 + 0*l. Factor p(k).
2*(k - 3)*(k + 10)/7
Let u(r) = 3*r**2 + 11*r + 12. Let i be u(-14). Let l = i + -446. Factor -1/4*s**2 + 1/4*s**3 + l + 0*s.
s**2*(s - 1)/4
Let u = -54 + 61. Let w be (-2 + 10)*u/14 - -1. Let -12*x**w + 6*x**4 + 0*x + 0 + 3/4*x**2 + 21/4*x**3 = 0. Calculate x.
-1/4, 0, 1
Let k be (-5 + (8 - 7))*3/(-2). Let c be (-344)/774 + 4/k. Factor 0 + 20/9*p**2 - 2/9*p**3 - c*p**4 - 16/9*p.
-2*p*(p - 2)*(p - 1)*(p + 4)/9
Suppose 0 = -7*b + 178 + 172. Factor 86*i**3 + 6*i**4 - i**4 - 51*i**3 + b*i**2.
5*i**2*(i + 2)*(i + 5)
Let w = 1311/11 - 119. Let z be 27/21 - ((-336626)/5698 + 60). Factor -z*y + 6/11 - w*y**2.
-2*(y - 1)*(y + 3)/11
Let q = -53/77 + 86/77. Factor 0*p + 0*p**2 - q*p**4 + 3/7*p**3 + 0.
-3*p**3*(p - 1)/7
Let y be 1/2 + 33 + -34 + 30/12. Let w(i) be the first derivative of -1/6*i**6 - 2/5*i**5 - 13 - 2*i + 1/2*i**4 - 1/2*i**y + 4/3*i**3. Factor w(s).
-(s - 1)**2*(s + 1)**2*(s + 2)
Let h(g) be the third derivative of g**6/30 + 4*g**5/5 + 16*g**4/3 - 292*g**2. Factor h(b).
4*b*(b + 4)*(b + 8)
Let w be -20 - (51772/129)/(-14). Suppose 40*q**2 + 2/3*q**5 + 0 - 20/3*q**4 + 24*q + w*q**3 = 0. Calculate q.
-1, 0, 6
Let a(p) = -11. Let z(g) = g**2 - g + 21. Let w(h) = -7*a(h) - 4*z(h). Let f(o) = o**2 + o - 1. Let l(j) = 3*f(j) + w(j). Let l(t) = 0. What is t?
2, 5
Let b(x) be the first derivative of 3 + 6*x**2 + 0*x**3 - 1/12*x**5 - 5/24*x**4 + 0*x. Let u(c) be the second derivative of b(c). Find n such that u(n) = 0.
-1, 0
Let w(p) = p**3 - 12*p**2 + 9*p - 1. Let o be w(10). Let h = o + 115. Determine b, given that h - 60*b**2 - 5*b**3 + 21*b**4 - b**4 + 6 - 25*b = 0.
-1, 1/4, 2
Let k(t) be the third derivative of -t**7/350 - t**6/4 + 159*t**5/100 + 962*t**2. Factor k(o).
-3*o**2*(o - 3)*(o + 53)/5
Let a(p) be the first derivative of -11*p**6/12 - 12*p**5/5 + 29*p**4/8 + p**3 - 8072. What is s in a(s) = 0?
-3, -2/11, 0, 1
Suppose -2*h - 6*o = -8*o, -5*o + 24 = h. Suppose 5*d - 18 = -t, 4 - 13 = -h*t + d. Factor 2/3*z**5 - 4/3*z**4 + 14/3*z + 8/3 - 16/3*z**t - 4/3*z**2.
2*(z - 4)*(z - 1)*(z + 1)**3/3
Let v(y) be the second derivative of y**5/10 + 3*y**4/2 - 25*y**3/3 - 33*y**2 + 11*y - 20. Factor v(r).
2*(r - 3)*(r + 1)*(r + 11)
Let n(i) be the third derivative of 3*i**8/112 - 11*i**7/14 + 679*i**6/120 + 509*i**5/60 + 11*i**4/3 - i**2 + 9*i. Determine w, given that n(w) = 0.
-1/3, 0, 8, 11
Factor 101052 + 6*t**3 - 52547 - 311353 + 3549*t**2 + 523920*t.
3*(t + 296)**2*(2*t - 1)
Let z(w) be the second derivative of -5/8*w**4 + 5/3*w**3 + 0 + 9*w**2 + 1/12*w**5 + 5*w. Let b(d) be the first derivative of z(d). Factor b(p).
5*(p - 2)*(p - 1)
Let a(m) = 789*m**2 + 207*m + 408. Let f(s) = -44*s**2 - s - 1. Let u(i) = -a(i) - 18*f(i). Suppose u(o) = 0. Calculate o.
