*r**2 + 1/9*r**3 - r. Solve o(p) = 0.
-3, 1
Let y = -241 + 358. Factor -32*d**2 + 6*d - 4*d**4 + 10*d + y*d**3 - 97*d**3.
-4*d*(d - 2)**2*(d - 1)
Let o = 4 + 0. Let s be ((-4)/(-1))/(-5 + 2 + 4). Factor -q - 3 + 2*q**o - 9*q**5 - 10*q - 66*q**3 - 41*q**s - 54*q**2 - 10*q.
-3*(q + 1)**4*(3*q + 1)
Let a(z) be the second derivative of 1/60*z**6 - 1/84*z**7 - 30*z + 1/4*z**2 - 1/12*z**3 - 1/12*z**4 + 1/20*z**5 + 0. Factor a(o).
-(o - 1)**3*(o + 1)**2/2
Suppose 0 = -12*a + 8*a - 1568. Let j = a + 1569/4. Factor 1/4 + j*k**2 + 1/2*k.
(k + 1)**2/4
Let r(i) = -752*i**4 - 760*i**3 + 4*i**2 - 4*i + 4. Let h(v) = 753*v**4 + 757*v**3 - 5*v**2 + 3*v - 3. Let y(d) = 4*h(d) + 3*r(d). Let y(p) = 0. Calculate p.
-1, 0, 2/189
Let f(b) be the second derivative of -b**5/60 - b**4/6 - 2*b**3/3 - 4*b**2/3 + 539*b. Factor f(k).
-(k + 2)**3/3
Let r(p) be the third derivative of -7*p**2 - 1/150*p**5 + 1/20*p**4 - 5*p + 0 + 0*p**3 + 1/525*p**7 - 1/100*p**6. Factor r(d).
2*d*(d - 3)*(d - 1)*(d + 1)/5
Let s(f) = -55*f - 5*f**2 - 9*f**2 - 11*f**2 - 40. Let m be 7 - (1 + 8) - -5. Let i(g) = 8*g**2 + 18*g + 13. Let q(k) = m*s(k) + 10*i(k). What is n in q(n) = 0?
-2, -1
Let h(v) = -26*v**3 + 6*v**2 + 10*v - 6. Let l be 41/(-13) - (-2)/13. Let w(o) = -5*o**3 + o**2 + 2*o - 1. Let g(r) = l*h(r) + 16*w(r). Factor g(b).
-2*(b - 1)*(b + 1)**2
Let l(c) be the first derivative of -c**5/120 - 3*c**4/16 - 2*c**3/3 + 25*c**2/2 - c - 108. Let p(d) be the second derivative of l(d). Solve p(q) = 0.
-8, -1
Let t(g) be the third derivative of g**5/630 - 121*g**3/63 - 670*g**2. Factor t(x).
2*(x - 11)*(x + 11)/21
Suppose 23*p - 139 = 81*p - 1067. Let z(q) be the first derivative of q**5 - 20/3*q**3 - p + 15*q - 5/2*q**4 + 5*q**2. Suppose z(v) = 0. Calculate v.
-1, 1, 3
Let t(y) = 1819*y + 9098. Let u be t(-5). Let l(r) be the first derivative of -39/5*r**5 - 38 - u*r**3 + 51/4*r**4 + 3/2*r**6 + 12*r - 12*r**2. Factor l(j).
3*(j - 2)*(j - 1)**3*(3*j + 2)
Let x(u) be the first derivative of 5*u**6/6 + 18*u**5 + 585*u**4/4 + 1780*u**3/3 + 1290*u**2 + 1440*u - 871. Find j such that x(j) = 0.
-8, -3, -2
Suppose -27875 + 84*q**3 - 624*q + 27875 - 4*q**5 + 48*q**4 - 368*q**2 = 0. Calculate q.
-2, 0, 3, 13
Let s(y) be the second derivative of -3*y**7/14 + 472*y**6/5 - 7911*y**5/10 + 1623*y**4 - 923*y**3/2 - 1854*y**2 - 246*y - 2. Solve s(a) = 0 for a.
-1/3, 1, 4, 309
Suppose -216*w**2 + 19127*w + 213*w**2 - 32033*w - 13880403 = 0. Calculate w.
-2151
Let b(m) be the third derivative of m**6/30 + 6*m**5 + 288*m**4 - 9216*m**3 - 124*m**2 + 58*m. Factor b(u).
4*(u - 6)*(u + 48)**2
Let l(d) = 4*d**3 - 2*d**2 + 3*d - 1. Suppose 11 = 13*u - 2*u. Let r be l(u). Determine t so that 271*t**5 - 268*t**5 - t**r - 2*t**4 = 0.
