pose 832*x = 90*x - 1233*x + 3950. Determine n, given that -1/3*n**x + 5/3*n - 2 = 0.
2, 3
Let p be (-2*2/(-16))/(9/96). Let q = -5/2 + p. Solve 0 + 1/3*g**2 - q*g**4 + 0*g - 1/6*g**3 = 0 for g.
-2, 0, 1
Let j(x) = -75*x**5 - 12*x**4 + 10*x**3 + 17*x**2 - 5*x + 2. Let o(v) = 10*v**5 + v**4 - v**2 - 1. Let t(z) = -j(z) - 7*o(z). Let t(s) = 0. Calculate s.
-1, 1
Let m(l) be the second derivative of l**4/24 + 446*l**3/3 + 198916*l**2 + 5500*l. Factor m(f).
(f + 892)**2/2
Let n(o) = -49*o - 447. Let x be n(-9). Let g be x - ((-259)/28 + 3). Suppose g*r**2 - 1/4*r**3 + 0 + 1/2*r = 0. What is r?
-1, 0, 2
Let x(a) be the third derivative of a**7/105 + 9*a**6/20 + 119*a**5/30 - 49*a**4/4 + 3554*a**2. Solve x(f) = 0.
-21, -7, 0, 1
Factor 6*y + 768 - 3369*y**2 - 5*y + 6*y - 2*y**3 + 3177*y**2 + y.
-2*(y - 2)*(y + 2)*(y + 96)
Let o(l) be the second derivative of -l**5/4 - 245*l**4/12 - 3995*l**3/6 - 21675*l**2/2 - 9*l - 63. Suppose o(r) = 0. Calculate r.
-17, -15
Let z(d) be the first derivative of -3*d**5/10 + 189*d**4/4 - 306*d**3 + 1275*d**2/2 - 1089*d/2 + 4886. Solve z(k) = 0.
1, 3, 121
Let n = 283 - 281. Factor 11664 + 52*y - 160*y - 324*y - y**n + 5*y**2.
4*(y - 54)**2
Let c(y) = y**2 - 2136*y + 1142761. Let b(l) = 6*l**2 - 12815*l + 6856566. Let w(z) = -6*b(z) + 39*c(z). Let w(a) = 0. What is a?
1069
Let o(b) be the first derivative of 2*b**7/21 + 2*b**6/3 + 7*b**5/5 + b**4 + 37*b - 12. Let w(t) be the first derivative of o(t). Factor w(f).
4*f**2*(f + 1)**2*(f + 3)
Let b(o) be the second derivative of o**5/80 + 43*o**4/48 + 229*o**3/12 + 52*o**2 - 13*o + 121. Factor b(s).
(s + 1)*(s + 16)*(s + 26)/4
Determine p so that 32*p**2 - 100489*p**3 - 33*p**2 + 2*p + 100488*p**3 = 0.
-2, 0, 1
Factor -109/6*v - 18 - 1/6*v**2.
-(v + 1)*(v + 108)/6
Factor 241*o + 1152388*o**2 - 1152198*o**2 - 56*o + 5*o**3.
5*o*(o + 1)*(o + 37)
Suppose -21 = p - 15. Let v be (9/p)/((-8)/80). Factor 6*n**4 + 3*n**3 - 12*n**5 + n**4 + v*n**5 - n**4.
3*n**3*(n + 1)**2
Let p(j) be the first derivative of j**3 - 79 + 3*j**2 - 9/4*j**4 - 3/5*j**5 + 1/2*j**6 + 0*j. Factor p(m).
3*m*(m - 2)*(m - 1)*(m + 1)**2
Let k(u) = 9*u**2 + 1958*u - 3924. Let s(j) = -100*j**2 - 21540*j + 43165. Let i(n) = -45*k(n) - 4*s(n). Factor i(f).
-5*(f - 2)*(f + 392)
Let b(r) = -r**2 - r - 2. Let a(g) = -7*g**2 + 3*g + 26. Let v be -5 + 7/2*(-150)/(-175). Let w(m) = v*b(m) + a(m). Factor w(y).
-5*(y - 3)*(y + 2)
Suppose 650/7*m**2 + 320/7*m**3 - 320/7*m - 648/7 - 2/7*m**4 = 0. Calculate m.
-2, -1, 1, 162
Find o, given that 40*o - 16*o - 4*o**4 + 3*o**3 - 3*o**4 + 6*o**4 - 10*o**2 - 16*o**3 = 0.
-12, -2, 0, 1
Let q = -1041904 + 1041906. Factor -2/9*v**4 + 0 + 2/9*v**3 + 4/9*v**q + 0*v.
