*(7*a + 410)
Let a(v) be the first derivative of 5*v**6/6 + 11*v**5 + 175*v**4/4 + 125*v**3/3 - 2209. Factor a(s).
5*s**2*(s + 1)*(s + 5)**2
Let y be (5 + -4)/(225/495) - 4/(-5). Let j(p) be the first derivative of -10 - 23/16*p**2 - 19/32*p**4 - 1/4*p - 5/3*p**y. Find n such that j(n) = 0.
-1, -2/19
Let v(i) = -9*i**3 + 2370*i**2 + 7119*i + 4746. Let z(h) = -8*h**3 + 2369*h**2 + 7118*h + 4746. Let t(p) = 5*v(p) - 6*z(p). Suppose t(d) = 0. Calculate d.
-2, -1, 791
Factor 0*z**2 + 14/15*z**4 + 2/15*z**5 + 0*z + 0 + 4/3*z**3.
2*z**3*(z + 2)*(z + 5)/15
Let x(g) be the third derivative of -g**5/15 + 137*g**4/3 + 368*g**3 + 348*g**2 - 1. Factor x(j).
-4*(j - 276)*(j + 2)
Let v(s) = 8*s**2 - 11*s + 48. Let r be v(11). Let z = r - 893. Let 2/13*n**z + 6/13*n - 8/13 = 0. What is n?
-4, 1
Let a = 502/35 + -71/5. Let g be 13/(468/(-1512)) - -42. Factor a*y**2 + g - 1/7*y.
y*(y - 1)/7
Let f(l) = 2*l**2 - 7*l + 14. Let i(b) = 15*b - 19 + 6 + 3*b - 10*b - b**2. Let y(w) = 2*f(w) + 3*i(w). Determine x, given that y(x) = 0.
-11, 1
Let m(z) be the second derivative of 1/120*z**5 - 27*z + 1/36*z**4 - 1 - 1/36*z**3 - 1/6*z**2. Let m(k) = 0. What is k?
-2, -1, 1
Find o, given that 5248*o - 4210 + 4*o**2 - 4658 - 14112*o = 0.
-1, 2217
Let t = 33 + -25. Suppose 5*f - t = f. Find x such that 6*x**f + 12*x + 3*x**3 + 10*x - 19*x = 0.
-1, 0
Determine c, given that 1/2*c**2 - 520*c + 135200 = 0.
520
Let k be 1 + (-6)/4 + 182/(-936)*-18. Let n(b) be the first derivative of 243/17*b**2 + 1458/17*b + 18/17*b**k + 1/34*b**4 - 18. Factor n(h).
2*(h + 9)**3/17
Let t(f) = -5*f - 5. Let l be t(-2). Suppose -x + 11 = l*z - 4*x, 5*z + 2*x = 26. Determine a, given that 2*a + z - 2*a**2 - 5*a + a = 0.
-2, 1
Let r(d) = 6*d**3 + 340*d**2 + 4688*d - 10888. Let a(o) = -2*o**3 - 113*o**2 - 1563*o + 3633. Let b(t) = -8*a(t) - 3*r(t). Factor b(i).
-2*(i - 2)*(i + 30)**2
Let j(z) be the third derivative of -13/96*z**4 + 0 - 11/240*z**5 - 176*z**2 - z + 1/96*z**6 + 1/8*z**3. Solve j(m) = 0.
-1, 1/5, 3
Suppose -26*y + 27*y - a = 20, a - 72 = -3*y. Suppose 0 = y*p + 7*p - 90. Factor -1/4*g**4 + 0 + 0*g**2 + 1/4*g**p + 0*g.
-g**3*(g - 1)/4
Let s = -603 + 351. Let t be 7/2*(-216)/s. Factor -18/13*h**4 - 84/13*h**t - 50/13*h**2 - 8/13*h + 0.
-2*h*(h + 4)*(3*h + 1)**2/13
Let z(x) = 41*x**2 + 225*x - 211. Let t(v) = -57*v**2 - 337*v + 317. Let u(o) = 5*t(o) + 7*z(o). Factor u(c).
2*(c - 54)*(c - 1)
Let l(t) be the second derivative of -3/2*t**4 + 0*t**3 - 6*t - 3/4*t**5 - 1/10*t**6 + 0*t**2 - 15. Factor l(g).
-3*g**2*(g + 2)*(g + 3)
Let y(k) be the second derivative of -k**4/12 + 17*k**3/3 - 32*k**2 + 3522*k. Find v, given that y(v) = 0.
2, 32
Let l be ((57/380)/((-3)/(-25)))/((-5)/(-3)). Let c(d) be the third derivative of 1/80*d**6 + 75/4*d**4 + l*d**5 + 250*d**3 + 0 + 0*d - 27*d**2. Factor c(f).