0, 1
Let x(z) be the third derivative of z**7/140 + 31*z**6/240 + 19*z**5/20 + 15*z**4/4 + 26*z**3/3 + 8*z**2 - 180*z. Factor x(g).
(g + 2)**3*(3*g + 13)/2
Let h = -206 + 251. Factor -492*p**2 - p**3 + 462*p**2 + 6*p**3 + h*p.
5*p*(p - 3)**2
Let s(n) be the first derivative of 27*n**6/10 + 639*n**5/25 + 701*n**4/10 - 6*n**3/5 - 351*n**2/2 + 135*n - 3914. Factor s(o).
(o + 3)**3*(9*o - 5)**2/5
Let p(u) be the first derivative of u**3/6 + 369*u**2/4 - 185*u - 3853. Determine d, given that p(d) = 0.
-370, 1
Suppose 1 = -5*p + 2*f, 3*f = -3756 + 3780. Factor p*d + 0 - 1/5*d**2.
-d*(d - 15)/5
Let p = -218 + 220. What is b in -13*b - 31*b**2 + 28*b**p + 21*b + 16*b = 0?
0, 8
Let o be 4/10 - 104/(-65). Suppose -4*z + o = -4*y + 22, 3*z + 3 = 0. Suppose -y*k**3 - 29 - 12*k + 20 + 11*k**2 + 13 + k**3 = 0. What is k?
2/3, 1, 2
Let s(o) be the third derivative of o**6/660 + 23*o**5/165 - 8*o**4/11 + 912*o**2. Factor s(w).
2*w*(w - 2)*(w + 48)/11
Let a(f) = 2*f**3 - 46*f**2 - 44*f. Let h(n) = 9*n**3 - 231*n**2 - 218*n. Let q(c) = -11*a(c) + 2*h(c). Determine r so that q(r) = 0.
-1, 0, 12
Suppose -7*t - 176*t + 549 = 0. Suppose -3/7*i**t + 6/7 - 15/7*i + 12/7*i**2 = 0. What is i?
1, 2
Solve -111*m + 471/8*m**2 + 435/8 - 9/4*m**3 = 0 for m.
1, 145/6
Let j(f) be the second derivative of -f**5/48 + 5*f**4/12 - 10*f**3/3 - 31*f**2 - 5*f - 2. Let l(g) be the first derivative of j(g). Factor l(q).
-5*(q - 4)**2/4
Let f(m) be the first derivative of -2*m**5/25 - 7*m**4/10 - 22*m**3/15 + 7*m**2/5 + 24*m/5 + 1311. Solve f(j) = 0 for j.
-4, -3, -1, 1
Suppose -15 = -2*d - 3*d. Suppose 5225*l - 5225*l - d*l**2 = 0. What is l?
0
Let n(f) = f**3 + 10*f**2 + 18*f + 6. Let u be n(-9). Let t = u - -77. Let -48*d**2 + 13*d**t - 53*d**4 + 8*d**4 + 100 + 46*d + 240*d**3 - 266*d = 0. What is d?
-1, 2/3, 5
Let j(f) = 12*f**2 - 70*f + 80. Let x(l) = -2*l**2 + 14*l - 16. Suppose 3*p + 2 = 5, -5*p = -5*s - 115. Let a(h) = s*x(h) - 4*j(h). Solve a(t) = 0 for t.
-8, 1
Let y be ((-12)/162 + 7/((-3024)/(-104)))*24. Determine s, given that 9/4*s**y - 3/4*s - 1/2 + 21/4*s**2 - 25/4*s**3 = 0.
-2/9, 1
Let x(b) = 5*b**3 - 21*b**2 - b + 35. Let r(g) = 2*g**3 + 7. Let q(o) = -6*r(o) + 3*x(o). What is i in q(i) = 0?
-1, 1, 21
Suppose 7*i - 5*i + 4 = 0, 4*i = 2*d - 4. Let v be d*-4*(-15)/(-24). Determine z, given that -1/4*z**v + 1/4*z**3 - 1/4*z**4 + 0 + 1/4*z**2 + 0*z = 0.
-1, 0, 1
Let h(d) = -8*d**3 + 83*d**2 - 192*d + 135. Let l(o) = 7*o**3 - 77*o**2 + 193*o - 135. Let t(m) = 2*h(m) + 3*l(m). Factor t(n).
5*(n - 9)*(n - 3)*(n - 1)
Factor 134/5*g**3 + 0*g + 0 - 2/5*g**4 - 1232/5*g**2.
