3*d*(d + 9)*(2*d + 1)/2
Suppose 4*p = 4*q + 32, -4*p - 13 = 69*q - 64*q. Let x(i) be the first derivative of 4/7*i**2 - 2/21*i**p - 8/7*i + 4. Factor x(t).
-2*(t - 2)**2/7
Let m(p) be the second derivative of 2/5*p**5 + 1/2*p**4 + 3*p + 0*p**2 + 1/42*p**7 + 7/45*p**6 + 56 + 5/18*p**3. Determine x, given that m(x) = 0.
-5/3, -1, 0
Solve 820/3 - 2/3*m**3 - 994/3*m + 176/3*m**2 = 0.
1, 5, 82
Let z(s) be the third derivative of 0 + 0*s**3 + 8/15*s**5 - 2*s - s**4 + 14*s**2 + 1/105*s**7 - 7/60*s**6. Suppose z(p) = 0. Calculate p.
0, 2, 3
Let v(d) be the second derivative of 1350*d**2 + 1 + 1/4*d**4 + 30*d**3 + d. Factor v(w).
3*(w + 30)**2
Suppose -j + 23 = 4*v, -9*v + 5*v + 30 = 2*j. Factor 39*o**4 - j*o**4 - 527*o**3 + 543*o**3 + 12*o**5.
4*o**3*(o + 2)*(3*o + 2)
Suppose 25*d - 136 = -33*d - 20. Factor -4/9*v**3 - 32/9*v**d - 28/9*v + 0.
-4*v*(v + 1)*(v + 7)/9
Let j(o) be the second derivative of o**4/54 + 506*o**3/9 + 64009*o**2 + 77*o. Factor j(y).
2*(y + 759)**2/9
Let z(w) be the second derivative of w**10/10080 - w**9/1260 + w**8/560 + w**4/3 + 5*w**3/6 - 49*w - 2. Let u(x) be the third derivative of z(x). Factor u(v).
3*v**3*(v - 2)**2
Suppose 12*s - 4 = 9*s - 4*u, -4*u = 8. Suppose 3*a - a = -s*w + 260, 5*a = -3*w + 195. Factor 38*b**4 + 15 - 4*b**4 + 90*b**3 + b**4 + w*b + 5*b**5 + 110*b**2.
5*(b + 1)**4*(b + 3)
Let x(u) = -u**3 - 6*u**2 - 2*u + 15. Let y be x(-5). Let j(o) = -3*o**2 + 2. Let r be j(y). Factor -z**3 + 20 + 65*z**r - 60*z + 5*z**4 + 16*z**3 - 45*z**3.
5*(z - 2)**2*(z - 1)**2
Let g be (4/68 - (-38)/(-646))*(-2)/4. Determine a so that 1/4*a**2 + g*a + 0 - 1/8*a**3 = 0.
0, 2
Let r(f) = 7*f - 9. Let q be r(-3). Let y be (-1 + (-17)/(-21))/(10/q). Factor -1/7*x**2 - y + 4/7*x.
-(x - 2)**2/7
Let z = -3378/7 + 13533/28. Let n(g) be the second derivative of 3/20*g**5 + 0*g**3 + 0*g**2 - z*g**4 + 0 - 14*g. What is y in n(y) = 0?
0, 3
Suppose -3*h + 27 = -3*j, -4 - 20 = -4*h + j. Let -272*x**4 - 96*x - 73*x**5 - 3*x**4 + 13*x**h - 10 - 445*x**3 + x - 315*x**2 = 0. Calculate x.
-2, -1, -1/3, -1/4
Solve -910 + r**5 + 61889*r**3 - 61616*r**3 + 1509*r**2 - 69*r**4 + 312*r - 1118 + 2*r**5 = 0.
-2, 1, 13
Factor 115*l - 2145/2 - 5/2*l**2.
-5*(l - 33)*(l - 13)/2
Suppose -1 = -w + 1. Let s(j) = -j + 1 + 59*j**w - 60*j**2 - 1. Let o(v) = 5*v**2 + 4*v - 1. Let b(n) = 3*o(n) + 12*s(n). Solve b(q) = 0 for q.
-1, 1
Suppose 70*n + 863*n = 0. Suppose -2*k - 10 = -7*k + 5*l, -8 = -4*k - 2*l. Factor -3*m**4 + 0 + 3/2*m**5 + n*m**3 - 3/2*m + 3*m**k.
3*m*(m - 1)**3*(m + 1)/2
Suppose -2/3*p**2 + 134*p - 400/3 = 0. What is p?
1, 200
Let g(k) = 250*k**3 + 70*k**2 + 5*k - 10. Let