3*(f + 10)**3/2
Let u = 76 + -69. Factor q - 10*q**2 + u*q**2 - 3*q**3 + 3*q**4 + 2*q**3.
q*(q - 1)*(q + 1)*(3*q - 1)
Let x = -472570 + 472570. Find z such that -10*z**3 + x + 15/2*z + 5/2*z**5 - 5*z**2 + 5*z**4 = 0.
-3, -1, 0, 1
Let n(g) = -2*g - 12. Let b be n(-6). Suppose r + 25 = 5*d, -3*d + d - 3*r - 7 = b. Solve t**5 + 0*t**d - t**2 + t**4 + 2*t**5 - t**3 - 2*t**5 = 0 for t.
-1, 0, 1
Let l(k) = 9484*k - 18966. Let x be l(2). Determine u, given that 4/9*u**x + 0 + 2/9*u**4 - 16/9*u + 10/9*u**3 = 0.
-4, -2, 0, 1
Let g(z) = -13*z**4 - 30*z**3 - 51*z**2 - 19*z. Let v(p) = -20*p**4 - 44*p**3 - 76*p**2 - 28*p. Let n(s) = -8*g(s) + 5*v(s). Find r such that n(r) = 0.
-3, -1, 0
Let g(m) = -m**2 + 14*m - 41. Let l be g(6). What is s in l*s**2 - 8*s**2 - 2*s + 2*s**2 - 4*s + 5 = 0?
1, 5
Let v(u) be the third derivative of 5/78*u**4 + 1/30*u**5 + 20*u**2 + 10*u + 0 + 1/780*u**6 - 8/13*u**3. Determine m so that v(m) = 0.
-12, -2, 1
Let p(o) = o**3 - 2*o**2 - 8*o + 3. Let y be p(4). Let f be y/(-6*((-2)/8 - 0)). Solve f*v**2 + 4*v + 65*v - 10*v**2 - 9*v - 28 = 0 for v.
1/2, 7
Let z(l) = -15*l**3 - 175*l**2 + 1135*l - 1385. Let x(a) = 8*a**3 + 87*a**2 - 572*a + 693. Let c(v) = 5*x(v) + 3*z(v). Suppose c(o) = 0. Calculate o.
-23, 2, 3
Let p(t) be the first derivative of -3/5*t**5 - 152 - 21/2*t**4 - 225*t - 68*t**3 - 195*t**2. Factor p(o).
-3*(o + 1)*(o + 3)*(o + 5)**2
Let k(x) be the third derivative of 529*x**5/15 + 23*x**4/6 + x**3/6 - 1814*x**2. What is r in k(r) = 0?
-1/46
Suppose 2528*f = 2648*f - 360. Let m(r) be the first derivative of 0*r + 1/4*r**4 - 1/3*r**f - 37 + 0*r**2. Let m(w) = 0. Calculate w.
0, 1
Factor 24 - 2/7*r**3 + 8/7*r - 6*r**2.
-2*(r - 2)*(r + 2)*(r + 21)/7
Let a(u) be the first derivative of -10/3*u**3 + 0*u - 1/2*u**4 - 204 + 24*u**2. Let a(m) = 0. What is m?
-8, 0, 3
Let y(b) be the third derivative of -b**9/20160 - 3*b**8/2240 - 3*b**7/280 - 17*b**4/8 - 2*b**2 + 54. Let c(o) be the second derivative of y(o). Factor c(s).
-3*s**2*(s + 6)**2/4
Let h(t) be the third derivative of -1/280*t**7 + 7 + 1/160*t**6 - 1/8*t**4 + 1/20*t**5 + 0*t + 0*t**3 - 2*t**2. Determine r so that h(r) = 0.
-2, 0, 1, 2
Let d = 40 + -36. Suppose -g = 5, 4*x - d*g = g + 213. Factor 11*n**3 - 2*n**4 + 9*n + x*n**2 - 28*n**2 + 3*n**4.
n*(n + 1)**2*(n + 9)
Let k be (2920/7008)/((-10)/(-48)). Suppose -2/7*q + 2/7*q**3 + 4/7*q**k - 4/7 = 0. Calculate q.
-2, -1, 1
Let u = -419 - -423. Factor -5*y**4 + 2*y**2 + 5*y**5 - 11*y**3 - u*y**3 + 18*y**2 - 5*y**3.
5*y**2*(y - 2)*(y - 1)*(y + 2)
Let q(r) be the first derivative of r**7/35 - 11*r**6/60 + r**5/6 + r**4/4 - 29*r**2/2 + 166. Let p(u) be the second derivative of q(u). Factor p(h).