-2*g**2*(g - 56)*(g - 11)/5
Let n(p) be the second derivative of p**8/6720 + p**7/1120 - p**6/1440 - p**5/160 - 83*p**3/3 + 129*p. Let c(u) be the second derivative of n(u). Factor c(i).
i*(i - 1)*(i + 1)*(i + 3)/4
Let v(t) be the first derivative of t**5/5 - 51*t**4 + 202*t**3 - 302*t**2 + 201*t - 39. Find b such that v(b) = 0.
1, 201
Let c be -96 + 99 + 46/(-2). Let p be (50/63 - c/(-90))/1. Find n, given that -1/7*n**3 + n - 2/7*n**2 - p = 0.
-4, 1
Suppose -39 = -8*q - 5*q. Solve 26*p**2 - 79*p**3 + 16 - 2*p**2 + 83*p**q + 19*p + 17*p = 0.
-4, -1
Let k = -810 + 816. Let c(u) be the first derivative of -k + 0*u**2 + 0*u - 5/12*u**3. Find m, given that c(m) = 0.
0
Let k = -123 + 172. Let l = k - 46. Factor -a - 88 + 182 - 92 - 2*a**2 + a**l.
(a - 2)*(a - 1)*(a + 1)
Let t(n) = -8*n**2 + 131*n - 306. Let x(m) = -9*m**2 + 148*m - 308. Let d(s) = -4*t(s) + 3*x(s). Let d(r) = 0. What is r?
6, 10
Let 196*f**2 - 2/9*f**4 + 590/9 - 1768/9*f - 584/9*f**3 = 0. What is f?
-295, 1
Suppose p = -4*f + 1481, -5*p + 16 = -9. Let x = 1109/3 - f. Factor -2/3*g**4 + x*g**2 - 2/3*g**3 + 0 + 2/3*g.
-2*g*(g - 1)*(g + 1)**2/3
Let s(c) be the third derivative of -c**7/84 - c**6/12 + 5*c**5/24 - 544*c**2 - 2*c. Determine l so that s(l) = 0.
-5, 0, 1
Suppose 0 = -3*k + 5*k - 16. Let d(q) = -31*q + 248. Let u be d(k). Let -1/3*i**2 + 0 + 1/3*i**3 + u*i = 0. Calculate i.
0, 1
Factor 118*q**2 + 2/3*q**4 - 1232/3*q + 1568/3 - 44/3*q**3.
2*(q - 7)**2*(q - 4)**2/3
Let m(v) be the second derivative of v**5/30 - 25*v**4/8 + 37*v**3/6 + 177*v**2/2 + 18*v - 8. Let p(h) be the first derivative of m(h). Factor p(s).
(s - 37)*(2*s - 1)
What is c in 51328*c + 5120 + 646404/5*c**2 + 20*c**4 + 3208*c**3 = 0?
-80, -1/5
Let k(p) be the third derivative of -p**6/160 - 41*p**5/40 - 48*p**4 - 1044*p**3 + 1116*p**2 + 2*p - 2. Solve k(r) = 0 for r.
-58, -12
Let w(b) be the third derivative of -b**8/84 + 2*b**7/15 + 4*b**6/3 + 44*b**5/15 - 10*b**2 + 6. Find f such that w(f) = 0.
-2, 0, 11
Let l(z) be the first derivative of 3*z**4/26 - 460*z**3/39 + 596*z**2/13 - 592*z/13 + 3178. Find t, given that l(t) = 0.
2/3, 2, 74
Let t = 1333789/7 + -189814. Let y = t - 727. Let 12/7*c + y*c**2 + 10/7 = 0. Calculate c.
-5, -1
Let s = -68 + 46. Let u be s/(-33) + 0/(-4)*1. Solve -8/9*v - 2/9*v**2 - u = 0.
-3, -1
Factor 438048/5 - 877968/5*j - 1876/5*j**3 + 441794/5*j**2 + 2/5*j**4.
2*(j - 468)**2*(j - 1)**2/5
Let g(q) = -q**2 + 8*q + 71. Let v be g(14). Let p be (((-832)/(-24))/v)/(-2). Factor -p*a + 8/3 - 1/6*a**4 - 5/2*a**2 + 4/3*a**3.
-(a - 4)**2*(a - 1)*(a + 1)/6
Let d(z) be the first derivative of -1/2*z**4 + 32*z - 56 - 2/5*z**5 + 8*z**3 + 28*z**2. Let d(b) = 0. What is b?
-2, -1, 4
Solve -210*u**2 + 576*u**4 + 6214*u**3 + 55*u**5 + 624*u**4 - 5279*u**3 = 0.
-21, -1, 0, 2/11
Let n be (4 - 4)/(-3 + 4). Suppose n*h = -2*h + 4. Factor 108 - y**h + 9*y + 27*y + y**2 + 3*y**2.
3*(y + 6)**2
Suppose 1229 + 2943 