.
1, 7
Factor -377*n + 77*n - 380*n**2 + 770*n**2 + 64 + 520 - 386*n**2.
4*(n - 73)*(n - 2)
Let f be (0 - -4) + (11 + -1)/(-10). Factor 0*y + 289*y**4 + y**3 + 0*y + 5*y**5 - 11*y**f - 284*y**4.
5*y**3*(y - 1)*(y + 2)
Let m(q) = -q**2 - 84*q + 10. Let o(v) be the third derivative of -v**5/20 - 49*v**4/4 + 6*v**3 - 19*v**2 + 5*v. Let b(a) = -18*m(a) + 5*o(a). Factor b(y).
3*y*(y + 14)
Let v = 121067 + -121065. Factor 2/5*q**v - 24/5*q + 8.
2*(q - 10)*(q - 2)/5
Let z = -135561 + 677842/5. Solve 14/5 - 11/5*l**3 + 1/5*l**4 + 33/5*l**2 - z*l = 0 for l.
1, 2, 7
Let l be (4 + -140)*(-90)/540. Factor -1156/3 - l*v - 1/3*v**2.
-(v + 34)**2/3
Let d(v) be the third derivative of -v**5/450 - 151*v**4/15 - 91204*v**3/5 - 5*v**2 - 26*v - 3. Let d(g) = 0. What is g?
-906
Suppose 311 - 262 = 7*u. Factor -u - 3*m - 3*m**2 + 7 + 21*m**3 + 3*m**4 - 18*m**3.
3*m*(m - 1)*(m + 1)**2
What is w in -76829*w**3 + 4*w**5 - 6*w + 76775*w**3 - 18*w**4 + 130*w**2 - 20*w**2 - 36 = 0?
-3, -1/2, 1, 6
Let t(b) be the second derivative of 16/9*b**4 - 1/15*b**5 + 111*b + 0*b**3 + 0*b**2 + 0. Suppose t(r) = 0. Calculate r.
0, 16
Let j(h) be the first derivative of h**5/40 - 103*h**4/16 - 415*h**3/24 - 13*h**2 - 4789. Factor j(k).
k*(k - 208)*(k + 1)**2/8
Let b(w) be the first derivative of 2*w**3/27 + 152*w**2/3 + 3616*w/9 + 1136. Factor b(f).
2*(f + 4)*(f + 452)/9
Determine b, given that 69*b - 177/4*b**3 - 18 + 129/2*b**2 - 15*b**4 + 27/4*b**5 = 0.
-2, -1, 2/9, 2, 3
Suppose 10*g + 10 = 12*g. Suppose -2*p = 2*p + 2*f - 4, -p + 12 = -g*f. Factor 9*m - 7*m**2 + 0 + m**3 + 0*m**3 - 4 + m**p.
(m - 4)*(m - 1)**2
Factor -900*l**4 - 129*l - 334*l**2 - 39*l - 164*l**3 + 449*l**4 + 453*l**4.
2*l*(l - 84)*(l + 1)**2
Let u be (1496/7293)/((-15)/18*2 + 3). Determine l so that 16/13 - 10/13*l**4 + 34/13*l**2 - 44/13*l + u*l**3 + 2/13*l**5 = 0.
-2, 1, 4
Let t be ((-6)/18)/((-3)/10809). Let v = t - 4803/4. Suppose 7/2*k - v*k**2 - 49/4 = 0. What is k?
7
Let p be -1 - 165/(-22)*(-6)/(-5). Factor 54 + p*k**3 + 36*k**2 + 2/3*k**4 + 72*k.
2*(k + 3)**4/3
Let s = -44 + 46. Let u(o) = 2*o**2 - 2*o - 1. Let r be u(s). Factor -r*h**5 + 13*h + 6*h**3 - h - 15*h.
-3*h*(h - 1)**2*(h + 1)**2
Let o(r) be the first derivative of 20 - 5/4*r**4 + 3*r**3 + 3/20*r**5 + 0*r**2 + 24*r. Let d(m) be the first derivative of o(m). Let d(z) = 0. What is z?
0, 2, 3
Let q(k) = -k + 6. Let j be q(6). Let b = 35950 + -179738/5. Factor b*w + j*w**2 - 3/5*w**3 + 0.
-3*w*(w - 2)*(w + 2)/5
Let t(r) = -6*r**2 - 3*r - 1. Let n(u) = -11*u**2 + 531*u - 2. Let b(k) = 3*n(k) - 6*t(k). Factor b(o).
3*o*(o + 537)
Let s(g) be the first derivative of 3*g**4/4 - 2*g**3 - 969*g**2/2 + 296. Determine r so that s(r) = 0.
