60*f**2 - 1230. Factor w(l).
5*l*(l - 9)*(l - 2)**2*(l + 4)
Let i(y) be the third derivative of 1/120*y**5 - 3*y**2 + 0 + 0*y + 0*y**3 - 1/2*y**4. Determine c, given that i(c) = 0.
0, 24
Let r(j) = 15*j**3 - 1179*j**2 + 1284*j + 48. Let q(v) = 3*v**3 - 236*v**2 + 258*v + 10. Let a(i) = -24*q(i) + 5*r(i). Factor a(b).
3*b*(b - 76)*(b - 1)
Find t such that 61*t + 111*t**3 - 36*t**3 - 3*t**5 + 38*t - 180*t**2 - 3*t + 12*t = 0.
-6, 0, 1, 2, 3
Let r(d) be the first derivative of d**6/15 + 46*d**5/25 + 77*d**4/5 + 668*d**3/15 + 293*d**2/5 + 182*d/5 + 1442. Suppose r(l) = 0. Calculate l.
-13, -7, -1
Let y(a) be the first derivative of 2*a**3/3 + 214*a**2 - 1302*a - 7459. Factor y(i).
2*(i - 3)*(i + 217)
Factor 1/6*a**5 + 1261*a**3 - 3855735 + 73/3*a**4 + 24336*a**2 - 19773/2*a.
(a - 10)*(a + 39)**4/6
Suppose -3*s - 20 = 4*v + 11, 4*s = 3*v + 17. Let g(x) = 69*x + 486. Let y be g(v). Factor -3/2*b**4 - 4*b**2 + 9/4*b + 1/4*b**5 - 1/2 + 7/2*b**y.
(b - 2)*(b - 1)**4/4
Suppose -249*n + 245*n - 3*l + 5 = 0, 0 = 4*n + 8*l + 20. Let d(j) be the third derivative of -j**2 + 0*j + 0*j**4 + 1/360*j**n - 1/9*j**3 + 0. Factor d(a).
(a - 2)*(a + 2)/6
Let i be (-3)/2412*-358*-2. Let o = -15/67 - i. Let -2*s**2 - o*s**3 - 2*s - 2/3 = 0. Calculate s.
-1
Find x, given that -x**4 + 10*x**4 - 13*x**4 + 140*x**2 + 268*x - 76*x - 56*x**3 = 0.
-16, -1, 0, 3
Let y(m) be the first derivative of m**4/2 - 254*m**3/15 + 34*m**2 - 96*m/5 + 1247. Factor y(g).
2*(g - 24)*(g - 1)*(5*g - 2)/5
Suppose -248*t = -242*t - 768. Find j such that t + 5*j**2 + 21*j + 29*j - 3 = 0.
-5
Let x(u) = 3*u**2 - 27*u - 16. Let n(s) = -s**2 + 9*s + 5. Let m(b) = -7*n(b) - 2*x(b). Let g be m(12). Suppose g - 69 - 10*i + 21 + 5*i**2 = 0. Calculate i.
-1, 3
Suppose -5*l - 25 = 0, 40 + 6 = 2*x + 2*l. Find s such that x*s**3 - 19*s**5 + 12 + 22*s**5 - 4*s**3 - 18*s**4 + 6*s**2 - 27*s = 0.
-1, 1, 4
Let x(l) = -289*l**4 - 359*l**3 - 70*l**2 - 4*l + 4. Let d(z) = -z**3 + z**2 + 2. Let g(r) = -6*d(r) + 3*x(r). Factor g(c).
-3*c*(c + 1)*(17*c + 2)**2
Let s be 1/(-6)*-3*36. Factor -s*r**2 - 4*r**3 - 25*r**2 + 0*r**3 + 7*r**2.
-4*r**2*(r + 9)
Let r be (-1064)/1140*400/(-35). Let -r - 4/3*u**2 + 12*u = 0. Calculate u.
1, 8
Factor -1/5*d**2 + 6324/5*d - 9998244/5.
-(d - 3162)**2/5
Let g = -197293/3 - -65768. Suppose 1/3*x**3 + 5/3 + 7/3*x**2 + g*x = 0. Calculate x.
-5, -1
Let m = 9953 - 49762/5. Let f(b) be the first derivative of 1/6*b**6 - 15 + 0*b**3 + 0*b**2 - m*b**5 + 0*b + 1/2*b**4. Factor f(s).
s**3*(s - 2)*(s - 1)
Let q be 276/8 - (-4)/8. Let h be q*(-1 + -2 + 4). Determine b so that 72*b**2 - 62*b + h*b - b**5 - 66*b**3 + 24*b**4 - 2*b**5 = 0.
0, 1, 3
Let p(x) be the third derivative of 5*x**2 + 5/3*x**4 - 10/3*x**3 + 0 + 1/42*x**7 - 1/4*x**5 + 7*x - 1/12*x**6. Suppose p(r) = 0. What is r?
