-1, 0
Let o(h) be the first derivative of -8*h**3/21 + 13*h**2/7 + 10*h - 1645. Factor o(z).
-2*(z - 5)*(4*z + 7)/7
Factor 4052/7*z + 0 + 16/7*z**2.
4*z*(4*z + 1013)/7
Suppose 2*s + 10*r + 463 = 423, 0 = 4*s - 2*r - 8. Solve -2/7*y**2 - 2/7*y**4 + s - 12/7*y + 8/7*y**3 = 0.
-1, 0, 2, 3
Suppose 2*s - 197 = -133. Factor -2 - 12 - 2*x**4 + 16*x**3 - s*x**2 - 6 + 20.
-2*x**2*(x - 4)**2
Let n be 240/18 - 23 - -13. Solve 0 + 2/3*m**4 - n*m**3 + 0*m + 4*m**2 = 0.
0, 2, 3
Let k(c) be the first derivative of -c**6/18 - 31*c**5/15 - 28*c**4/3 - 12*c**3 - 40. Let k(n) = 0. What is n?
-27, -2, 0
Let n(l) be the third derivative of -l**7/42 - 11*l**6/6 + 349*l**5/12 - 265*l**4/3 - 680*l**3 + 2*l**2 - 2368. Factor n(t).
-5*(t - 4)**2*(t + 1)*(t + 51)
Suppose 2*f + 325 - 355 = 4*q, 2*q = -3*f + 45. Factor -11*c**3 - 21*c**2 + 1/3*c**5 - 1/3*c**4 + 0*c + q.
c**2*(c - 7)*(c + 3)**2/3
Let o = 115849 + -231695/2. Factor 30 + o*q - 3/2*q**2.
-3*(q - 5)*(q + 4)/2
Suppose 46656 + 48388*g**2 + 201159*g**4 + 585*g**3 + 287*g**3 - 201155*g**4 + 94176*g = 0. Calculate g.
-108, -1
Let r(a) be the first derivative of -31 + 4*a**2 - 4/3*a**3 + 32*a. Factor r(g).
-4*(g - 4)*(g + 2)
Let c(x) = -32*x**2 + 4134*x - 4074. Let z(o) = -7*o**2 + 827*o - 814. Let j(k) = 3*c(k) - 14*z(k). Find m such that j(m) = 0.
-413, 1
Let i(g) = 6*g**5 + 11*g**4 - 44*g**3 - 65*g**2 - 36*g - 4. Let v(x) = 2*x**5 + x**3 + x**2 + 2*x. Let b(q) = i(q) + 4*v(q). Let b(z) = 0. Calculate z.
-1, -1/2, -2/7, 2
Suppose 18*d = -6*d + 48. Factor -83 + 23 + 32*q - d*q**2 - 6*q.
-2*(q - 10)*(q - 3)
Let g be (-10*(-4)/(-10))/(-2). Let a(j) = j**2 + 59*j. Let w(x) = -x. Let t(k) = g*a(k) + 22*w(k). Suppose t(c) = 0. What is c?
-48, 0
Suppose 4*n + 17 = 2202*q - 2203*q, 2*n = -q - 7. Find m such that 2/19*m**q - 20/19 - 16/19*m**2 - 2*m = 0.
-1, 10
Let x be 534/89*(24/9 + -2). Let u(g) be the second derivative of -9*g + 5/12*g**x + 0 - 5*g**2 - 5/6*g**3. Let u(f) = 0. Calculate f.
-1, 2
Suppose 0 = -81*d + 75*d + 4128. Factor d*j**3 - 503*j**3 + 1932*j**2 - 2301*j**3 + 180*j + 4.
-4*(j - 1)*(23*j + 1)**2
Let k = 507 + -504. Suppose -k*j = 17*j - 40. Let -2/7*q**j + 0 - 2/7*q**3 + 4/7*q = 0. Calculate q.
-2, 0, 1
Let y(n) = n**2 - 21*n - 19. Let m be y(22). Let 36*d**m + 0*d**4 - 8*d**5 - 80*d**2 - 112*d + 64 - 4*d**4 + 64*d**3 = 0. Calculate d.
-4, -1, 1/2, 2
Let m(k) be the second derivative of -3*k**5/20 + 9*k**4/4 - 162*k**2 - 814*k. Solve m(u) = 0 for u.
-3, 6
Suppose -3*v = g - 0*v - 9, g = 4*v + 9. Let h be g/4 - 14/56. Solve 2/5*n**4 + 4/5*n + 2*n**h + 8/5*n**3 + 0 = 0.
-2, -1, 0
Let w(p) be the second derivative of 24*p - 11/15*p**3 + 1/50*p**5 + 6/5*p**2 - 4 + 2/15*p**4. Factor w(v).
