/5*n**b = 0.
-2, 0, 1
Let t(k) be the first derivative of 4*k**5/25 + 29*k**4/5 + 68*k**3/5 - 162*k**2/5 + 74. Factor t(c).
4*c*(c - 1)*(c + 3)*(c + 27)/5
Factor 2/9*t**2 + 111392/9 - 944/9*t.
2*(t - 236)**2/9
Let h(b) be the second derivative of 3*b**5/140 + 3*b**4/7 + 3*b**3/2 - 21*b**2 - 1046*b - 2. Factor h(y).
3*(y - 2)*(y + 7)**2/7
Let z(v) = 9*v**4 + 90*v**3 - 241*v**2 + 7. Let r(a) = 4*a**4 + 38*a**3 - 120*a**2 + 3. Let j(q) = 7*r(q) - 3*z(q). Factor j(w).
w**2*(w - 13)*(w + 9)
Let s = -4/901 + -233311/10812. Let l = 97/4 + s. Determine j, given that -16/3*j + 44/9*j**3 + 4/9*j**5 + 8/9*j**2 - 32/9 + l*j**4 = 0.
-2, -1, 1
Let w(l) be the second derivative of 9*l**5/20 + 5*l**4/2 - 22*l**3 + 36*l**2 - 3*l. What is p in w(p) = 0?
-6, 2/3, 2
Let b(k) be the third derivative of k**6/1020 + 2*k**5/51 - 7*k**4/68 + 6247*k**2. Factor b(v).
2*v*(v - 1)*(v + 21)/17
Let d(t) = -4*t**3 - 14*t**2 + 32*t + 8. Let v(n) = 17*n**3 + 57*n**2 - 128*n - 36. Let m(a) = 9*d(a) + 2*v(a). Factor m(f).
-2*f*(f - 2)*(f + 8)
Factor 4704/5*r - 231/5*r**2 + 3/5*r**3 - 28812/5.
3*(r - 49)*(r - 14)**2/5
Let u(t) = 15*t**2 + 51*t - 12. Let h(q) be the first derivative of -7*q**3/3 - 25*q**2/2 + 8*q - 53. Let i(s) = 9*h(s) + 4*u(s). Factor i(w).
-3*(w - 1)*(w + 8)
Let u(d) be the first derivative of -3*d**4/16 + 207*d**3/2 + 2493*d**2/8 + 312*d - 3799. Factor u(p).
-3*(p - 416)*(p + 1)**2/4
Let m(g) = -2*g**3 + 82*g**2 - g + 41. Suppose -23*n = -26*n, -5*n = 3*k - 123. Let r be m(k). Determine s so that 8/9 - 2/3*s**2 + 2/9*s**3 + r*s = 0.
-1, 2
Let g = 1753/10206 - 26/5103. Factor 2/3*x**4 - 1 + 1/3*x**2 - 11/6*x - g*x**5 + 2*x**3.
-(x - 6)*(x - 1)*(x + 1)**3/6
Find u such that -133/5*u**2 + 198/5*u - 72/5 + u**4 + 2/5*u**3 = 0.
-6, 3/5, 1, 4
Factor 21*z**2 - 958*z - 323*z - 3*z**3 + 9*z**2 + 3969 + 93*z**2.
-3*(z - 27)*(z - 7)**2
Let t(p) be the first derivative of -2/35*p**5 + 20/21*p**3 + 107 - 18/7*p + 1/21*p**6 + 9/7*p**2 - 5/7*p**4. Let t(h) = 0. What is h?
-3, -1, 1, 3
Suppose -1/7*g**2 - 28 + 4*g = 0. What is g?
14
Let 818*j - 561*j**2 - 81*j + j**4 - 174*j**2 - 246 + 243*j**3 = 0. What is j?
-246, 1
Let t(b) be the third derivative of -b**5/210 + 93*b**4/28 + b**2 - 717. Factor t(r).
-2*r*(r - 279)/7
Suppose 3*l = 857 - 281. Factor 6144*j + 3144 - 12608 - 2*j**3 + 4*j**3 + l*j**2 + 0*j**3 + 75000.
2*(j + 32)**3
Let 8*a**3 - 60*a**2 - 10*a - 10*a**4 - 2*a**4 + 159*a**2 + 2*a**5 - 87*a**2 = 0. What is a?
-1, 0, 1, 5
Let 12*c**4 - 140 + 119*c**3 - 114*c**2 - 116 - 1130*c**2 + 97*c**3 + 128*c**3 + 1144*c = 0. Calculate c.
-32, 1/3, 1, 2
Let b(g) = -g**3 - 6*g**2 - 5*g + 1. Let p be b(-5). Let v be p*(-2)/(-1 - 1). Suppose -11 + 45*f - 21*f - 9*f**2 - v = 0. Calculate f.