-2, 1, 2
Let v(u) = -4*u - 37. Let o be v(-10). Let z be o/(36/8) - 56/120. Factor 2/5 + 1/5*b - z*b**2.
-(b - 2)*(b + 1)/5
Let l(u) = 2*u**3 - 19*u**2 - u + 4. Let s(p) = -p**3 + 10*p**2 - 2. Let z(v) = -3*l(v) - 5*s(v). Let d be z(7). Factor 23*h**3 + 1 - 8*h - 1 - d*h**3 + 4*h**2.
4*h*(h - 1)*(h + 2)
Let f(v) be the first derivative of 6*v**4 - 32/3*v**3 + 0*v - 2/3*v**6 + 6*v**2 + 86 + 0*v**5. What is z in f(z) = 0?
-3, 0, 1
Let g(q) = -q**3 - 2*q**2 + q - 31. Let p(a) = 5*a**4 - 176*a**3 + 1728*a**2 - 6224*a + 4469. Let b(x) = 6*g(x) - p(x). Factor b(r).
-5*(r - 19)*(r - 7)**2*(r - 1)
Factor -72*r - 1/2*r**2 + 296.
-(r - 4)*(r + 148)/2
Let a(v) be the third derivative of 5*v**8/21 + 1178*v**7/315 - 62*v**6/45 - 28*v**5/9 - 2*v**2 + 6194*v. Find i, given that a(i) = 0.
-10, -2/5, 0, 7/12
Let i be (-22)/(-209) - (4 + -501*6/684). Suppose -23/2*f**3 + i*f**4 + 0 + 60*f**2 + 72*f = 0. Calculate f.
-1, 0, 12
Factor -71 - 1/2*a**2 + 73/2*a.
-(a - 71)*(a - 2)/2
What is m in -148/13*m**2 - 6/13*m**3 - 4 + 206/13*m = 0?
-26, 1/3, 1
Suppose 3*u = -2*w, -5*u + 4 = -4*w + 26. Suppose 94*j**3 - 183*j**3 + 28*j + 85*j**w - 16*j**2 + 40 = 0. Calculate j.
-5, -1, 2
Let v be 2303/42 - 54 - (-2)/3. Suppose -v*a**3 + a**5 - 1/2*a**2 + 1/2*a + 1/2*a**4 + 0 = 0. What is a?
-1, 0, 1/2, 1
Let r(x) be the first derivative of x**3 - 2061*x**2/2 + 2058*x + 1299. Solve r(v) = 0 for v.
1, 686
Suppose 3*d + 3*z + 6 = 0, 8*z = -5*d + 4*z - 5. Suppose 24*u**4 - 24*u**2 - 27*u - 361*u**5 + 358*u**5 + 32*u**d - 2*u**3 = 0. Calculate u.
-1, 0, 1, 9
Let w = 429/16 + -2097/80. Factor 0*o + 0*o**2 + 0 + 0*o**3 + 12/5*o**4 + w*o**5.
3*o**4*(o + 4)/5
Let x(p) = 8*p**2 + 13*p - 21. Let w(c) = 3*c**2 + 7*c - 12. Let t(i) = -5*w(i) + 2*x(i). Suppose t(u) = 0. Calculate u.
3, 6
Let o(n) be the third derivative of 0 + 0*n**4 + 4/105*n**7 - 1/84*n**8 + 0*n**3 - 36*n**2 + 0*n**5 - n - 1/30*n**6. Solve o(p) = 0.
0, 1
Factor 1973*h + 3*h**2 + 438 + 1899*h - 3647*h.
3*(h + 2)*(h + 73)
Let y = 157044 - 157042. Suppose 104/3 + 34/3*r**y - 112/3*r - 2/3*r**3 = 0. Calculate r.
2, 13
Let y(d) = d**3 + d. Let x be ((-20)/90)/(3/(-27)). Let z(j) = 4*j**3 + 5*j**2 + 9*j. Let u(n) = x*z(n) - 6*y(n). Determine o so that u(o) = 0.
-3, -2, 0
Determine u, given that -422/11*u**3 - 718/11*u**2 - 202/11*u - 8/11*u**4 + 102/11 = 0.
-51, -1, 1/4
Let q(d) = -167*d**3 - 199*d**2 - 1319*d - 1057. Let h(l) = 29*l**3 + 33*l**2 + 220*l + 176. Let g(c) = 23*h(c) + 4*q(c). Factor g(i).
-(i + 1)*(i + 6)*(i + 30)
Suppose -17*k = -1189178 + 1189127. Factor 0 + 0*r - 5/3*r**k + 2/3*r**2.
