
Factor -3*r**4 + 260820*r - 19*r**4 + 38*r**4 - 11*r**4 + 27585*r**2 + 690*r**3 + 714420.
5*(r + 6)**2*(r + 63)**2
Let v(p) be the second derivative of -p**5/20 + 965*p**4/12 - 116644*p**3/3 + 116162*p**2 - 125*p - 16. Factor v(o).
-(o - 482)**2*(o - 1)
Suppose -5*c - 15 = 5*b, 1191*c - 1187*c = 5*b + 33. Factor -2/13*p**3 - 30/13*p**c + 32/13*p + 0.
-2*p*(p - 1)*(p + 16)/13
Let c be (-36)/90 + 1891*2/30. Let v = c + -364/3. Find a, given that 11/3*a**3 - 4/3*a**5 + 4/3 - 16/3*a + v*a**2 - 8/3*a**4 = 0.
-2, 1/2, 1
Let b(r) = r**2 + 345*r - 106. Let t(h) = 3*h**2 + 346*h - 104. Let i(u) = -2*b(u) + 3*t(u). Factor i(k).
(k + 50)*(7*k - 2)
Let n(g) = -g**3 + g**2 + 3*g. Let i be n(-3). Suppose 0 = -2*b - b + i. Factor -3*f**2 + 3*f**5 - 5*f**2 + b*f**4 + 3*f**3 - 6*f - f**2.
3*f*(f - 1)*(f + 1)**2*(f + 2)
Let k = 468799 + -468794. What is m in -k*m**3 + 20/3*m - 5/3*m**5 + 25/3*m**4 - 25/3*m**2 + 0 = 0?
-1, 0, 1, 4
Let l(n) = n**2 + 37*n - 40. Let o be l(-42). Let r be (o/30 + -5)*1. What is m in r*m + 0 - 2/3*m**2 = 0?
0, 1
Suppose -4*h = 2*v - h - 14, -4*v = -5*h - 6. Solve v*x**2 - 271 + x**2 + 91 + 85*x + 90 = 0.
-18, 1
Let r(t) = 3*t**3 + 311*t**2 - 132*t - 2910. Let c be r(-104). Let -4/3*l + 0 + 13/3*l**4 + 37/3*l**3 + 20/3*l**c = 0. What is l?
-2, -1, 0, 2/13
Let r(j) be the first derivative of -j**3/3 + 7*j**2/2 - 8*j + 24. Let l be r(5). Let 9 - 1 + 0*p**l + 4 - 3*p**2 + 16*p = 0. Calculate p.
-2/3, 6
Let m be (8/20)/(336861/45)*7. Let k = m + 459832/26735. Determine o so that 4/5 - 48/5*o**2 - k*o**3 - 8*o**4 + 2/5*o = 0.
-1, -2/5, 1/4
Let b(t) be the first derivative of 0*t + 1/25*t**5 + 6 - 1/150*t**6 + 0*t**4 + 2*t**2 - 8/15*t**3. Let p(s) be the second derivative of b(s). Factor p(x).
-4*(x - 2)**2*(x + 1)/5
Let x be ((-240)/(-168))/(65/182) + 74/(-19). Factor -6/19*y**3 - 8/19*y**4 + 0*y - x*y**5 + 0 + 0*y**2.
-2*y**3*(y + 1)*(y + 3)/19
Let k(t) = -25*t**2 - 49*t + 209. Let i(q) = 3*q**2 + q - 1. Suppose 6*m = -6*m - 216. Let s(d) = m*i(d) - 2*k(d). Factor s(a).
-4*(a - 10)**2
Let t be (-11 - 700/(-60)) + (-2)/3. Find c such that -11/5*c**2 + t - 4/5*c**4 + 13/5*c**3 + 2/5*c = 0.
0, 1/4, 1, 2
Let m(a) be the third derivative of a**7/280 + 2*a**6/15 + 8*a**5/5 + 31*a**3/2 + 116*a**2. Let j(x) be the first derivative of m(x). Factor j(i).
3*i*(i + 8)**2
Let m(x) be the first derivative of 729*x**5/16 + 405*x**4/8 + 45*x**3/2 + 5*x**2 - 120*x + 17. Let n(t) be the first derivative of m(t). Factor n(w).
5*(9*w + 2)**3/4
Determine c so that 16/3*c**5 - 2672/3*c**2 + 889/3*c + 1192*c**3 - 37 - 1808/3*c**4 = 0.
1/2, 111
Let j(q) be the third derivative of q**8/112 - 3*q**7/2 + 891*q**6/10 - 8748*q**5/5 - 17496*q**4 - 1181*q**2 + 1. Factor j(c).