-2, 65
Let j = 65 - 63. Suppose j*t - 21 = 3*k + 2*k, -3*t - k + 6 = 0. Find z such that 0*z - 3 + 1 + z**2 - t*z + 4*z = 0.
-2, 1
Let h = -221 + 223. Factor 105*a**h + 18*a - 52*a**2 - 55*a**2.
-2*a*(a - 9)
Let q(k) be the second derivative of -7/16*k**2 + 0 + 36*k + 1/96*k**4 - 1/8*k**3. Solve q(u) = 0 for u.
-1, 7
Let w(u) = 9*u**2 + 46*u + 5. Let q(c) = 2*c**3 + 32*c**2 + 31*c + 10. Let r be q(-15). Let o be w(r). Factor 4/5*m**4 + o*m**3 - 4/5*m**2 + 0 + 0*m.
4*m**2*(m - 1)*(m + 1)/5
Let q(v) be the first derivative of -137 - 6*v**3 - 2/3*v**4 + 7/3*v**2 + 0*v. Factor q(j).
-2*j*(j + 7)*(4*j - 1)/3
Let p = -128375 - -128381. Determine t so that -p + 18/7*t**4 + 30/7*t**3 - 3/7*t**5 - 48/7*t**2 - 99/7*t = 0.
-1, 2, 7
Let v(o) = 10*o**3 - 560*o**2 + 39184*o - 148016. Let u(k) = k**3 - k**2 + 2*k - 6. Let n(b) = 8*u(b) - v(b). Factor n(p).
-2*(p - 136)**2*(p - 4)
Let a(s) = -5*s**3 + 844*s**2 + 7046*s + 14240. Let x(u) = u**2 - u. Let d(f) = -a(f) - 6*x(f). Factor d(n).
5*(n - 178)*(n + 4)**2
Factor 96800/3 - 32560*n - 2/3*n**3 + 294*n**2.
-2*(n - 220)**2*(n - 1)/3
Let g(x) be the second derivative of -7*x**6/15 + 1321*x**5/10 - 749*x**4/2 + 559*x**3/3 + 374*x**2 + 5400*x. Solve g(h) = 0 for h.
-2/7, 1, 187
Let i = 747119/9 + -83013. Suppose 0*t**2 + i*t**5 + 0 - 4/9*t**3 + 0*t**4 + 2/9*t = 0. Calculate t.
-1, 0, 1
Let f(v) be the second derivative of 4*v - 1/6*v**4 + 4 - 16*v**2 + 10/3*v**3. Solve f(a) = 0 for a.
2, 8
Let i(u) = -104*u + 3. Let b be i(0). Let z(h) be the second derivative of 0*h**2 + 0*h**b + 5*h - 1/72*h**4 + 0 + 1/120*h**5. Find w such that z(w) = 0.
0, 1
Let x(k) = -k**3 + 7*k**2 + 27*k + 21. Let t be x(-2). Let a(w) be the first derivative of -10/3*w**t - 8*w + 12*w**2 - 31. Factor a(m).
-2*(m - 2)*(5*m - 2)
Let n(s) = -s**3 + 11*s**2 - 24*s + 30. Let i be n(8). Let g be (-1)/(21/35 + 59/(-90)). Determine d so that -i*d - g*d**2 - 25/2 = 0.
-5/6
Let i(w) be the third derivative of 11/24*w**4 + 18*w + 0 + 7/60*w**5 + 2/3*w**3 - 2*w**2. Determine d so that i(d) = 0.
-1, -4/7
Suppose -2*f - 32 = -4*i - 6*f, -2*i = 3*f - 19. Factor 92*x**3 - 171*x**3 + 9*x**4 + 3*x**2 + 3*x**i + 88*x**3.
3*x**2*(x + 1)**3
Factor -1478 + 559 - 827 + 1749*m + 38*m**2 - 41*m**2.
-3*(m - 582)*(m - 1)
Let u(h) be the first derivative of -h**3/5 + 1422*h**2/5 - 5922. Determine d, given that u(d) = 0.
0, 948
Let g(h) be the second derivative of h**4/4 - 12*h**3 + 285*h**2/2 + 3*h + 718. Suppose g(v) = 0. What is v?
5, 19
Let v(c) be the first derivative of -c**4/21 - 44*c**3/21 - 6*c**2 + 83*c + 85. Let q(k) be the first derivative of v(k). Factor q(b).
-4*(b + 1)*(b + 21)/7
Factor -494*z - 26*z + z**2 + 4*z**2 + 7*z**2 - 67600 - 13*z**2.
