
(g - 3)*(g + 1)/2
Let p = -73 - -81. Suppose -p = -2*q + 20. Determine h, given that -2*h**2 - h**2 + q*h**3 - 23*h**3 - 6*h + 12*h**3 = 0.
-1, 0, 2
Let j = -13513 + 13513. Let w(s) be the third derivative of 0 + j*s**3 + 4*s**2 + 0*s - 3/40*s**4 + 1/200*s**6 - 1/50*s**5. Factor w(q).
3*q*(q - 3)*(q + 1)/5
Suppose -25*n - 51875 = -51975. Let b(r) be the third derivative of 0*r - 47*r**2 + 2/21*r**3 + 0 + 1/210*r**5 - 1/28*r**n. Factor b(h).
2*(h - 2)*(h - 1)/7
Suppose 20*l = 17*l + 12. Let p**l - 540*p + p**5 + 12 - 9*p**3 + 11*p**2 - 24*p**2 + 548*p = 0. Calculate p.
-2, -1, 1, 3
Let j(k) = -k**3 + 24*k**2 - 22*k - 20. Let l be j(23). Let u be ((-4)/6)/(l/(-9)). Solve -1/5*c**3 - 9/5*c + 6/5*c**u + 0 = 0 for c.
0, 3
Let a(k) be the second derivative of -7*k**6/120 + 15*k**5/8 + 11*k**4/4 - 8*k**3 + 5*k + 7. Let w(s) be the second derivative of a(s). What is r in w(r) = 0?
-2/7, 11
Suppose -7*n + 90 = -2*n + 5*c, 0 = -3*n + 3*c + 66. Suppose -40 = -10*w - n. Factor -6 - 1/6*g**2 - w*g.
-(g + 6)**2/6
Let m(y) be the first derivative of 2/5*y**4 + 2/5*y**2 - 33 - 2/3*y**3 + 0*y - 2/25*y**5. Find g, given that m(g) = 0.
0, 1, 2
Let j(v) be the first derivative of v**3/9 + 34*v**2 + 3468*v + 463. Factor j(c).
(c + 102)**2/3
Let f(r) = 5*r**5 + 4*r**4 - 4*r**2 + r - 3. Let u(l) = 11*l**5 + 8*l**4 - 8*l**2 + 3*l - 7. Let z = -209 + 212. Let y(w) = z*u(w) - 7*f(w). Factor y(p).
-2*p*(p - 1)*(p + 1)**3
Let p(q) = -q**2 - 4*q - 12. Let d(i) = i**2 + 3*i + 11. Let w(x) = -6*d(x) - 7*p(x). Let s be w(-2). What is k in -2/3*k**s - 8/15*k - 2/15 - 4/15*k**3 = 0?
-1, -1/2
Let z be 1125/(-18) + 1/(-2)*3. Let t be (z/(-150))/(14/140) - 4. Determine k so that -2/15*k**2 - t - 2/5*k = 0.
-2, -1
Factor 74884/3*i**2 - 152320/3*i - 157/3*i**4 - 11846/3*i**3 - 1/6*i**5 + 102400/3.
-(i - 2)**3*(i + 160)**2/6
Let j(f) be the third derivative of -f**5/30 - 37*f**4/24 - 8*f**3/3 + 11*f**2. Let w be j(-18). Factor -369*y**w + 5*y**3 - 15*y - 10 + 369*y**2.
5*(y - 2)*(y + 1)**2
Let n be (-3)/12*3*(-30)/30. Let h(f) be the third derivative of 0*f - 1/32*f**6 + n*f**3 + 0 - 13*f**2 - 3/20*f**5 + 11/32*f**4. Factor h(p).
-3*(p - 1)*(p + 3)*(5*p + 2)/4
Let q(d) be the second derivative of -2*d**7/21 - 343*d**6/30 - 773*d**5/10 - 44*d**4 + 525*d**3 - 729*d**2/2 + 516*d - 10. Let q(j) = 0. Calculate j.
-81, -3, 1/4, 1
Let c be 8/154*(-5071)/(-2766). Suppose -c*n**2 + 0 + 4/7*n = 0. Calculate n.
0, 6
Let j be ((-2475)/900)/(11/(-16)). Let -2/15*m**2 + 4/15 - 2/15*m**j + 2/5*m - 2/5*m**3 = 0. What is m?
-2, -1, 1
Let a(u) be the first derivative of 38 + 49/2*u**4 + 14*u**3 + 8*u - 24*u**2. Factor a(i).
2*(i + 1)*(7*i - 2)**2
Let i(q) be the third derivative of -4/9*q**3 + 7/72*q**4 + 1/180*q**5 + 0*q + 5*q**2 + 0. Find g such that i(g) = 0.
