-3*g**2 + 3*g**4 + 3 + 0*g**2 + 246*g**3 + 72*g**3 - 318*g - 3.
3*g*(g - 1)*(g + 1)*(g + 106)
Let d(b) be the third derivative of -b**7/70 - 231*b**6/10 - 160083*b**5/10 - 12326391*b**4/2 - 2847396321*b**3/2 - 708*b**2. Find f, given that d(f) = 0.
-231
Let g be (((-140)/(-15))/7*24)/2. Let q be 2/((-6)/(-21)) - (g - 11). Factor 0 + 15/7*r**4 + 0*r + 12/7*r**q + 24/7*r**3 + 3/7*r**5.
3*r**2*(r + 1)*(r + 2)**2/7
Let k(r) be the third derivative of -r**7/84 + r**6/90 + r**5/20 - 13*r**3/2 - 64*r**2. Let b(j) be the first derivative of k(j). Factor b(o).
-2*o*(o - 1)*(5*o + 3)
Let y(t) be the first derivative of t**3/9 - 160*t**2/3 - 107*t - 6213. What is d in y(d) = 0?
-1, 321
Let z(s) = s**2 - 20*s - 20. Suppose 0 = -3*d - 4*m + 28, 5*d - 5*m - 35 = -0*m. Let c(j) = -d*j**2 + 7*j**2 + 2*j**2. Let k(x) = 6*c(x) - z(x). Factor k(a).
5*(a + 2)**2
Factor 5263*f - 5*f**2 - 13*f**2 + 256 - 2*f**2 - 5895*f.
-4*(f + 32)*(5*f - 2)
Let p(m) be the third derivative of m**6/300 + m**5/3 + 49*m**4/60 - 4834*m**2 - 1. Suppose p(a) = 0. What is a?
-49, -1, 0
Let w(r) be the first derivative of 2*r**6/3 - 184*r**5/5 + 123*r**4 + 1144*r**3/3 - 2456*r**2 + 4128*r + 3385. Factor w(y).
4*(y - 43)*(y - 2)**3*(y + 3)
Suppose -3*v + 1 = -11. Suppose -t + 4*q + 0 = -1, 0 = t - q - v. Factor 9*z**2 - t*z**3 + 6 + 6*z**2 - 10*z - 6.
-5*z*(z - 2)*(z - 1)
Let c(j) = j**5 + 39*j**4 - 112*j**3 + 119*j**2 - 81*j + 61. Let o(h) = -10*h**4 + 28*h**3 - 30*h**2 + 20*h - 14. Let s(f) = 2*c(f) + 9*o(f). Factor s(k).
2*(k - 2)*(k - 1)**4
Factor 835*j - 30*j**2 - 27*j**2 + 840 + 28*j**2 + 24*j**2.
-5*(j - 168)*(j + 1)
Let a(c) be the second derivative of -59*c + 0*c**3 - 1/42*c**7 + 1/15*c**6 + 0 - 1/6*c**4 + 1/20*c**5 + 0*c**2. Factor a(f).
-f**2*(f - 2)*(f - 1)*(f + 1)
Let z(x) be the first derivative of 4/5*x - 1/10*x**4 - 2/25*x**5 + x**2 + 75 + 2/5*x**3. Factor z(y).
-2*(y - 2)*(y + 1)**3/5
Let a(c) be the second derivative of -c**6/780 + c**5/65 - 5*c**4/156 - 83*c**2 + 18*c - 1. Let y(h) be the first derivative of a(h). Factor y(l).
-2*l*(l - 5)*(l - 1)/13
Let d(p) = 3*p**2 + 4*p - 2. Let i be (-4)/(-7) - (-434)/98. Suppose -13 = i*t - 23. Let b(h) = h**2 + h - 1. Let w(v) = t*d(v) - 4*b(v). Solve w(g) = 0 for g.
-2, 0
Let m(i) be the second derivative of 3*i + 0*i**3 + 10 + 1/13*i**4 + 0*i**2 + 1/195*i**6 + 7/130*i**5. Factor m(o).
2*o**2*(o + 1)*(o + 6)/13
Factor 9/4*p**2 + 135/2 - 177/4*p.
3*(p - 18)*(3*p - 5)/4
Suppose 114*q + 0 + 3/5*q**3 - 129/5*q**2 = 0. What is q?
0, 5, 38
Let r(w) = -w + 14. Let g be r(-37). Suppose g = -14*q + 31*q. Solve 15/4*o**4 - 39/4*o**q + 3/4*o - 3/2 + 27/4*o**2 = 0.
-2/5, 1
Let h be ((-6)/16)/(2/(-16)). Let z be h*2/6 - (-128)/4. Factor -26 - 5*g**5 + 59 - 10*g**2 - z + 15*g**3.
