, 1/2
Let t = 2925/7 - 5849/14. Let f(u) be the second derivative of -t*u**3 + 1/28*u**4 + 22*u - 3/14*u**2 + 0 + 3/140*u**5. Factor f(z).
3*(z - 1)*(z + 1)**2/7
Let r(n) = 66*n**2 - 62*n - 8. Suppose 4*x = 4, 4*h = 5*x - 11 - 10. Let p(t) = -t**2 + t - 1. Let f(z) = h*p(z) + r(z). Solve f(v) = 0.
-2/35, 1
Let d(m) be the second derivative of 3/4*m**5 - 1/5*m**6 + 0*m**3 - 67*m - 2/3*m**4 - 1/42*m**7 + 0 + 0*m**2. Factor d(u).
-u**2*(u - 1)**2*(u + 8)
Suppose -653*s - 297*s**2 + 4888*s + 7500 - 1269*s + 4234*s + 3*s**3 = 0. What is s?
-1, 50
Let f(c) be the second derivative of -2/9*c**4 - 12*c + 0 + 14/9*c**3 - 1/15*c**5 - 8/3*c**2. Factor f(p).
-4*(p - 1)**2*(p + 4)/3
Factor 645/2*g + 0 + 35/4*g**2.
5*g*(7*g + 258)/4
Find a, given that 257/5*a**2 + 1/5*a**3 + 1572/5 - 1304/5*a = 0.
-262, 2, 3
Let u(g) be the third derivative of -g**5/210 - 331*g**4/84 - 328*g**3/7 - 152*g**2 + 6*g. What is r in u(r) = 0?
-328, -3
Let q(p) = 7*p**2 - 10*p - 4. Let o be q(-1). Let z be (o + -12)/(2*(-2)/(-6)). Suppose -z*x**3 - 5/2*x**2 - x + 1/2*x**5 + 0 + 1/2*x**4 = 0. What is x?
-1, 0, 2
Suppose -136 = -f - 2*z - 39, -2*z - 224 = -2*f. Factor -11 - 12*k**3 - 124*k**2 - 24*k + 3 + 205*k**2 - 2*k**4 - f*k**2.
-2*(k + 1)**2*(k + 2)**2
Solve 8/9*b**2 + 0 - 4/9*b**4 - 4/9*b**3 + 0*b = 0 for b.
-2, 0, 1
Let j = 58 - 55. Suppose -2 = z - j*z. Solve 0 - 3 + 12*o**3 + z + 14*o**2 - 4*o - 4*o**2 = 0.
-1, -1/3, 1/2
Let p(k) be the third derivative of -k**7/147 + 31*k**6/420 - 17*k**5/70 + 3*k**4/28 + 8*k**2. What is t in p(t) = 0?
0, 1/5, 3
Let c(g) be the second derivative of 5*g**4/12 - 335*g**3/6 - 1295*g**2 + 2136*g. Factor c(s).
5*(s - 74)*(s + 7)
Suppose 2*z = 3*u + 18, -4*z + z + 27 = -4*u. What is j in 290*j**5 - 4 - 292*j**5 - 6*j + z*j**3 + 4*j**2 - j**3 = 0?
-1, 1, 2
Let a(c) be the first derivative of 2*c**5/15 + 17*c**4/3 + 214*c**3/3 + 544*c**2/3 + 512*c/3 + 757. Factor a(p).
2*(p + 1)**2*(p + 16)**2/3
Factor -4*m**3 - 89 + 3911*m + 289*m + 207 - 118 - 4196*m**2.
-4*m*(m - 1)*(m + 1050)
Let f(o) = -18*o**2 - 11464*o + 3317704. Let g(x) = 4*x**2 + 2292*x - 663540. Let s(w) = 6*f(w) + 28*g(w). Find d such that s(d) = 0.
576
Let k(h) = -h**2 + h + 20. Let q be 2/12*-3 - 33/(-6). Let c be k(q). Find j, given that 3/4*j**3 + 1/4*j**5 + c*j + 1/4*j**2 + 0 + 3/4*j**4 = 0.
-1, 0
Suppose 0 = -18*x + 716 + 310. Let p be (-38)/x - (-1)/((-27)/(-30)). What is n in -4/9*n - p*n**2 + 8/9 = 0?
-2, 1
Let k be (0 - 2) + (342/60 - (-21)/70). Let l(t) be the second derivative of 1/8*t**2 + 1/80*t**5 + 0 + 1/16*t**k - 11*t + 1/8*t**3. Factor l(u).
(u + 1)**3/4
Let h(p) be the second derivative of -25*p**4/48 - 5*p**3/6 + 35*p**2/2 - 3023*p. Let h(d) = 0. What is d?