3*c*(c - 36)**3*(c + 3)
Let j be -3 + 5 + 0 + -2 - -24. Suppose -18*q = -20*q + j. Factor q*f + 5*f**2 + 0*f**2 - 2*f**2.
3*f*(f + 4)
Let d be (-357)/850*(19 + -29). Suppose -5*u = 5*z - 40, 5 = z - 3*u + 17. Factor 0*h + 0 - 6/5*h**2 + d*h**z - 3*h**4.
-3*h**2*(h - 1)*(5*h - 2)/5
Let s = 565/273 + -184/91. Let g(v) be the second derivative of 0 - 2/105*v**6 - 2/35*v**5 + 0*v**3 + 0*v**2 + 24*v - s*v**4. Determine h, given that g(h) = 0.
-1, 0
Let h be (-1 - 28) + (-28518)/(-980). Determine d so that 0 + h*d**2 - 3/2*d = 0.
0, 15
Let o = 737 - 939. Let v = o + 206. What is a in -9/8*a**3 + 0 + 3/2*a + 0*a**2 - 3/8*a**v = 0?
-2, 0, 1
Factor -5400 + 377*t**2 - 1170*t - 827*t**2 - 2*t**3 + 366*t**2.
-2*(t + 12)*(t + 15)**2
Let j(g) be the first derivative of -5*g**4/4 + 85*g**3/3 - 75*g**2 - 1548. Let j(x) = 0. What is x?
0, 2, 15
Let l(h) be the second derivative of h**4/16 + 13*h**3/8 - 18*h**2 - 1558*h. Suppose l(k) = 0. Calculate k.
-16, 3
Let a = 353/8 + -44. Let j(m) = 3*m**3 - 116*m**2 + 189*m - 146. Let h be j(37). What is p in -p - 2 - a*p**h = 0?
-4
Let s(t) = t**2 - 4. Let k be s(3). Suppose 5*b + k = 15. Factor -2*n - 5*n**3 + n**2 - 3*n**b + 7*n**3 + 2.
2*(n - 1)**2*(n + 1)
Let w(f) be the second derivative of -f**5/300 - f**4/10 - 9*f**3/10 + 93*f**2/2 - 2*f - 126. Let h(p) be the first derivative of w(p). Factor h(g).
-(g + 3)*(g + 9)/5
Let x(d) be the first derivative of 4/13*d + 58 + 94/39*d**3 + 49/13*d**2. Factor x(r).
2*(r + 1)*(47*r + 2)/13
Let p = -61900 - -61902. Determine g, given that -46/3*g + 11/3*g**p + 8/3 = 0.
2/11, 4
Let r be ((-33)/45 + (-1)/(-3))*80355/(-21428). Suppose 0 = -0*c + 5*c - 5, 0 = -m - c + 4. Suppose 2 - 1/2*a**4 - 2*a - r*a**2 + 2*a**m = 0. What is a?
-1, 1, 2
Let c(g) be the second derivative of g**4/54 + 4*g**3/3 + 155*g**2/9 + 129*g - 1. Factor c(i).
2*(i + 5)*(i + 31)/9
Let x(v) be the third derivative of 9*v**5/5 + 9*v**4/2 - 16*v**3/3 - 67*v**2. Let a(t) = -36*t**2 - 37*t + 11. Let o(j) = 8*a(j) + 3*x(j). Factor o(m).
4*(m + 1)*(9*m - 2)
Let j(z) = -z**3 - 9*z**2 - 6*z + 14. Let w be j(-7). Let s be (-15)/150 + w/(-20). Factor 5/3*y**s - 1/3 + 4/3*y.
(y + 1)*(5*y - 1)/3
Let z = 57 + -32. Factor 35*m**5 - 10*m**3 + 23*m**2 + 12 - 12 - z*m**4 - 23*m**2.
5*m**3*(m - 1)*(7*m + 2)
Let t(g) be the third derivative of g**5/120 - 19*g**4/48 + 35*g**3/6 + 3*g**2 - 4*g + 2. Factor t(q).
(q - 14)*(q - 5)/2
Determine g so that 24*g**3 - 333*g**2 + 159*g**2 - 310*g**2 + 1534*g - 336 + 562*g = 0.
1/6, 6, 14
Factor 3*g**4 - 195*g**3 + g**5 - 5*g**4 + 187*g**3.
g**3*(g - 4)*(g + 2)
Suppose 544/7 + 540/7*o - 4/7*o**2 = 0. Calculate o.
-1, 136
Suppose 355*q + 269*q + 135 + 391*q - 200*q + 681 - q**2 = 0. Calculate q.