-5*g**2*(g - 1)**2*(g + 2)
Suppose 26 = 4*f + 5*z, z = 2*f - 5*f + 14. Let m(t) = -2*t**2 - 81*t - 198. Let v(d) = -d**2 - 27*d - 66. Let j(i) = f*m(i) - 11*v(i). Factor j(x).
3*(x - 11)*(x + 2)
Let x(w) = -w**4 + w**3 - w**2 - w - 1. Let k(g) = g**4 - 4226*g**3 - 890414*g**2 + 6*g + 6. Let i(f) = k(f) + 6*x(f). Factor i(t).
-5*t**2*(t + 422)**2
Let -2/7*f**2 + 18/7*f**3 - 18/7*f + 2/7*f**4 + 0 = 0. Calculate f.
-9, -1, 0, 1
Solve -34453*c**3 - 522*c**2 - 838*c**2 - 347*c**2 + 34450*c**3 = 0 for c.
-569, 0
Let p(q) be the first derivative of 2*q**3/57 - 10*q**2/19 + 42*q/19 + 1253. Let p(f) = 0. What is f?
3, 7
Let j(d) be the second derivative of -d**4/12 + 10*d**3/3 - 75*d**2/2 - 339*d. Let m be j(5). Suppose -4/7*y**4 + 0*y - 8/7*y**2 + 12/7*y**3 + m = 0. What is y?
0, 1, 2
Factor -24*t**4 + 4390*t**3 - 13*t**2 - 4393*t**3 + 37*t**2 + 3*t**5.
3*t**2*(t - 8)*(t - 1)*(t + 1)
Let v(z) be the first derivative of z**4/24 + 37*z**3/18 - 40*z**2/3 + 82*z/3 - 1856. Factor v(m).
(m - 2)**2*(m + 41)/6
Let d(t) be the second derivative of 11 - 25/2*t**2 - 2*t - 85/36*t**4 - 155/18*t**3 - 1/12*t**5. Find i, given that d(i) = 0.
-15, -1
Factor 7/6*v**3 - 1/12*v**4 + 49/12*v**2 + 0 + 17/6*v.
-v*(v - 17)*(v + 1)*(v + 2)/12
Let c(m) = 2*m**3 - 12*m**2 - 10*m - 26. Suppose -208 = -26*j - 26. Let y be c(j). Suppose 1/4*d**3 + 0 - 1/4*d**y - 1/2*d = 0. Calculate d.
-1, 0, 2
Solve -4*x**5 + 646608*x - 5924345/4*x**3 - 4866*x**4 - 2948801/4*x**2 - 92416 = 0.
-608, -1, 1/4
Let x be (5038/(-66))/(0 - (-1)/(-9)). Let z = 10309/15 - x. Suppose z + 2/5*l + 2/15*l**2 = 0. Calculate l.
-2, -1
Let y(x) = -27*x**4 - 36*x**3 + 180*x**2 + 915*x. Let i(m) = -2*m**4 + m**3 + 4*m**2 + m. Let v(j) = -15*i(j) + y(j). Factor v(g).
3*g*(g - 10)**2*(g + 3)
Let h(n) = -3*n**2 + 17. Suppose 0 = 16*b - 11*b - 30. Let m(t) = 3*t**2 - 18. Let p(g) = b*h(g) + 5*m(g). Solve p(v) = 0 for v.
-2, 2
Suppose -1201*q = -1146*q - 220. Determine a so that -64/5*a**q + 179/5*a + 708/5*a**2 + 3 + 912/5*a**3 = 0.
-1/4, 15
Let p(c) = 9*c**3 + c**2 + 24*c + 4. Let o(y) = 360 - y**3 - y**2 - y - 182 + 0*y**3 - 180. Let s(n) = 40*o(n) + 5*p(n). Determine t so that s(t) = 0.
2, 3
Let x be (-2054)/7 - (-9 + (-536)/(-56)). Let i = 297 + x. Factor 1/2*n**4 + 1/2*n**i - 3/2*n**2 + 1 - 1/2*n.
(n - 1)**2*(n + 1)*(n + 2)/2
Let f(d) be the third derivative of d**5/120 - 10*d**4 + 4800*d**3 - 10*d**2 + 28*d. Solve f(w) = 0 for w.
240
Let s(o) be the second derivative of -5/6*o**2 - 4 - 8*o + 1/36*o**3 + 1/8*o**4. Solve s(f) = 0 for f.
-10/9, 1
Let b(t) = -54*t**2 + 28*t**2 + 5*t**2 - 25*t - 6 - 13*t**3. Let c(w) = -w**3 - w**2 - w. Let i(m) = 2*b(m) - 22*c(m). Factor i(g).
-4*(g + 1)**2*(g + 3)
Let x(v) = 11*v + 11. Let l be x(4). Let z(p) = -13*p**2 - 64*p + 65. Let o(y) = 180*y**2 + 895*y - 910. Let j(h) = l*z(h) + 4*o(h). Factor j(q).