-8, 1
Let k(m) be the second derivative of -3*m**5/140 + 307*m**4/28 + 155*m**3/7 - 132*m**2 + 7426*m. Factor k(h).
-3*(h - 308)*(h - 1)*(h + 2)/7
Let -9*o**2 + 402 - 1583*o + 942*o + 824*o = 0. What is o?
-2, 67/3
Let x(v) be the third derivative of -8*v**3 - 1/15*v**5 + 3 + 0*v - 4/3*v**4 + 19*v**2. Factor x(l).
-4*(l + 2)*(l + 6)
Let a(p) be the third derivative of -p**7/42 + 7*p**6/8 - 157*p**5/12 + 805*p**4/8 - 1225*p**3/3 - 2*p**2 + p - 506. Suppose a(i) = 0. What is i?
2, 5, 7
Let q(g) be the third derivative of -13/420*g**5 + 0*g + 0*g**3 + 11/840*g**6 + 0 + 1/84*g**4 - 33*g**2. Let q(n) = 0. What is n?
0, 2/11, 1
Let n = -140/221 - -310/221. Solve 22/13*f**2 + 2*f**3 - n*f**5 - 14/13*f**4 - 16/13*f - 8/13 = 0.
-2, -1, -2/5, 1
Let j(s) be the second derivative of s**8/84 - s**6/15 + s**4/6 + 45*s**2/2 - 2*s - 11. Let h(c) be the first derivative of j(c). Factor h(u).
4*u*(u - 1)**2*(u + 1)**2
Let b(l) be the second derivative of 0 - 8/3*l**2 + 72*l + 1/30*l**5 - 1/3*l**4 + 4/3*l**3. Determine x so that b(x) = 0.
2
Let y(q) = 8*q + 13*q + 6*q - 7 - 2*q**2 - 49*q + 7*q. Let v = -10 - 0. Let k(a) = 5*a**2 + 45*a + 20. Let h(l) = v*y(l) - 3*k(l). Factor h(r).
5*(r + 1)*(r + 2)
Let p(z) be the first derivative of -z**6/2700 + 7*z**5/900 - z**4/15 - 52*z**3 + 141. Let g(y) be the third derivative of p(y). Factor g(t).
-2*(t - 4)*(t - 3)/15
Let -3888/7 + 69/7*d**2 - 1/7*d**3 - 1080/7*d = 0. Calculate d.
-3, 36
Find c, given that -200/7 + 1312/7*c + 24/7*c**5 - 354*c**2 + 1844/7*c**3 - 502/7*c**4 = 0.
1/4, 1, 2, 50/3
Suppose 3*t = y + 5 - 10, 10 = 3*y - 4*t. Find i, given that 13*i**y + 15*i**2 + 3*i**4 - 2*i**4 - 60*i + 12*i**3 - 72 - 5*i**4 = 0.
-2, -1, 3
Let d be 37/(-30) + 8 + 792/(-120). Let q(k) be the first derivative of 3/2*k**2 - d*k**3 + 0*k - 8. Determine f so that q(f) = 0.
0, 6
Let d(o) be the third derivative of 0 + 0*o - 1/12*o**5 - 90*o**2 - 1/12*o**6 - 1/42*o**7 + 0*o**3 + 0*o**4. Find c such that d(c) = 0.
-1, 0
Let x(m) be the second derivative of -1 + 1/20*m**4 - 113*m - 11/10*m**2 + 4/15*m**3. Solve x(f) = 0 for f.
-11/3, 1
Let v = 20 + -226. Let t = 311 + v. Let t*o**4 - 4*o**3 + 6*o - 18*o**2 + 18 - 10*o**2 - 2*o**5 - 95*o**4 = 0. What is o?
-1, 1, 3
Let f(p) be the first derivative of p**6/50 - p**4/5 + 91*p + 46. Let l(k) be the first derivative of f(k). Solve l(y) = 0 for y.
-2, 0, 2
Let b be ((-10)/(-24))/((-517)/(-94) - (-195)/(-36)). Let k(w) be the second derivative of -b*w + 1/2*w**3 + 1 + 0*w**2 + 3/10*w**5 + 3/4*w**4. Factor k(o).
3*o*(o + 1)*(2*o + 1)
Factor 488*j**2 + 6*j**4 - 24*j**4 + 1608*j + 42*j**3 + 61*j**2 + 1104 + 15*j**4.
-3*(j - 23)*(j + 1)*(j + 4)**2
Let a = 6603/26 + -32859/130. Let 0 - 2*n**2 - 22/5*n**3 - 6/5*n**4 + a*n = 0. Calculate n.