-14/5, 2
Suppose 8*q = -3*q - 528. Let m be q/54*(-27)/6. Solve 1/4*s**5 - 3*s**2 + 13/4*s**3 - 3/2*s**m + s + 0 = 0.
0, 1, 2
Let r(o) be the first derivative of -o**7/42 + 11*o**6/90 - o**5/4 + o**4/4 - o**3/9 - 58*o - 96. Let d(b) be the first derivative of r(b). Factor d(n).
-n*(n - 1)**3*(3*n - 2)/3
Let c(t) be the third derivative of -t**7/1050 + 1139*t**6/600 - 324899*t**5/300 + 323761*t**4/120 + 4282*t**2. Determine k so that c(k) = 0.
0, 1, 569
Let t = -25 - -33. Let g be 1/7 + 26/14. Let -t*b + 2*b**3 + 119*b**2 + 131*b**2 - 244*b**g = 0. Calculate b.
-4, 0, 1
Let v = 5/138 - 1183/28842. Let k = v + 1677/1045. Find g, given that -14/5*g**2 + 2/5 + 4/5*g + k*g**3 = 0.
-1/4, 1
Suppose -408/5*s**2 + 336/5*s + 93/5*s**4 + 144/5 - 336/5*s**3 + 63/5*s**5 = 0. What is s?
-2, -1/3, 6/7, 2
Let r(y) be the first derivative of -2*y**3/3 + 473*y**2 + 62. Factor r(d).
-2*d*(d - 473)
Determine a, given that 682954375 - 798771302*a + 1378938*a**2 + 2869189*a**2 - 7730*a**3 + 6*a**4 - 262027*a**2 + 111838552*a - a**4 = 0.
1, 515
Suppose 5*v = -25, -2*q - 4*v = -4*q + 30. Factor -1 - 3 - 1033*w - 2*w**5 + 1029*w - 4*w**4 + 8*w**2 - 2*w**q + 8*w**3.
-4*(w - 1)**2*(w + 1)**3
Suppose 2*x - 250 + 246 = 0. Suppose 0 = p - x*v + 4, -4*p - v - 10 = -12. Factor -2/9*j**2 + 2/3*j**4 + p + 4/9*j**3 + 0*j.
2*j**2*(j + 1)*(3*j - 1)/9
Suppose -9*h = -12 - 123. Suppose 31*m = 26*m + h. Factor 3*q**3 - 2*q**3 + q**m.
2*q**3
Let q(o) = o**3 + 24*o**2 + 18*o - 57. Let t be q(-23). Let -t*y + 4 + 56*y - 3*y**2 + y**2 = 0. What is y?
-2, 1
Let l = -37 - -39. Let q be l/3 - (-68)/51. Suppose -i**2 - 2*i**2 + 7*i + q*i = 0. What is i?
0, 3
Let y be 43460/525 + (-2)/9*3. Let n = 422/5 - y. Factor 4/7*d**3 - 2/7*d**5 + 2*d - 4/7*d**4 + 4/7 + n*d**2.
-2*(d - 2)*(d + 1)**4/7
Suppose 0 = -2*y, 15 = j + 4*j + 2*y. Factor -11*h**2 - 9*h**3 - 7*h**j - 12*h**5 + 20*h + 3*h**2 - 8 + 16*h**4 + 8*h**5.
-4*(h - 2)*(h - 1)**3*(h + 1)
Suppose 0 - 4/5*i**2 - 108/5*i = 0. Calculate i.
-27, 0
Let u(f) be the third derivative of 0 + 1/12*f**5 - 50/3*f**3 + 0*f + 95/24*f**4 - 64*f**2. Factor u(d).
5*(d - 1)*(d + 20)
Let t(c) = -c**3 + 23*c**2 + c - 26. Let a be t(23). Let m be -5*((-2)/a)/(45/(-27)). Factor -9*d**3 - 2*d**3 + 2*d**m + 0*d**3 + 10*d**3.
-d**2*(d - 2)
Let h(v) = 2*v**4 + 1626*v**3 - 2194*v**2 + 518*v - 32. Let m(y) = 326*y**3 - 439*y**2 + 104*y - 6. Let x(b) = 3*h(b) - 16*m(b). Factor x(k).
2*k*(k - 55)*(k - 1)*(3*k - 1)
Let u(r) be the first derivative of 124 - 1/5*r**3 + 3/10*r**2 + 6/5*r. Factor u(f).
-3*(f - 2)*(f + 1)/5
Let g(i) be the first derivative of 97*i**4/20 + 116*i**3/3 + 861*i**2/10 - 18*i/5 - 2544. Suppose g(y) = 0. Calculate y.
-3, 2/97
Let p be (-46)/(-15) + (-1 - -33 - (-73892)/(-2262)). Solve 0 - 4/5*c**2 + p*c = 0.