5*(q - 1)*(q + 13)
Let -2/7*b**5 - 40/7*b**4 + 216/7*b + 0 - 62/7*b**3 + 192/7*b**2 = 0. What is b?
-18, -3, -1, 0, 2
Factor -126 - 81/4*v**2 + 201/2*v + 3/4*v**3.
3*(v - 21)*(v - 4)*(v - 2)/4
Let w(h) = 2*h**2 + 1. Suppose -127 + 130 = -3*p. Let o(y) = -9*y**2 + 3*y - 4. Let a(t) = p*o(t) - 4*w(t). Let a(l) = 0. Calculate l.
0, 3
Let m(w) = -w**3 + 19*w**2 - 1. Let r be m(19). Let n be 0*r*(-6 + 5). Factor 6*y**2 + 8/3*y**3 + 4/3*y + n.
2*y*(y + 2)*(4*y + 1)/3
Let k(j) be the first derivative of j**8/840 + j**7/70 + j**6/36 - j**3/3 + 29*j**2/2 + 1. Let x(y) be the third derivative of k(y). Factor x(z).
2*z**2*(z + 1)*(z + 5)
Let p(z) = 3*z**3 - 4*z**2 - z + 4. Let n be p(1). Let r be ((-3)/n)/(15/(-5)). Solve 1/2*x**4 + 0*x**2 + x - x**3 - r = 0.
-1, 1
Let o be (2*(-9)/54)/(1/9). Let c be (-5)/o - (-52)/39. Factor -6/7*u**c + 0 + 3/7*u**4 + 3/7*u**2 + 0*u.
3*u**2*(u - 1)**2/7
Let l = -1693/338 - -1100/169. Factor 0*t + 0*t**3 + 0 + 3/2*t**4 + l*t**5 + 0*t**2.
3*t**4*(t + 1)/2
Suppose 3*i + b = 48, i = -i - 3*b + 39. Let y be 5/(7 + i - 12). Factor 3/2*n + y*n**2 + 1.
(n + 1)*(n + 2)/2
Let c be 207/46 + 5/(-2). Determine z, given that -z**2 - 6*z**5 + 2*z**2 + 2*z**c - 11*z + 9*z**3 - 3*z**4 + 8*z = 0.
-1, 0, 1/2, 1
Suppose -f - 34 + 42 = -2*x, -2*f + 16 = 3*x. Solve x + 4/3*i - 5/3*i**3 + 8/3*i**2 = 0 for i.
-2/5, 0, 2
Factor 27*o**2 - 1/3*o**3 + 0 + 616/3*o.
-o*(o - 88)*(o + 7)/3
Suppose 690 - 750 = -4*q. Suppose 10*m - 17 = 6*m - y, -3*y + q = 0. Factor -3/5*c**4 - 3/5 + 0*c + 0*c**m + 6/5*c**2.
-3*(c - 1)**2*(c + 1)**2/5
Let t be (-20)/(-30) - (-7)/((-21)/(-25)). Let p(m) = -m**3 + 10*m**2 - 11*m + 20. Let i be p(t). Factor -27/8*q - 3 - 3/8*q**i.
-3*(q + 1)*(q + 8)/8
Let f = -37864 - -151465/4. Suppose r = 6 - 3. Factor -9/4*u**2 - 3/4*u**4 - 3/4*u - f*u**r + 0.
-3*u*(u + 1)**3/4
Let y(z) be the third derivative of -1 - 1/24*z**6 + 30*z**3 + 2*z**2 + 20/3*z**4 + 5/12*z**5 + 0*z. Determine m, given that y(m) = 0.
-2, 9
Let r(w) = -2*w**4 + 102*w**3 - 384*w**2 + 196*w. Let l(d) = -d**4 + 51*d**3 - 192*d**2 + 80*d. Let x(s) = 5*l(s) - 3*r(s). Factor x(q).
q*(q - 47)*(q - 2)**2
Let h(y) = y**3 + 6*y**2 - 2*y + 2. Let d be h(-6). Let p = 16 - d. What is m in 166*m**4 + 4*m**2 - p + 0 - 168*m**4 = 0?
-1, 1
Let m = 47625/29689 - -87/2699. Factor m*r**2 - 16/11*r + 0 - 2/11*r**3.
-2*r*(r - 8)*(r - 1)/11
Determine t, given that 1112643/2*t - 225866529/2 + 1/2*t**3 - 1827/2*t**2 = 0.
609
Suppose -3*n = -4*n + 2. Let i(w) = -w - 13. Let u be i(-16). Determine f, given that 197*f**u + 3*f - 192*f**3 - f**4 + 4*f**2 - 11*f**n = 0.
0, 1, 3
Determine h so that 0 - 1600*h - 4/5*h**2 = 0.
-2000, 0
Let n be 