2*h*(h - 3)*(h - 1)*(3*h + 1)
Let q(f) be the third derivative of -f**5/40 - 7*f**4/16 - 5*f**3/2 + 1340*f**2. Find g, given that q(g) = 0.
-5, -2
What is p in 3/4*p**5 - 345/4*p**2 - 15/4*p**4 + 0 - 99/2*p - 165/4*p**3 = 0?
-3, -2, -1, 0, 11
What is a in -148*a**2 + 571 - 320*a + 1264*a**3 - 1262*a**3 + 645 = 0?
-4, 2, 76
Let h(b) be the second derivative of -3 - 676/7*b**2 + 46*b + 208/7*b**3 + 17/14*b**4 + 1/70*b**5. Let h(a) = 0. What is a?
-26, 1
Let u(k) be the third derivative of -k**8/112 + 2*k**7/7 - 97*k**6/40 + 39*k**5/10 + 2*k**2 + 40*k + 2. Find a, given that u(a) = 0.
0, 1, 6, 13
Let r(b) = -b**4 - 2*b**3 - b**2 + b. Let z be 7*((-162)/42 + 4). Let p(o) = -4*o**4 + 2*o**3 + 21*o**2 - o. Let s(q) = z*r(q) + p(q). Factor s(j).
-5*j**2*(j - 2)*(j + 2)
Let j(b) = -2*b - 65. Let x be j(-15). Let y = x + 96. Determine u so that -9*u**2 - 4 - 54*u**3 - 34*u - 142*u**2 + y*u**2 + 54*u**4 = 0.
-1/3, 2
Let h be (9 - 7)*(1 - -162). Let q = h + -1301/4. What is w in 0*w - q*w**3 - 1/4*w**2 + w**4 + 0 = 0?
-1/4, 0, 1
Let z(m) be the first derivative of m**4/42 - 8*m**3/21 + 15*m**2/7 - 115*m + 49. Let x(y) be the first derivative of z(y). Determine c so that x(c) = 0.
3, 5
Let c(s) be the first derivative of 5*s**4/2 - 76*s**3/3 - 19*s**2 + 48*s + 234. Factor c(l).
2*(l - 8)*(l + 1)*(5*l - 3)
Let g(c) = 100*c**2 + 353*c + 33124. Let a(x) = -9*x**2 + x. Let w(u) = 22*a(u) + 2*g(u). Find z, given that w(z) = 0.
-182
Let g(n) be the first derivative of -16*n**3/27 - 122*n**2/9 - 4716. Find p such that g(p) = 0.
-61/4, 0
Factor -1882 + 942*o - 1/2*o**2.
-(o - 1882)*(o - 2)/2
Suppose -34 + 46 = 3*a. Let j be 4 + 5/((-2)/(-8)*2). Factor 8*i**3 - j - 2*i**a + 14 + 0*i**4 - 32*i + 32.
-2*(i - 2)**3*(i + 2)
Let h(k) be the third derivative of -k**6/15 - 23*k**5/3 - 139*k**4/3 - 110*k**3 + 10*k**2 + 75*k. Find f, given that h(f) = 0.
-55, -3/2, -1
Let m = 337 + -169. Let v be m/36*-3*1/(-9). Factor -v*p**2 + 0 + 2/9*p**4 + 4/9*p**3 + 8/9*p.
2*p*(p - 1)**2*(p + 4)/9
Let n(s) = 42*s**2 - 978*s + 274. Let b(u) = -14*u**2 + 328*u - 92. Let o(y) = -7*b(y) - 2*n(y). Solve o(a) = 0 for a.
2/7, 24
Let a be 4696542/(-787416) - (-14)/56. Let u = -1/4687 - a. Solve -8/7 - 6/7*r**2 - u*r + 54/7*r**3 = 0 for r.
-2/3, -2/9, 1
Solve 40*l - 113*l**3 + 10*l**4 - 18*l + 82*l + 178*l**3 - 360*l**2 + 181*l**3 = 0 for l.
-26, 0, 2/5, 1
Let v = 156834 - 156830. Factor 0 - 8*s**3 - 2/13*s**v - 104*s**2 + 0*s.
-2*s**2*(s + 26)**2/13
Let c(t) = t**2 + 2*t + 1. Let f(w) = w**3 - 38*w**2 + 148*w - 123. Let m(z) = 6*c(z) + 2*f(z). Factor m(r).
2*(r - 30)*(r - 4)*(r - 1)
Let w = 60 - 27. Let u = w + -31. Suppose -15*c**2 - 10 - 7*c**3 - 122*c + 5*c**4 + 147*c + u*c**3 = 0. Calculate c.
-2, 1
Let g = -13392 - -13395. Le