3
Let i be (-12)/20 - 219/(-15). Let n(b) = 5*b**2 - 5*b + 3. Let x be n(1). Factor -11*l**2 + x*l**4 + 9*l**3 - 9*l + i*l**2 + 13 - 19.
3*(l - 1)*(l + 1)**2*(l + 2)
Let j(s) be the third derivative of -87*s**2 + 0 + 0*s - 25/12*s**4 - 1/12*s**5 - 40/3*s**3. Factor j(m).
-5*(m + 2)*(m + 8)
Suppose -102 + 1170 = 2*b. Solve 65*a**3 + 484*a + 28*a**2 - 194*a**2 - b*a - 193*a**3 + 6*a**2 = 0.
-5/8, 0
Let w(g) = 87*g**3 + 180*g**2 + 397*g + 11. Let r(a) = -8*a**3 + a**2 - a - 1. Let h(n) = -33*r(n) - 3*w(n). Factor h(f).
3*f*(f - 193)*(f + 2)
Let n = -1900 + 1904. Let p(v) be the second derivative of 9/2*v**2 + 3/20*v**5 - 14*v + 5/4*v**n + 0 + 7/2*v**3. Determine b, given that p(b) = 0.
-3, -1
Let a(b) = -12*b**2 - 68*b. Let q(c) = -c**2. Let s(u) = 2*u**2 - 77*u + 112. Let d be s(37). Let g(i) = d*a(i) - 10*q(i). Factor g(o).
-2*o*(o + 34)
Let x = -283459/10 + 28346. Let d(t) be the second derivative of -x*t**6 + 0*t**2 - 121/4*t**4 + 0*t**3 - 33/10*t**5 + 33*t + 0. What is k in d(k) = 0?
-11, 0
Let l(h) be the third derivative of -5*h**4/24 + 86*h**3/3 + 38*h**2. Let a be l(34). Factor 2/7*t**a - 4/7 - 6/7*t + 6/7*t**3 + 2/7*t**4.
2*(t - 1)*(t + 1)**2*(t + 2)/7
Let -45/7*j + 1/7*j**5 + 6/7*j**2 + 0 + 4*j**3 + 10/7*j**4 = 0. Calculate j.
-5, -3, 0, 1
Find l, given that 9/2*l**2 + 61/4*l + 21/2 - 1/4*l**3 = 0.
-2, -1, 21
Let v(i) = -4632*i - 13894. Let x be v(-3). Find d such that -2/11*d**4 - 4/11 + 6/11*d**x - 2/11*d + 2/11*d**3 = 0.
-1, 1, 2
Factor 452/3*f + 0 + 1/3*f**2.
f*(f + 452)/3
Let p be (-6)/(-7) - (-10168)/28. Suppose 0 = 348*b - p*b + 48. Let 4/7*y**4 + 0 - 4/7*y**5 + 16/7*y**b + 0*y - 16/7*y**2 = 0. What is y?
-2, 0, 1, 2
Let v(m) = -m**3 + 8*m**2 + 2*m - 7. Let i be v(8). Suppose l - 12 = -2*f - 2*f, -3*f = 5*l - i. Factor 0 + 3/5*z**3 + l*z + 1/5*z**5 + 1/5*z**2 + 3/5*z**4.
z**2*(z + 1)**3/5
Let r be 41*(9 + 1 + -8). Let u = r - 404/5. Find j such that -2/5*j**3 + 6/5*j**2 + 2/5*j - u = 0.
-1, 1, 3
Find b such that 57*b**3 - 1/2*b**4 - 289*b + 60*b**2 + 345/2 = 0.
-3, 1, 115
Let k(i) be the third derivative of i**5/150 - 293*i**4/60 + 66*i**2 - 8*i + 2. Solve k(n) = 0 for n.
0, 293
Let p(y) be the first derivative of -y**7/70 - 3*y**6/8 - 13*y**5/10 + 7*y**2/2 + 8*y - 11. Let m(c) be the second derivative of p(c). Factor m(g).
-3*g**2*(g + 2)*(g + 13)
Let d(c) be the first derivative of c**8/6720 - c**7/840 + c**6/360 + 17*c**3/3 - c**2 + 111. Let q(p) be the third derivative of d(p). Factor q(g).
g**2*(g - 2)**2/4
Let v be 2/(-10) - 754/(-145). Suppose -5*u + q = -23, -16*q = 2*u - 15*q - v. Factor 2/5*d**u + 0 + 0*d - 2/5*d**2 + 0*d**3.