-17, 0, 19
Suppose 4*z + 2*r = 3*r + 35, -z - 4*r = -30. Factor 35*u**2 + 2 + 5*u**5 + 15*u**4 + 1064*u**3 + z*u**4 + 10*u - 1019*u**3 - 2.
5*u*(u + 1)**3*(u + 2)
Let a be (-2)/5 - (-224)/35. Suppose -3*h - a + 12 = 0. Solve 0*x**3 + 76*x**4 - 77*x**4 + 4*x**h - 3*x**3 = 0 for x.
-4, 0, 1
Let k = -292 + 294. Suppose 0 = 5*r + y + 2*y - 22, -k*y = -8. Suppose -8/13*j - 8/13 - 2/13*j**r = 0. Calculate j.
-2
Determine u so that -143532*u + 107892 + 87589*u**2 + 2*u**5 - 15768*u**3 + 1284*u**4 - 16093*u**2 + 2*u**5 = 0.
-333, 3
Let x = 8958 + -107495/12. Let r(j) be the second derivative of -x*j**4 + 8*j - 8*j**2 - 4/3*j**3 + 0. Factor r(b).
-(b + 4)**2
Let p(s) = -55*s**3 - 45820*s**2 - 27665*s + 18400. Let w(x) = -x**3 + 9*x**2 - x - 1. Let t(v) = p(v) - 30*w(v). Find f such that t(f) = 0.
-1843, -1, 2/5
Let k(p) be the second derivative of 0 - 225/13*p**2 + 1/130*p**5 - 31/78*p**4 + 88*p + 85/13*p**3. Factor k(q).
2*(q - 15)**2*(q - 1)/13
Let s = -721604 - -125560009/174. Let t = s + 17/29. Find c such that -1715/3*c**2 + 1/6*c**5 - t*c**4 + 245/3*c**3 + 12005/6*c - 16807/6 = 0.
7
Let x(a) be the third derivative of a**6/240 - a**5/20 - 3*a**4/16 + 9*a**3/2 + 1175*a**2. Factor x(r).
(r - 6)*(r - 3)*(r + 3)/2
Factor -4704/5*b**2 + 1442/5*b**3 + 0*b + 2/5*b**5 + 0 - 124/5*b**4.
2*b**2*(b - 48)*(b - 7)**2/5
Let f(q) be the first derivative of 4*q - 4/3*q**3 - 114 + 0*q**2. Factor f(z).
-4*(z - 1)*(z + 1)
Suppose -79 + 37 = -2*r. Factor 32*s - 4*s**4 + 216*s**5 + 5*s**4 + s**3 - 16 - 4*s**2 - r*s**3 + 3*s**4 - 212*s**5.
4*(s - 1)**3*(s + 2)**2
Let g(r) = -8*r**5 + 15*r**4 + 15*r**3 - 15*r**2 - 7*r - 7. Let j(h) = 3*h**5 - 5*h**4 - 5*h**3 + 5*h**2 + 2*h + 2. Let c(x) = 2*g(x) + 7*j(x). Solve c(t) = 0.
-1, 0, 1
Factor -80 + 36*l + 26*l + 8*l + 12*l**2 - 28*l**3 + 112 + 2*l.
-4*(l - 2)*(l + 1)*(7*l + 4)
Let d(u) be the third derivative of u**5/15 - 4*u**4 + 238*u**3/3 - 19*u**2. Factor d(b).
4*(b - 17)*(b - 7)
Let y(o) be the second derivative of o**5/20 - 3*o**4/4 - 5*o**3/3 + o**2 + 2*o. Let w be y(10). Factor 0*k**2 + 3*k**2 - k**w - 9*k**3 + 2*k**4 + 5*k**3.
2*k**2*(k - 1)**2
Let a = -8896819/9438 + -23/3146. Let m = a + 944. Let -8/3*o + 0*o**2 + 8/3*o**3 + 4/3*o**4 - m = 0. What is o?
-1, 1
Let n(l) be the second derivative of 2*l**6/45 - 9*l**5/5 + 65*l**4/3 - 338*l**3/9 + 9*l - 381. Let n(s) = 0. Calculate s.
0, 1, 13
Let d(k) = 30*k**3 + 30*k**2 - 238*k - 262. Let f(x) = 19*x**3 + 20*x**2 - 159*x - 175. Let i(t) = 5*d(t) - 8*f(t). Solve i(g) = 0.
-9, -1, 5
Let h = 251 - 55. Suppose k - 2*y - h = 3*y, -5*k = -4*y - 980. Factor -12*d - k*d**2 - 3*d**3 + 184*d**2 + 0*d**3.
-3*d*(d + 2)**2
Find c such that -115*c + 346519*c**2 + 68*c**4 - 346499*c**2 - 70 - 18*c**4 + 110*c**3 + 5*c**5 = 0.