2*(v - 1)**2*(v + 6)/5
Suppose -207*c = -226*c - 18392. Let i = -22262/23 - c. Factor -6/23*w**3 + 0 + i*w**5 - 4/23*w**2 + 0*w + 0*w**4.
2*w**2*(w - 2)*(w + 1)**2/23
Let f(u) be the second derivative of -5/2*u**4 - 3/20*u**5 + 2/5*u**6 - 2*u - 5 + 2*u**3 - 1/14*u**7 + 12*u**2. Factor f(b).
-3*(b - 2)**3*(b + 1)**2
Let s(n) be the first derivative of -135*n**4/2 - 12*n**3 + 192*n**2/5 - 64*n/5 - 85. Let s(r) = 0. What is r?
-2/3, 4/15
Determine q, given that 335/4*q + 195/2 - 55/4*q**2 = 0.
-1, 78/11
Let a(c) = -100*c**2 - 40480*c - 7448275. Let q(r) = -9*r**2 - 3680*r - 677116. Let i(n) = -4*a(n) + 45*q(n). Factor i(s).
-5*(s + 368)**2
Let a(k) = k**2 - k - 2. Suppose -5*t = 4*c - t - 52, -t = 4*c - 49. Let r(v) = -10*v**2 + 24*v + 40. Let y(z) = c*a(z) + r(z). Solve y(u) = 0 for u.
-4, -2
Let m = 657272 + -2628803/4. Factor -m*q - 75/2*q**2 - 5/4*q**3 - 35.
-5*(q + 1)**2*(q + 28)/4
Let w(m) = -32*m + 451. Let f be w(14). Let a(x) be the third derivative of 125/6*x**f + 0 - 25/12*x**4 - 23*x**2 + 1/12*x**5 + 0*x. Factor a(j).
5*(j - 5)**2
Let h = -66405 + 597665/9. Let 2/9*r**4 + 0 + h*r**2 + 0*r + 22/9*r**3 = 0. Calculate r.
-10, -1, 0
Let v(g) = -20*g**3 - 2*g**2 + g. Let k be v(1). Let h be -2*k/35*10/54. Suppose -2/9*p + h*p**4 - 2/3*p**3 + 2/3*p**2 + 0 = 0. What is p?
0, 1
Solve -44*z + 46*z**3 + 22*z**3 - 20*z**4 + 60*z - 64*z**2 = 0.
0, 2/5, 1, 2
Let l = 75320/9 - 8368. Let k(g) be the second derivative of 0 + l*g**3 - 11/54*g**4 + 1/90*g**5 + 23*g + 4*g**2. What is c in k(c) = 0?
-1, 6
Let h be (0 + 5)*(-1)/(-3)*21. Let b(k) = -k - 2. Let z(v) = -v**2 + 22*v + 30. Let a(x) = h*b(x) + 5*z(x). Factor a(u).
-5*(u - 16)*(u + 1)
Let c be 3/162 - (-6 + 6). Let f(d) be the second derivative of 0 - 4/27*d**3 - 14*d - c*d**4 - 4/9*d**2. Factor f(y).
-2*(y + 2)**2/9
Let r(i) be the second derivative of i**5/600 + 4*i**4/15 + 256*i**3/15 + 103*i**2/2 - 9*i - 2. Let d(f) be the first derivative of r(f). Solve d(b) = 0 for b.
-32
Suppose 18 = 5*k + 8. Let m be 444/15 + ((-16)/(-20))/k. Factor -m*r - 5*r**2 + 21 - 32 - 2 - 32.
-5*(r + 3)**2
Let v be (723/2169)/(3*(-4)/(-108)). Let 0 + 0*q - 1/6*q**v + 7/3*q**2 = 0. Calculate q.
0, 14
Let h(o) be the second derivative of -o**4/18 + 13*o**3/36 - 5*o**2/6 + 527*o - 2. Determine v so that h(v) = 0.
5/4, 2
Let t(v) = v + 2. Let d(o) = 4*o**3 - 192*o**2 + 3056*o - 16192. Let x(j) = d(j) + 4*t(j). Find k, given that x(k) = 0.
14, 17
Let x(y) be the second derivative of -y**4/18 + 41*y**3/3 - 122*y**2/3 - 261*y - 1. Factor x(o).
-2*(o - 122)*(o - 1)/3
Factor 350*n**2 - 350 - 10679033*n - 2*n**3 - 3*n**3 + 10679038*n.
-5*(n - 70)*(n - 1)*(n + 1)
Let c(r) be the second derivative of 0*r**2 - 1/7*r**4 + 0 + 2/7*r**3 + 3/140*r**5 - 61*r. Factor c(o).
3*o*(o - 2)**2/7
Suppose -j = s - 174, -2 = 5*j + 8. Let l be (-28)/210 + s/120. Suppose -l*v + 1/3*v**4 + 2/9*v**3 - v**2 - 4/9 = 0. What is v?