2*d**2*(d - 1)*(d + 1)/5
Let k(o) = -o**4 + o**3 - 2*o - 1. Let f(b) = -192 - 5*b**2 + 6*b**3 + 87 + 99 - 12*b - b**4. Let a(p) = -f(p) + 6*k(p). Factor a(w).
-5*w**2*(w - 1)*(w + 1)
Factor -67*n**3 - 1/4*n**5 + 17/2*n**4 + 3136*n - 322*n**2 + 10976.
-(n - 14)**3*(n + 4)**2/4
Suppose -10*a = -37*a + 54. Factor 81*k**a + 19683 + k**3 - 2187*k + 5*k**3 - 3*k**3 - 4*k**3.
-(k - 27)**3
Let o(d) be the first derivative of -2*d**6/15 + d**5 - 4*d**4/3 + 57*d + 58. Let m(h) be the first derivative of o(h). Factor m(x).
-4*x**2*(x - 4)*(x - 1)
Let k = -91388 - -91388. Solve 3/7*q**2 - 3/7*q**3 + 0*q + k = 0 for q.
0, 1
Let g(o) be the first derivative of o**6/7 + 284*o**5/35 + 317*o**4/14 + 60*o**3/7 - 892. Suppose g(x) = 0. Calculate x.
-45, -2, -1/3, 0
Factor 856 + 5*n**2 - 3908*n + 194 + 3763*n.
5*(n - 15)*(n - 14)
Find o such that 1056*o**3 + 696960*o**2 + 2/5*o**4 + 0*o + 0 = 0.
-1320, 0
Let i(m) be the second derivative of m**7/273 - 593*m**6/195 + 44104*m**5/65 - 43808*m**4/39 - 4706*m. Factor i(d).
2*d**2*(d - 296)**2*(d - 1)/13
Let n(o) be the third derivative of o**8/728 - o**7/1365 - 7*o**6/52 + 61*o**5/78 - 43*o**4/26 + 56*o**3/39 + 5*o**2 - o + 159. What is l in n(l) = 0?
-7, 1/3, 1, 2, 4
Let v(l) be the second derivative of l**7/735 - l**6/105 - 104*l**2 + 31*l. Let j(m) be the first derivative of v(m). Solve j(g) = 0.
0, 4
Let p(q) be the second derivative of q**4/12 - 161*q**3/3 + 3*q + 37. Let p(w) = 0. Calculate w.
0, 322
Factor 42/5*q + 1/5*q**2 + 41/5.
(q + 1)*(q + 41)/5
Suppose 0 = -14*s + 4*s + 40. Suppose h**2 - 10*h**2 - 2 + 38*h - 31*h - h**s + 3*h**3 + 2*h**3 = 0. What is h?
1, 2
Solve -57/4*n**2 + 3/4*n**3 - 42 + 111/2*n = 0 for n.
1, 4, 14
Let f(j) be the first derivative of -j**3/2 + 102*j**2 - 402*j - 2839. Suppose f(g) = 0. Calculate g.
2, 134
Let y(a) = -a**3 - 4*a**2 + 6*a + 6. Let h be y(-5). Factor 4*b**2 - 44 + b**2 - 35 - h.
5*(b - 4)*(b + 4)
Let l(j) be the third derivative of 41*j + 1/24*j**6 - 2*j**2 + 0 + 0*j**3 - 1/6*j**5 + 0*j**4. Factor l(f).
5*f**2*(f - 2)
Let z(r) be the first derivative of r**8/2520 - r**7/42 + 5*r**6/12 - 79*r**3/3 + 121. Let n(l) be the third derivative of z(l). Factor n(t).
2*t**2*(t - 15)**2/3
Let z(u) be the second derivative of -21*u**5/40 - 17*u**4/4 + 13*u**3/4 + 30*u**2 + 3*u + 3. Determine r, given that z(r) = 0.
-5, -1, 8/7
Let u(k) be the first derivative of -9/10*k**5 + 0*k**2 + 0*k + 1/4*k**6 + 9/8*k**4 - 1/2*k**3 - 45. Factor u(d).
3*d**2*(d - 1)**3/2
Let w(f) be the first derivative of f**5/20 - f**4/2 + 3*f**3/2 - 7*f - 10. Let j(s) be the first derivative of w(s). Solve j(u) = 0 for u.
0, 3
Let h(a) = -12*a**4 - 71*a**3 - 133*a**2 - 115*a - 26. Let o(b) = -b**3 - 9*b + 8*b - 21*b**2 + 22*b**2 + 2 + 0*b**3. Let c(s) = -h(s) + 3*o(s). Factor c(i).