-3, -1, 0, 1/3
Let i(j) = -2*j**2 + 14*j + 340. Let z be i(-10). Let v(q) be the third derivative of -14*q**2 + 1/40*q**5 + 4*q**3 + 1/2*q**4 + z*q + 0. Factor v(w).
3*(w + 4)**2/2
Let k be 48/(-15) - (-4892368)/51965. Find s such that -2/19*s**4 - 432/19*s**2 + k*s - 2592/19 + 48/19*s**3 = 0.
6
Suppose 1646/13*c**2 - 48/13 + 20*c + 518/13*c**3 = 0. What is c?
-3, -2/7, 4/37
Let a(u) be the second derivative of -u**4/3 + 74*u**3/3 - 684*u**2 - 296*u + 4. What is g in a(g) = 0?
18, 19
Let k(r) = r**3 + 49*r**2 - 38*r - 10. Let w be k(1). Factor -w + 20/11*l + 2/11*l**2.
2*(l - 1)*(l + 11)/11
Suppose 2*u = 4*t - 17 + 3, -17 = -4*t + 5*u. Factor -2*o**3 - 4*o**3 - 112 + 128*o - 44*o**2 - 10*o**t + 20*o**3.
4*(o - 7)*(o - 2)**2
Let g(s) be the first derivative of -s**6/72 + s**5/6 - 5*s**4/6 + s**3/3 + s + 91. Let b(c) be the third derivative of g(c). Factor b(v).
-5*(v - 2)**2
Factor -1/3*r**2 - 46 + 139/3*r.
-(r - 138)*(r - 1)/3
Let d(p) = -p**3 - p + 1. Let v(o) = 25*o**3 + 4640*o**2 + 20*o - 20. Let c(s) = -20*d(s) - v(s). Let c(x) = 0. What is x?
-928, 0
Suppose -12/5*n + 0 + n**4 - 1/5*n**5 + 1/5*n**3 - 17/5*n**2 = 0. Calculate n.
-1, 0, 3, 4
Let c(x) be the third derivative of -29/15*x**5 + 3*x**4 + 0*x**3 + 333*x**2 + 0 + 1/10*x**6 + 0*x. Let c(n) = 0. What is n?
0, 2/3, 9
Suppose -15*i = -0*i - 750. Let n = -3 + 5. Let -8*j**2 + 2*j**2 - 24*j + i*j**n - 598*j**3 + 582*j**3 - 4*j**4 = 0. Calculate j.
-6, 0, 1
Suppose -13 = -10*y + 27. Suppose 21*j**3 - 42*j**3 + 5*j**y + 33*j**3 - j**4 = 0. Calculate j.
-3, 0
Factor -125/6*a - 64 + 1/6*a**2.
(a - 128)*(a + 3)/6
Let n(w) be the third derivative of w**8/2100 - w**6/225 + w**4/30 - 29*w**3/3 - w**2 - 16. Let x(d) be the first derivative of n(d). Factor x(h).
4*(h - 1)**2*(h + 1)**2/5
Let a = -2308 + 3259. Factor 8*h - 911 + 2*h + a - 5*h**2.
-5*(h - 4)*(h + 2)
Let z(g) = 226*g - 674. Let m be z(3). Let n(y) be the second derivative of -9*y + 0 - 4*y**3 - 18*y**2 - 1/3*y**m. What is c in n(c) = 0?
-3
Let d be (330/(-132))/(6 + 10 + -26). Factor -d*c**3 - 19/4*c - 2*c**2 - 3.
-(c + 1)*(c + 3)*(c + 4)/4
Suppose w - 8*a = -3*a + 13, w + 4*a - 49 = 0. Suppose -22*y + w = -55. Factor 2/11*h**y + 0*h**3 + 0*h - 2/11*h**2 + 0.
2*h**2*(h - 1)*(h + 1)/11
Determine d, given that -998*d**2 - 360*d - 243*d**4 + 200 + 127*d**4 - 636*d**3 - 10*d**4 = 0.
-2, -5/3, 2/7
Let g(x) be the second derivative of 16*x + 2/9*x**5 + 55/144*x**4 + 0 + 5/18*x**3 + 7/144*x**6 - 3*x**2. Let v(k) be the first derivative of g(k). Factor v(q).
5*(q + 1)**2*(7*q + 2)/6
Let z be (-6)/45 + (-2 - 802864/420). Let d = 1915 + z. Suppose -d*k**2 + 6/7*k + 3/7 = 0. What is k?
-1/3, 1
Let j be 4/(-8) + -3 - 663/(-182). Let q(y) be the first deriv