-2*v**2*(v - 2)*(v + 1)/9
Let s(t) = -28*t**2 + 56*t - 28. Let h(k) = 2*k**2 - 20*k + 8*k**2 + 9 - 3*k + 4*k. Let w(y) = 8*h(y) + 3*s(y). Factor w(c).
-4*(c - 3)*(c - 1)
Let x(m) = -m**2 - 125*m + 653. Let h be x(5). Let n(a) be the second derivative of 1/8*a**4 + 0 + 3/4*a**2 + 1/2*a**h + 7*a. Factor n(c).
3*(c + 1)**2/2
Let o = 108832/183 - 36074/61. Let -168 + 2/3*n**3 - 32*n + o*n**2 = 0. What is n?
-6, 7
Let y(d) be the third derivative of -6*d - 1/24*d**6 + 1/12*d**5 + 5/3*d**4 - 10*d**3 + 0 - 4*d**2. Factor y(i).
-5*(i - 2)**2*(i + 3)
Let h(n) be the first derivative of n**5/75 - 7*n**4/60 + n**3/3 - n**2 - 8*n - 52. Let w(g) be the second derivative of h(g). What is t in w(t) = 0?
1, 5/2
Solve 864/5*w**2 - 128/5*w**3 + 1216/5 - 4/5*w**4 - 1792/5*w = 0 for w.
-38, 2
Let z = -27 + 37. Suppose z*k - 6*k = 340. Factor -20*a + 160 - 40*a**3 + 5*a**5 + k*a - 80*a**2 + 15*a + 10*a**4.
5*(a - 2)**2*(a + 2)**3
Let b(c) be the first derivative of -13*c**6/360 - 3*c**5/40 + c**4/6 + 187*c**3/3 + 15. Let g(h) be the third derivative of b(h). Factor g(s).
-(s + 1)*(13*s - 4)
Suppose -2*y + 3*j - 786 = 0, -66*y - 1162 = -63*y + 4*j. Let u = y - -390. What is w in -1/6*w**5 + 1/6*w**2 - 1/6*w**4 + 1/2*w**3 - 1/3*w + u = 0?
-2, -1, 0, 1
Suppose -7*h = -4*h - 27. Suppose h*x - 23 = -g + 5*x, -5*g + 30 = 3*x. Find q such that 0*q**2 - 12/7*q**5 - 2/7 - 8/7*q + 2/7*q**4 + 20/7*q**g = 0.
-1, -1/2, -1/3, 1
Let q(v) = 2*v + 60. Let f be q(0). Solve 35*m**3 - 7*m**3 + 22*m**3 - 190*m**2 - 84 + 128*m + f = 0.
2/5, 3
Let f = -781655/2 + 390830. Solve -f*z**3 - 25/2*z**2 + 25/2 + 5/2*z = 0 for z.
-5, -1, 1
Let o(i) be the first derivative of -i**4 - 12*i**3 + 2*i**2 + 36*i + 496. Suppose o(c) = 0. Calculate c.
-9, -1, 1
Let w(j) be the second derivative of j**8/2688 - j**7/1008 - j**6/288 + j**5/48 + 19*j**4/4 + 25*j + 1. Let l(h) be the third derivative of w(h). Factor l(n).
5*(n - 1)**2*(n + 1)/2
Factor 25/2*o + 1/2*o**3 + 0 + 13*o**2.
o*(o + 1)*(o + 25)/2
Let q(d) be the first derivative of 4*d + 1/3*d**3 - 5/2*d**2 + 15. Factor q(u).
(u - 4)*(u - 1)
Let f(d) be the first derivative of d**4/8 - 2597*d**3/6 + 421850*d**2 - 842402*d - 1750. Suppose f(t) = 0. What is t?
1, 1298
Suppose -3*y - 6 = -y. Let j = y - -8. Factor 2 - j*s - 18*s**3 - 2 + 23*s**3.
5*s*(s - 1)*(s + 1)
Find w, given that 896/3*w - 4/3*w**5 + 404/3*w**3 + 52/3*w**4 + 940/3*w**2 + 304/3 = 0.
-2, -1, 19
Factor 2/3*f + 1/3*f**2 - 2/3*f**3 + 0 - 1/3*f**4.
-f*(f - 1)*(f + 1)*(f + 2)/3
Let t(g) be the second derivative of 0*g**2 + 0 + 1/6*g**6 - 5/6*g**3 + 15*g - 5/12*g**4 + 1/4*g**5. Find n, given that t(n) = 0.
-1, 0, 1
Let v(y) be the second derivative of 3*y**5/100 + 7*y**4/20 + 7*y**3/10 - 9*y**2/2 - 208*y. Solve v(s) = 0 for s.
-5, -3, 1
Let u(f) be the first derivative of 145/2*f**2 - 75 - 80/3*f**3 + 5/4*f**4 - 70*f. What is g in u(g) = 0?