4*(i + 1)*(i + 2)**2*(3*i + 2)
Let r(o) be the second derivative of 55*o**4/72 - 215*o**3/36 - 5*o**2/3 + 2087*o. Suppose r(p) = 0. Calculate p.
-1/11, 4
Suppose 0 = -j - 6*j - 42. Let s be (-68)/j - (-24)/36. Factor -s*b - b**2 - 4*b**2 + 20 - 3*b**2.
-4*(b - 1)*(2*b + 5)
Let v(d) be the second derivative of d**4/18 + 892*d**3/9 + 297*d**2 - 3*d - 62. Solve v(m) = 0 for m.
-891, -1
Let o(b) be the third derivative of b**9/544320 - b**8/90720 + b**7/45360 - 7*b**5/12 + 2*b**2 - 3. Let r(p) be the third derivative of o(p). Factor r(v).
v*(v - 1)**2/9
Let m(l) = -6*l**3 - 254*l**2 + 3401*l + 17. Let x(q) = q**3 + 50*q**2 - 567*q - 3. Let r(c) = 6*m(c) + 34*x(c). Factor r(n).
-2*n*(n - 94)*(n + 6)
Let b(d) be the second derivative of d**4/6 + 20*d**3/3 - 21*d**2 + 2927*d. Factor b(u).
2*(u - 1)*(u + 21)
Let w(d) be the first derivative of -d**3/12 - 127*d**2/4 + 600. Determine g so that w(g) = 0.
-254, 0
Suppose 7*p + p = -3008. Let g = p - -379. Factor 0 - 1/2*t**5 + 0*t + 1/2*t**2 - 1/2*t**4 + 1/2*t**g.
-t**2*(t - 1)*(t + 1)**2/2
Let o be (-250)/(-165) - 7/(-33)*(-102)/119. Let u(m) be the first derivative of 1/3*m**4 - 8/3*m - o*m**2 - 25 - 2/15*m**5 + 2/3*m**3. Let u(f) = 0. What is f?
-1, 2
Suppose -40 = -5*h + 5*z, 627*z - 624*z + 6 = -3*h. Factor -7/5 + 1/5*v**h - 13/5*v - v**2.
(v - 7)*(v + 1)**2/5
Suppose -23*k + 24*k - 123 = -40*k. Let t(x) be the first derivative of -1/8*x**4 - 108*x**2 - 6*x**k - 864*x - 28. Find l such that t(l) = 0.
-12
Factor 86/3*z - 46/3*z**2 + 2/3*z**3 - 14.
2*(z - 21)*(z - 1)**2/3
Let l(m) be the first derivative of 0*m**2 - 17*m + 1/33*m**3 - 21 + 1/66*m**4. Let p(d) be the first derivative of l(d). Factor p(s).
2*s*(s + 1)/11
Let g be (-2)/(-2)*-3*(2 + -14 - (-2 + -9)). Determine m, given that 0 - 4/11*m + 4/11*m**g - 2/11*m**4 + 2/11*m**2 = 0.
-1, 0, 1, 2
Let z = 317524/217965 - 44/19815. Factor -38/11*c - 2/11*c**3 - z*c**2 - 24/11.
-2*(c + 1)*(c + 3)*(c + 4)/11
Let r(g) be the first derivative of 53 - 1/2*g**4 + 0*g + 1/9*g**6 - 4/3*g**2 + 4/15*g**5 - 16/9*g**3. Determine w so that r(w) = 0.
-2, -1, 0, 2
Let h(f) be the second derivative of f**6/10 - 3867*f**5/10 + 1664097*f**4/4 - 1660232*f**3 + 2488416*f**2 + 5574*f. Let h(b) = 0. Calculate b.
1, 1288
Let f = 1153/10359 - 2/10359. Let o(u) be the third derivative of -1/45*u**5 + 0*u - 19*u**2 - f*u**3 + 0 + 1/12*u**4. Find x, given that o(x) = 0.
1/2, 1
Let q(j) be the first derivative of -j**2/2 - 8*j + 24. Let l be q(-11). Determine r, given that -1 + 4*r - r**l - r + r**2 - 2*r + 0*r = 0.
-1, 1
Let g(k) be the first derivative of k**9/9072 + k**8/2520 + k**7/2520 - 107*k**3/3 + 76. Let a(v) be the third derivative of g(v). Factor a(c).
c**3*(c + 1)**2/3
Suppose h + 47 = -5*f, 38 = -0*h - h - 2*f. Let v be -9*h/156 - 6/(-39). Suppose 1/2 + 1/4*a**v - 3/4*a = 0. Calculate a.
1, 2
Let g(s)