-7, -2, -1, 1
Factor -117990*s + 175446 + 40359/2*s**2 - 115*s**3 + 1/6*s**4.
(s - 342)**2*(s - 3)**2/6
Let r be (-36)/((-7740)/301) + 44/(-60). Find u such that 0*u**2 - 8/9*u**5 + 0 + 2/9*u**3 + r*u**4 + 0*u = 0.
-1/4, 0, 1
Factor -2445/2*w**3 + 204*w**2 + 0 - 9*w**4 + 0*w.
-3*w**2*(w + 136)*(6*w - 1)/2
Let o(j) = -j**4 - j. Let q(g) = 3*g + 19. Let t be q(-6). Let d(m) = 75*m**5 - 82*m**4 - 18*m**3 + 36*m**2 - 5*m. Let c(w) = t*d(w) + 3*o(w). Solve c(s) = 0.
-2/3, 0, 2/5, 1
Let b(r) be the first derivative of -2*r**5/15 + 13*r**4/6 - 62*r**3/9 - 15*r**2 + 3336. Find h such that b(h) = 0.
-1, 0, 5, 9
Let g(l) be the second derivative of l**7/84 - 2*l**6/5 - 167*l**5/40 - 63*l**4/4 - 89*l**3/3 - 30*l**2 - l - 3739. Let g(d) = 0. Calculate d.
-2, -1, 30
Let z be 0/(-2 - (-17 - -16)). Let i(o) be the second derivative of 1/75*o**6 - 10*o + 0*o**3 - 1/25*o**5 + 1/30*o**4 + 0*o**2 + z. Factor i(j).
2*j**2*(j - 1)**2/5
Let c be (0 - 164/42)/(780/(-1170)) - 5. Let f = -425/7 - -61. Factor 0 - c*w + 4/7*w**2 + f*w**3.
2*w*(w - 1)*(w + 3)/7
Suppose -5*p + 6 = -2*k, -5*p = 2*k + 3*k - 20. Let g be 5/(7 - 2) + k/(-18). Factor 0 + 2/9*b**5 + 4/3*b**3 + 8/9*b**2 + g*b**4 + 2/9*b.
2*b*(b + 1)**4/9
Let z(r) be the first derivative of 2/5*r**2 - 4/25*r**5 + 52/15*r**3 - 48/5*r - 1/5*r**4 - 10. What is v in z(v) = 0?
-4, -1, 1, 3
Let w(j) be the second derivative of -1/3*j**4 - 11*j + 0 - 17/12*j**3 - 1/2*j**2. Factor w(z).
-(z + 2)*(8*z + 1)/2
Let z = -148428/55 + 29690/11. Determine l, given that -z*l**4 + 2/5*l + 6/5*l**3 - 6/5*l**2 + 0 = 0.
0, 1
Let q(s) be the second derivative of -5*s**7/42 - 51*s**6 - 152*s**5 + 5*s**4/6 + 1015*s**3/2 + 760*s**2 + 1320*s + 3. What is a in q(a) = 0?
-304, -1, 1
Let f(z) be the second derivative of -z**5/4 - 1705*z**4/2 - 870400*z**3 + 5242880*z**2 - 3*z + 1594. Find o such that f(o) = 0.
-1024, 2
Let m(z) = 3*z**2 + 9*z - 6. Let r(g) = -g. Suppose 2 = 4*h - 2. Let a(t) = -11*t**2 - 3*t + 2. Let k be a(h). Let b(s) = k*r(s) - m(s). Factor b(f).
-3*(f - 2)*(f + 1)
Find b, given that 1983018 - 7438*b - 43637*b - b**3 - 1932393 + 451*b**2 = 0.
1, 225
Let r(u) be the second derivative of -u**6/6 - 343*u**5/2 - 591665*u**4/12 - 195510*u**3 - 292410*u**2 + 47*u - 44. What is c in r(c) = 0?
-342, -1
Let w = -268745 - -268745. Suppose -1/2*h**2 - 1/2*h**3 + w*h - 1/8*h**4 + 0 = 0. What is h?
-2, 0
Let w(m) be the first derivative of -5*m**3/9 - 110*m**2/3 - 1295*m/3 + 1189. Factor w(b).
-5*(b + 7)*(b + 37)/3
Let k(m) be the third derivative of -m**6/120 - 13*m**5/30 + 29*m**4/8 - 3*m**2 + 1724. Factor k(n).
-n*(n - 3)*(n + 29)
Let u(r) be the first derivative of 1/14*r**4 - 53 - 2/7*r**3 + 8/7*r + 0*r**2. Find m such that u(m) = 0.
-1, 2
Let u(b) be the second derivative of -5/3*b**3 + 0 - 3/10*b**5 - 14*b + 3/2*b**4 + 