1, 14
Let x = 391 + -387. Let b be (-8)/2 + (142/17 - x). Solve -b*n**4 + 18/17*n**5 + 4/17*n**2 - 28/17*n**3 + 10/17*n + 2/17 = 0.
-1, -1/3, 1
Let t(b) be the second derivative of 0*b**4 + 2*b + 1/360*b**6 + 0 + 0*b**2 + 0*b**5 + 1/6*b**3. Let n(z) be the second derivative of t(z). Factor n(a).
a**2
Let d = -212/597 + 1445/2388. Find v, given that -1 + 7/4*v - 1/2*v**2 - d*v**3 = 0.
-4, 1
Let 40/3*u**2 - 374/9*u + 2/9*u**3 + 28 = 0. What is u?
-63, 1, 2
Solve 6/17*q**5 - 56/17 - 536/17*q**3 - 660/17*q**2 - 148/17*q**4 - 334/17*q = 0 for q.
-1, -1/3, 28
Let n be 8/10*(-3)/(-1). Let m = 228/629 - -1376/3145. Find g such that 2/5*g**4 + 0 - 2*g**2 - n*g + m*g**3 = 0.
-3, -1, 0, 2
Let d(c) be the second derivative of 3*c**5/140 - c**4/7 + 3*c**3/14 + 885*c. Suppose d(t) = 0. What is t?
0, 1, 3
Let l be 25/10*(-12)/(-15). Suppose -k + l*y - 10 = -3*k, -4*y + 18 = 3*k. What is f in -1/6*f**3 + 1/6*f - 1/3*f**k + 1/3 = 0?
-2, -1, 1
Let g(w) = -w**3 - 12*w**2 - 33*w + 17. Let n be g(-7). Let v be 8/(-10)*(-215)/86. Find f such that 3*f**3 + 3/2 + 0*f**v - n*f - 3/2*f**4 = 0.
-1, 1
Let h = -7793 - -7795. Let v(p) be the first derivative of -2*p**3 + 0*p - 3/5*p**5 + 9/4*p**4 + 26 + 0*p**h. Factor v(r).
-3*r**2*(r - 2)*(r - 1)
Let r(t) = t**2 + 21*t + 31. Let k be r(-19). Let l be 16/(-7) + 2 - 184/k. Suppose h**2 + l*h - 6*h**2 - 66*h - 80 = 0. What is h?
-4
Suppose 43*t + 250 = -25*t + 250. Factor 8/3*p + t + 14/3*p**2.
2*p*(7*p + 4)/3
Let b(r) be the third derivative of r**9/5040 - 3*r**8/2240 + r**7/420 + r**4/24 + 19*r**3/3 + 68*r**2. Let s(d) be the second derivative of b(d). Factor s(c).
3*c**2*(c - 2)*(c - 1)
Let b be (1 + -2643)/(2256/94*(-3)/8). Factor -800/9 + 1046/9*n**3 - 86/9*n**4 + 2/9*n**5 - b*n**2 + 2480/9*n.
2*(n - 20)**2*(n - 1)**3/9
Factor -2/5*h**2 + 1088/5 + 108*h.
-2*(h - 272)*(h + 2)/5
Let i(d) be the third derivative of 5*d**8/336 + d**7/21 - 5*d**6/8 + 1829*d**2. Factor i(p).
5*p**3*(p - 3)*(p + 5)
Let t(u) be the third derivative of -u**6/30 - 17*u**5/5 - 120*u**4 - 1152*u**3 - 138*u**2 - 3*u. Solve t(a) = 0 for a.
-24, -3
Let j(b) = 4*b**4 - 39*b**3 + 141*b**2 - 91*b + 10. Let y(t) = 4*t**4 - 40*t**3 + 140*t**2 - 92*t + 8. Let p(w) = -4*j(w) + 5*y(w). Let p(h) = 0. What is h?
0, 1, 4, 6
Suppose -4*b + 12 = -0*b. Suppose 5*v + 39 - 53 = -2*v. Solve 3/2*r**b + 15/2*r**v + 12*r + 6 = 0.
-2, -1
Let c(h) be the second derivative of 2*h - 3/5*h**2 - 1/20*h**4 + 0 + 3/10*h**3. Suppose c(u) = 0. What is u?
1, 2
Suppose v + 137 = 258. Factor 55*r - 77*r**2 - 44*r + 29*r - 4 - v*r**3.
-(r + 1)*(11*r - 2)**2
Let f be 4/6 - (-5)/((-105)/224). Let u be 3 + f/30 + (-4)/6. Factor 9*j**3 - 9*j**5 + 6*j**u + 0*j**5 + 6*j**5.