2/3, 2
Let f(c) be the second derivative of -c**4/20 - 28*c**3 + 846*c**2/5 + 390*c - 2. Solve f(k) = 0 for k.
-282, 2
Let f(x) be the third derivative of 2*x**3 + 1 + 13/40*x**4 - 7/100*x**5 + 0*x - 12*x**2. Factor f(a).
-3*(a + 1)*(7*a - 20)/5
Suppose 4*a = f - 20, 4*a - 53 - 95 = -41*f. Suppose -4/7*y**f + 6/7*y**3 - 8/7*y + 8/7*y**2 + 0 - 2/7*y**5 = 0. What is y?
-2, 0, 1
Find v, given that 352/5*v**2 - 28/5*v**4 + 224/5*v - 192 - 2/5*v**5 - 48/5*v**3 = 0.
-10, -6, -2, 2
Let u(b) be the first derivative of -4*b**6/33 + 134*b**5/55 - 116*b**4/11 - 292*b**3/11 + 108*b**2/11 + 486*b/11 - 6748. Determine i so that u(i) = 0.
-1, 3/4, 9
Let p(s) = 3*s**2 - 50*s - 7. Let y be p(17). Suppose 5*n - 17*r + 12*r - y = 0, 2*n = -5*r + 4. Find f, given that 0*f + 0*f**n + 0 + 1/5*f**3 - 1/5*f**4 = 0.
0, 1
Let a(i) = 17*i**2 - 127*i - 20. Let z(w) = -27*w**2 + 192*w + 32. Let f(d) = -8*a(d) - 5*z(d). Factor f(j).
-j*(j - 56)
Suppose -23*g + 1094 = -1505. What is l in 37*l**2 + 1 - g - 33*l**2 + 108*l = 0?
-28, 1
Suppose -233 = -4*y - 41. Let o = 58 - y. Factor 20*r + 2*r + 100*r**2 - o + 35*r**3 + 9*r + 24*r.
5*(r + 1)*(r + 2)*(7*r - 1)
Let l = -176977 - -884966/5. Let 6/5 - 69/5*q**3 - l*q + 144/5*q**2 = 0. What is q?
2/23, 1
Let b(h) be the second derivative of -h**4/27 + 130*h**3/27 - 304*h**2/3 + 10*h + 70. Suppose b(s) = 0. Calculate s.
8, 57
Let t(o) be the third derivative of o**8/3360 - o**7/420 + o**6/180 + 7*o**4/24 - o**3/3 - 69*o**2. Let g(m) be the second derivative of t(m). Factor g(k).
2*k*(k - 2)*(k - 1)
Let o = -40803 - -40803. Factor 3/4*u**2 + 3/2*u - 3/4*u**3 + o.
-3*u*(u - 2)*(u + 1)/4
Let w = 218/721 - -17589/1442. Solve w*q**2 - q**4 - 5/2 + 27/4*q + 9/4*q**3 = 0 for q.
-2, -1, 1/4, 5
Let u(f) be the first derivative of 0*f - 2/3*f**3 + 0*f**2 - 60 + 1/2*f**4. Determine x so that u(x) = 0.
0, 1
Let a = 21901511/135 - 162235. Let p = -32/27 - a. Suppose 0 - p*n - 8/5*n**3 + 8/5*n**2 = 0. Calculate n.
0, 1/2
Let x(f) be the second derivative of -53*f + 0 + 3/80*f**5 - 1/40*f**6 + 1/16*f**4 + 0*f**3 - 1/56*f**7 + 0*f**2. Factor x(v).
-3*v**2*(v - 1)*(v + 1)**2/4
Let g = 5792 + -115813/20. Let p(l) be the second derivative of l - 27*l**2 - 1/10*l**6 + 0 - 29/4*l**4 + g*l**5 + 39/2*l**3. Determine f so that p(f) = 0.
1, 2, 3
Let l(y) be the second derivative of -98*y + 3/4*y**2 + 0 - 9/40*y**6 + 57/80*y**5 - 19/8*y**3 + 7/16*y**4. Solve l(b) = 0 for b.
-1, 1/9, 1, 2
Let m = -86713 + 86713. Factor m - 5/2*v**2 - 1/2*v**3 - 2*v.
-v*(v + 1)*(v + 4)/2
Let a(l) = -40*l**2 + 167*l - 79. Let w(k) = 7*k**2 - 29*k + 13. Let n(u) = 6*a(u) + 34*w(u). Factor n(x).