-1, -2/3, 2
Let a(t) be the third derivative of 67*t**6/1020 + 197*t**5/510 - t**4/17 - 2*t**2 + 3228*t. Factor a(d).
2*d*(d + 3)*(67*d - 4)/17
Suppose 21*g**2 + 5*g**3 + 0 + 49/3*g + 1/3*g**4 = 0. What is g?
-7, -1, 0
Suppose -8*t - 1716 = 14*t. Let p be 4/t + 30926/31161. Factor -10/17*l**3 - 2/17*l**2 + 2/17*l**4 + p*l - 8/17 + 2/17*l**5.
2*(l - 1)**3*(l + 2)**2/17
Let t(i) = -3*i**2 - 2*i + 1. Let u(p) = -11*p**2 + 1270*p - 203519. Let n(o) = -3*t(o) + u(o). Determine f, given that n(f) = 0.
319
Solve 50*t**3 + 93*t**4 - 371*t**4 + 86*t**4 + 94*t**4 + 100*t**4 - 372*t**2 = 0.
-31, 0, 6
Suppose 10*y - 9*y = -47 + 60. Let d(k) be the first derivative of -45/8*k**4 + 3*k + 54/5*k**5 + 14 - y*k**3 + 9/4*k**2. Suppose d(o) = 0. What is o?
-2/3, -1/4, 1/3, 1
Suppose 12*c = -2*c + 3505908. Factor 3*q**4 - 250422 - 45*q**2 + 12*q**3 + c - 54*q.
3*q*(q - 3)*(q + 1)*(q + 6)
Let w(q) be the second derivative of q**4/12 - 124*q**3/3 + 246*q**2 + 2872*q. Factor w(x).
(x - 246)*(x - 2)
Let i = 1444 - 930. Suppose -247*k**3 + i*k**3 - 251*k**3 - 27*k - 16 + 12*k**2 + 4*k**4 + 11*k = 0. What is k?
-2, -1, 1
Let s(u) be the first derivative of -55*u**2 + 92 - 5/3*u**3 - 605*u. Solve s(b) = 0.
-11
Solve -14*i**3 + 11*i - 94*i**2 + 17*i + 0*i**3 + 101*i**2 - 101*i**2 = 0 for i.
-7, 0, 2/7
Let n = 14 + 10. Factor -7*s**2 - n*s - 4*s**2 + 22*s**2 - 22 - 13*s**2.
-2*(s + 1)*(s + 11)
Factor 137*j**2 + 24622*j - 24890*j + 132*j**3 - 2*j**4 + j**2.
-2*j*(j - 67)*(j - 1)*(j + 2)
Let d be (17/119*0)/(14 + -1). Suppose -3 = 2*o - 11. Solve 1/5*y**o - 1/5*y + d - 1/5*y**2 + 1/5*y**3 = 0 for y.
-1, 0, 1
Let x = 29905 - 29901. Factor 2/3*v**3 + 0 + x*v - 10/3*v**2.
2*v*(v - 3)*(v - 2)/3
Let x(n) = -3*n**3 - 68*n**2 - 22*n + 48. Let i be (-6 - 64/(-12))/(6/(-45)). Let p(u) = 3*u**3 + 34*u**2 + 10*u - 24. Let a(d) = i*p(d) + 3*x(d). Factor a(v).
2*(v - 6)*(v + 1)*(3*v - 2)
Suppose 5*c - 205 = -4*c - 169. Let o(d) be the first derivative of 0*d**2 - 10 + 0*d**3 + 0*d + 1/2*d**c. Factor o(l).
2*l**3
Let g(h) be the second derivative of -h**6/120 - 3*h**5/20 - 9*h**4/16 + h**3/6 + 9*h**2/2 + 384*h. Suppose g(r) = 0. What is r?
-9, -2, 1
Let a(i) be the third derivative of 5*i**8/112 - 13*i**7/21 + i**6 + 37*i**5/6 + 35*i**4/8 + 793*i**2 - 3*i. Determine c so that a(c) = 0.
-1, -1/3, 0, 3, 7
Let r(k) be the second derivative of 28/9*k**3 - 1/5*k**6 - 25/9*k**4 + 0 + 6/5*k**5 - 225*k - 5/3*k**2. Suppose r(z) = 0. Calculate z.
1/3, 1, 5/3
Let z(o) = -9*o + 247. Let s be z(27). Solve 376*b**3 - 15*b**2 - 5*b**5 + 376*b**3 + 10*b - 757*b**3 + 15*b**s = 0.
-1, 0, 1, 2
Let r(c) be the second derivative of 0 + 0*c**4 - 1/3*c**5 + 0*c*