-(z + 260)**2
Suppose -2*d + 2*z = 228, -23*z + 28*z = 4*d + 460. Let x be (((-20)/d)/2)/(1/14). Factor -x*g**2 + 0 - 4/11*g.
-2*g*(7*g + 2)/11
Let n = -95391 + 286198/3. Find h such that n*h**3 + 20/3*h + 0 + 35*h**2 = 0.
-4, -1/5, 0
Let f(o) be the first derivative of -o**9/10584 - o**8/2940 + o**7/2940 + o**6/630 - 23*o**3/3 - 84. Let n(m) be the third derivative of f(m). Solve n(r) = 0.
-2, -1, 0, 1
Let y = -305 + 621. Let d = 316 - y. Factor -4*h**4 - 16/3*h**3 + 4/3*h**5 + 64/3*h**2 + d*h - 64/3.
4*(h - 2)**3*(h + 1)*(h + 2)/3
Let k = 107971/5 - 21593. What is m in -2*m**2 + 4/5*m - k*m**3 + 0 = 0?
-2, 0, 1/3
Let r = -3/23372 + 631059/116860. Factor r*x**2 + 9*x - 15 + 3/5*x**3.
3*(x - 1)*(x + 5)**2/5
Let k(g) be the first derivative of 4*g**3/3 - 4816*g**2 + 5798464*g - 193. Factor k(d).
4*(d - 1204)**2
Let y(s) = s**2 - 16*s + 63. Let o be y(7). Suppose o = 3*t - 16 + 4. Let -25/4 - 10*i - t*i**2 = 0. What is i?
-5/4
Suppose 5*k - 15 = -4*r, 59*r - 61*r = 4*k - 12. Suppose -k*j + 3*a = -0*j + 6, 0 = 3*j + a - 10. Factor 0*v - 3/5*v**3 + 0 + 0*v**j - 3/5*v**5 + 6/5*v**4.
-3*v**3*(v - 1)**2/5
Find a, given that -1749*a**2 + 3*a**5 - 87*a**4 + 339*a**3 + 0*a**5 + 217*a**3 - 28*a**3 + 219*a**3 - 504 + 1590*a = 0.
1, 12, 14
Let c(d) be the third derivative of -4096*d**6/75 + 16128*d**5/25 - 15876*d**4/5 + 83349*d**3/10 + 561*d**2. Factor c(h).
-(32*h - 63)**3/5
Let c(x) be the third derivative of x**5/135 - 401*x**4/54 + 532*x**3/9 + 3541*x**2. Factor c(f).
4*(f - 399)*(f - 2)/9
Factor -738/23 - 100/23*n - 2/23*n**2.
-2*(n + 9)*(n + 41)/23
What is f in 0*f + 66/7*f**4 - 2/7*f**5 + 0 + 0*f**2 + 380/7*f**3 = 0?
-5, 0, 38
Let h(o) be the third derivative of -1/105*o**7 + 1/12*o**4 - 83*o**2 + 0*o - 2/3*o**3 + 0 + 1/10*o**5 - 1/60*o**6. Factor h(n).
-2*(n - 1)**2*(n + 1)*(n + 2)
Suppose j + 17 = -14. Let x = j + 31. Factor -9*b + 3*b**3 + b**3 + x*b**2 + 24*b**4 + 6*b**2 + 35*b**3.
3*b*(b + 1)**2*(8*b - 3)
Let a(m) be the second derivative of 5*m**4/12 + 15*m**3 - 95*m**2/2 + 11*m + 50. Factor a(q).
5*(q - 1)*(q + 19)
Let s(x) be the third derivative of -1/360*x**5 + 0*x + 3/4*x**4 - 48*x**2 - 81*x**3 + 0. Find t such that s(t) = 0.
54
Let b(n) be the first derivative of -n**5/15 - 565*n**4/12 - 11844*n**3 - 3375352*n**2/3 - 6644672*n/3 - 2906. Factor b(j).
-(j + 1)*(j + 188)**3/3
Let s(f) be the second derivative of -37/135*f**6 - 3 + 2/9*f**3 - 13*f + 1/27*f**7 - 35/54*f**4 + 0*f**2 + 59/90*f**5. Let s(a) = 0. Calculate a.
0, 2/7, 1, 3
Let n(t) be the second derivative of -t**5/10 - 581*t**4 - 1350244*t**3 - 1568983528*t**2 - 547*t. Factor n(o).
-2*(o + 1162)**3
Let t be (-24)/108 + 58/18*1. Suppose -t*c + 4 = q, -3*c - 4*q - 23 = -4*c. Let -2/17*k**4 - 2/17*k**2 - 6/17*k**c + 6/17*k + 4/17 = 0. Calculate k.
-2, -1, 1
Let a(w) = -8*w**2