-2*(x - 4)**2
Let h be -11 - (748/(-22) - -20). Let u(b) be the third derivative of 11*b**2 + 0*b**4 - 1/2*b**h + 0 + 0*b + 1/80*b**5. Suppose u(r) = 0. What is r?
-2, 2
Let o be (-1780)/2640*-11 - (-2)/(-24). What is y in -10/3*y + o*y**2 + 2/3*y**4 + 0 - 14/3*y**3 = 0?
0, 1, 5
Let m(z) be the second derivative of -z**4/144 + 101*z**3/72 - 25*z**2/6 + 622*z. Factor m(p).
-(p - 100)*(p - 1)/12
Let g = 296 - -894. Let b = -1188 + g. Determine n so that -1/3 - 2/3*n - 1/3*n**b = 0.
-1
Let l(s) = -116*s + 18102. Let g be l(156). Let a(v) be the first derivative of 0*v**3 + 36 - 1/21*v**g + 6/35*v**5 - 1/7*v**4 + 0*v + 0*v**2. Factor a(i).
-2*i**3*(i - 2)*(i - 1)/7
Factor -34*j**5 - 78*j**5 - 223*j**4 - 33996*j**3 + 33998*j**3.
-j**3*(j + 2)*(112*j - 1)
Let w(c) be the third derivative of -c**5/300 + c**4/40 + c**3/3 + c**2 - 80*c. Find o, given that w(o) = 0.
-2, 5
Let c(v) be the first derivative of 5*v**3/6 - 665*v**2/2 + 1320*v + 4671. Factor c(f).
5*(f - 264)*(f - 2)/2
Let y(r) be the third derivative of r**6/90 + 161*r**5/45 + 6059*r**4/18 - 68890*r**3/9 + 45*r**2 + r + 14. Factor y(n).
4*(n - 5)*(n + 83)**2/3
Let x(b) be the first derivative of -b**4/3 - 106*b**3/9 - 26*b**2/3 + 231. Find i such that x(i) = 0.
-26, -1/2, 0
Let z = -12412 - -12415. Let p(j) be the first derivative of 0*j - 32 + 3*j**2 + 2/3*j**z. Suppose p(o) = 0. Calculate o.
-3, 0
Let a(t) = 3*t**5 + t**3 + t**2 - t + 1. Let c(v) = -47*v**5 + 3*v**4 - 38*v**3 + 22*v**2 - 11*v - 9. Let k(j) = 48*a(j) + 3*c(j). Factor k(p).
3*(p - 1)**4*(p + 7)
Suppose 2*g + 3*g = -3*j + 25, g - 5 = -j. Suppose -2*z = -2*o + 7*o - 16, g*o + 2 = 4*z. Factor 25*d - 33*d**3 - 6 - 117*d**o - 3*d**2 + 26*d + 81*d**3.
3*(d - 2)*(4*d - 1)**2
Let k(m) be the first derivative of 13*m**7/42 - m**6/2 + m**5/10 + 95*m + 148. Let r(y) be the first derivative of k(y). Factor r(o).
o**3*(o - 1)*(13*o - 2)
Let x(q) be the second derivative of -6*q**2 - 51*q + 14*q**3 + 15/4*q**4 + 0. Factor x(d).
3*(d + 2)*(15*d - 2)
Suppose 151 + 53 = 4*s. Let d = -23 + s. Factor 24 - 4*b**2 - 22*b - 29*b + 83*b - d*b.
-4*(b - 3)*(b + 2)
Determine d, given that 400 - 2432*d**2 + 884 + 2417*d**2 + 3204*d = 0.
-2/5, 214
Let d(o) be the first derivative of -2*o**5/35 + 218*o**4/7 - 97628*o**3/21 + 281220*o**2/7 - 832050*o/7 + 9270. Factor d(r).
-2*(r - 215)**2*(r - 3)**2/7
Factor 2072*p**2 - 936*p + 645 + 5092*p + 471 - 40 - 4*p**3 + 1004.
-4*(p - 520)*(p + 1)**2
Let n(w) be the second derivative of w**4/90 - 5884*w**3/45 + 8655364*w**2/15 - 512*w - 3. Determine v so that n(v) = 0.
2942
Factor 488*x - 24*x**2 - 7442/3.
-2*(6*x - 61)**2/3
Factor 2/3*v**3 + 204610*v + 205350 - 2218/3*v**2.
2*(v - 555)**2*(v + 1)/3
Suppose 0 = -2*w - 0*w + 8. Suppose v - 3*n = w*v - 15, 0 = 4*n + 8. Let -o**3 - 26 + 14 - v*o + 9 - 5*o**2 = 0. Calculate o.
-3, -1
Let n be (4/(-2))/((-82)/78843). Let b = 1925 - n. Factor -2/3*p**3 + 1/6 -