-r**2*(5*r - 2)/3
Let u = -35 - -31. Let l(d) be the third derivative of -d**7/42 + d**6/8 + d**2. Let p(c) = c**4 - 4*c**3. Let m(w) = u*l(w) - 15*p(w). Factor m(h).
5*h**4
Let 132 - 4/3*b**2 + 40*b = 0. Calculate b.
-3, 33
Determine l, given that 135/2*l**2 + 5/6*l**4 + 105*l + 0 - 110/3*l**3 = 0.
-1, 0, 3, 42
Let o(g) be the second derivative of 3/8*g**5 + 8*g + 0*g**2 - 1/2*g**3 + 0 + 1/5*g**6 - 7/8*g**4. Find i, given that o(i) = 0.
-2, -1/4, 0, 1
Let s(z) be the first derivative of z**5/5 - 17*z**4/2 - 109*z**3/3 - 37*z**2 - 66. Solve s(q) = 0.
-2, -1, 0, 37
Factor -2*a**2 - 164*a + 83*a - a**2 - 24*a + 468.
-3*(a - 4)*(a + 39)
Determine d so that 180 + 450*d**3 + 493*d**5 + 65*d**2 - 217*d**5 - 474*d + 15*d**4 - 326*d**5 - 186*d = 0.
-2, 3/10, 1, 3
Let m(h) = -3*h**2 - 65*h + 130. Let b(d) = 5*d**2 + 64*d - 130. Let q(a) = 2*b(a) + 3*m(a). Factor q(k).
(k - 65)*(k - 2)
Let f(y) be the second derivative of 2*y**6/15 + 21*y**5/20 - 9*y**4/4 - 100*y**3/3 - 24*y**2 - 344*y - 2. Let f(l) = 0. Calculate l.
-4, -1/4, 3
Let v(j) be the third derivative of j**2 + 0*j + 1/80*j**5 - 107 + 1/16*j**4 - j**3. Factor v(w).
3*(w - 2)*(w + 4)/4
Let h = 102825 + -102823. Factor 0 - 1/6*x**4 + 2*x - 8/3*x**h + 7/6*x**3.
-x*(x - 3)*(x - 2)**2/6
Let t(i) be the third derivative of 2/105*i**7 + 2/15*i**5 - 3*i**2 + 2/15*i**6 + 1 - 2*i**3 - 2/3*i**4 + 0*i. Factor t(j).
4*(j - 1)*(j + 1)**2*(j + 3)
Let n(m) = 7*m - 21. Let v be n(-47). Let x be (-70)/v - (-1 - 8/10). Factor -2/5*w**x - 392/5 - 56/5*w.
-2*(w + 14)**2/5
Suppose w - 3*x - 31 = 0, 0 = -w - 3*x + 17 + 26. Determine d, given that 3*d**2 + 34*d**4 + 3*d**2 - 11 + 3 - w*d**4 + 12*d - 7*d**3 = 0.
-2, 2/3, 1
Suppose -5*v - 21 = -3*d, 55 = -d + 5*v + 72. Factor -1/2*l - 10 + 1/2*l**d.
(l - 5)*(l + 4)/2
Let h(n) be the third derivative of -n**6/24 + 25*n**5/12 + 905*n**4/24 + 775*n**3/6 + 1318*n**2 + 2*n + 1. Let h(u) = 0. Calculate u.
-5, -1, 31
Let w(s) be the first derivative of s**5/70 - s**4/6 - 40*s**3/21 - 44*s**2/7 + 69*s + 148. Let g(m) be the first derivative of w(m). Factor g(h).
2*(h - 11)*(h + 2)**2/7
Let i(j) = 5*j**4 + 180*j**3 + 895*j**2 + 1085*j - 2160. Let q(d) = 2*d**4 + 91*d**3 + 447*d**2 + 543*d - 1080. Let l(r) = 3*i(r) - 5*q(r). Factor l(o).
5*(o - 1)*(o + 6)**3
Let q(s) = -2*s**2 - s - 3. Let a(u) be the second derivative of -3*u**4/4 - u**3/2 - 3*u**2 + 162*u. Let n(v) = -3*a(v) + 12*q(v). Solve n(x) = 0 for x.
-2, 3
Let a(q) = 49*q**2 + 41*q. Let s(b) = -222*b**2 - 165*b. Let y(x) = -9*a(x) - 2*s(x). Factor y(m).
3*m*(m - 13)
Let w(q) be the third derivative of -q**6/120 + 13*q**5/20 - 143*q**4/24 + 35*q**3/2 + q**2 + 173*q - 7. Solve w(k) = 0.
1, 3, 35
Let x be (59/(-12) + -3)*((-17408)/(-320) + -55). Find k such that x*k + 2*k**2 + 5/2 - 1/4*k**3 = 0.
-1, 10
Suppose -4*c + 323 = -5*f - 273, 2*f = 2*c - 238. Let g be 15/(90/(-64))*6/f. Fa