0, 3
Let y = -75 - -107. Let u = 14 - 9. What is f in -9 - 8 + y - 20*f + u*f**2 = 0?
1, 3
Let u(l) be the third derivative of l**7/70 - 109*l**6/8 + 1623*l**5/10 - 1619*l**4/2 + 2156*l**3 - 299*l**2 - 4*l + 2. Factor u(f).
3*(f - 539)*(f - 2)**3
Let m(t) be the first derivative of 5*t**3/3 + 80*t**2 + 300*t - 1828. What is g in m(g) = 0?
-30, -2
Let d(b) be the first derivative of b**6/780 + b**5/65 + 3*b**4/52 + 5*b**2/2 + 5*b - 52. Let w(y) be the second derivative of d(y). Factor w(p).
2*p*(p + 3)**2/13
Let i = -152580 - -152584. Factor 14/13*r**3 + 4/13*r**i - 8/13*r + 8/13*r**2 + 0.
2*r*(r + 2)**2*(2*r - 1)/13
Let q be (-10 + 7 + (-4)/(-1))*251. Suppose -q*c + 132*c + 125*c = 0. Factor -1/7*o + 0 + c*o**2 + 1/7*o**3.
o*(o - 1)*(o + 1)/7
Suppose -16253*g - 610 = -16375*g. Suppose -35/6*t**3 + 0*t - 25/3*t**2 + 5/6*t**g + 10/3*t**4 + 0 = 0. What is t?
-5, -1, 0, 2
Solve 0 - 464/9*m - 124/9*m**4 + 124/9*m**2 + 2/9*m**5 + 154/3*m**3 = 0 for m.
-1, 0, 1, 4, 58
Let c(o) be the third derivative of -o**7/126 + 7*o**6/18 - 17*o**5/12 - 35*o**4/18 + 130*o**3/9 - 285*o**2. Determine b so that c(b) = 0.
-1, 1, 2, 26
Suppose 154/3*w**2 + 20/3 + 34*w + 6*w**4 + 30*w**3 = 0. What is w?
-2, -5/3, -1, -1/3
Suppose 0 = 71*d - 63*d - 16. Solve 1 - 6 - 12*k**4 + 207*k**2 + 8*k - 8*k**3 + 1 - 191*k**d = 0 for k.
-1, 1/3, 1
Let a(f) be the third derivative of 1/30*f**5 - f**3 + 7*f**2 + 0 + 0*f + 1/6*f**4. Solve a(l) = 0.
-3, 1
Let d be -4*(192/(-176) + (-543)/(-528)). Determine c so that -9*c + d*c**2 + 35/4 = 0.
1, 35
Let y be (8/6)/((-36)/(-1053)). Let r be (y/(-45))/(-1) + 29/(-145). Factor -8/3 + r*w + 1/3*w**2.
(w - 2)*(w + 4)/3
Factor 1616889*w + 2096568*w + w**3 + 465946*w + 5223*w**2 + 0*w**3 + 4913840*w + 5277112021.
(w + 1741)**3
Suppose l = -537 + 543. Factor l*h + h**3 + 560 - 560 - 5*h**2.
h*(h - 3)*(h - 2)
Let g = 1406 + -9818/7. Let a = 96/91 + 8/91. Factor a + 18/7*v**2 + g*v.
2*(3*v + 2)**2/7
Let a(y) be the second derivative of -1/21*y**3 - 1 + 0*y**2 - 1/70*y**6 + 1/28*y**4 + 13*y + 1/140*y**5 + 1/294*y**7. Factor a(z).
z*(z - 2)*(z - 1)**2*(z + 1)/7
Let b = -35 + 38. Let r(l) = -17*l**b + 11*l + 22*l**3 - 13*l**3 - 6*l**2. Let a(q) = q**3 + q**2 - q. Let g(o) = 18*a(o) + 2*r(o). Factor g(i).
2*i*(i + 1)*(i + 2)
Let t(b) = 10*b**2 - 362*b + 8470. Let u(o) = 28*o + 52. Let j be u(-3). Let p(x) = 108*x**2 - 3984*x + 93168. Let y(r) = j*t(r) + 3*p(r). Factor y(d).
4*(d - 46)**2
Solve 24*s**4 - 425*s**3 + 107*s**3 + 107*s**3 + 96*s**3 + 2*s**5 + 89*s**3 = 0.
-13, 0, 1
Let j = 1392 + -1390. Determine w, given that 0 + 0*w**j + 1/4*w**3 - 1/4*w**5 + 0*w + 0*w**4 = 0.
-1, 0, 1
Let f(v) be the third derivative of v**8/126 - v**7/45 - 19*v**6/180 + 7*v**5/90 + 5*v**4/12 + 618*v**2. Determine l, given that f(l) = 0.