-1, 816
Suppose 6*v + 0 = 24. Let d(k) = -k**3 + 7*k**2 - 2*k + 9. Let h be d(v). Factor -18*m**2 + 37*m - 4*m**3 - h*m**4 - 115*m**3 - 8 + 22*m - 15*m.
-(m + 1)*(m + 2)*(7*m - 2)**2
Let m = 599/6972 + -3/1162. Let j(f) be the second derivative of 0 - 1/20*f**5 + 0*f**3 - 7*f + 0*f**2 + m*f**4. Determine r so that j(r) = 0.
0, 1
Let r(u) be the first derivative of -6*u**5/5 - 481*u**4/2 + 1616*u**3/3 - 324*u**2 + 887. What is q in r(q) = 0?
-162, 0, 2/3, 1
Let k = -295 + 299. Factor -17 + 16*r + 58 - k*r**2 + 7.
-4*(r - 6)*(r + 2)
Factor 3080162 + 4964/3*h + 2/9*h**2.
2*(h + 3723)**2/9
Let w be 12*(-7)/((-168)/4). Let 5*l**w + 23120 + 804*l - 161*l + 37*l = 0. What is l?
-68
Let g(m) be the first derivative of -5*m**3/9 - 1544*m**2/3 + 412*m - 2949. Suppose g(v) = 0. What is v?
-618, 2/5
Factor -9*r**3 - 1930*r + 575 - 6*r**3 + 475*r**2 + 580 - 75.
-5*(r - 27)*(r - 4)*(3*r - 2)
Suppose m = -2*i + 3 + 5, 3*i = -m + 10. Factor -15*h + 51*h + 16*h**m - 8*h**2 - 5*h**2 - 31*h**2 - 8.
4*(h - 1)*(h + 2)*(2*h - 1)**2
Let n = -5285 + 5286. Let a(k) be the first derivative of n - 1/14*k**4 + 0*k - 1/21*k**2 + 2/105*k**5 + 2/21*k**3. Find o, given that a(o) = 0.
0, 1
Factor 0 + 2*i**2 + 13/8*i**3 + 5/8*i + 1/4*i**4.
i*(i + 1)*(i + 5)*(2*i + 1)/8
Let r = 2792 - 2357. Let x = r + -4773/11. Factor 14/11*k**3 + 26/11*k + 52/11*k**2 - x.
2*(k + 1)*(k + 3)*(7*k - 2)/11
Let y be (-36)/342 - 61/(-38). Let l = 7/4 - y. Suppose 0 - 1/2*a + 1/4*a**3 + l*a**2 = 0. What is a?
-2, 0, 1
Let v = -1489 + 23825/16. Let z(l) be the first derivative of 0*l + 17 + 0*l**2 + v*l**4 - 1/20*l**5 + 0*l**3. Let z(g) = 0. What is g?
0, 1
Let q be (-2)/3*((-138)/(-483) - 22/28). Let y(w) be the second derivative of q*w**4 + 10*w + 4*w**2 + 0 + 2*w**3. Factor y(r).
4*(r + 1)*(r + 2)
Let y = 112 - 109. Factor n**4 + n**5 - 5*n**y + 16*n**2 - 4*n**2 - 9*n**2.
n**2*(n - 1)**2*(n + 3)
Let s = -70 - -74. Suppose -s*l + 8 = -4. Factor -1/2*c**l + 1/2*c**2 + 1/2*c - 1/2.
-(c - 1)**2*(c + 1)/2
Let d = -3252 - -276416/85. Let c = d + 21/85. Find q such that -1/5*q + c*q**3 - 1/5 + 1/5*q**2 = 0.
-1, 1
Let l(f) = -7*f + 37. Let q be l(5). Let y be -4*q/(-96)*8. Factor -11/3*z**2 - 4*z - y*z**3 + 3.
-(z + 3)**2*(2*z - 1)/3
Factor 20*s**3 + 568*s + 245*s + 1257*s + 515*s**2 + 1575.
5*(s + 1)*(s + 21)*(4*s + 15)
Let a(c) = -6*c**2 - 9003*c - 3420169. Let o(h) = -3*h**2 - 4500*h - 1710085. Let y(x) = 10*a(x) - 19*o(x). Factor y(r).
-3*(r + 755)**2
Let c = -418 + 425. What is o in 2*o - 10 - 12*o**2 - 10*o + 7*o**2 - c*o = 0?
-2, -1
Let f(o) be the first derivative of o**3/8 + 489*o**2/8 + 79707*o/8 + 709. Factor f(x).
3*(x + 163)**2/8
Let a(i) be the third derivative of i**6/2880 + i**5/960 + 19*i**3/3 + 77*i**2. Let x(f) be the first derivative of a(f). Find r, given that x(r) = 0.
-1, 0
Suppose 0 = 