derivative of w**5/100 + w**4/60 - w**3/6 + 3*w**2/10 + 61*w + 82. Let i(k) be the first derivative of r(k). What is p in i(p) = 0?
-3, 1
Let h(o) = o**2 - 37*o + 57. Let z be h(35). Let x be z/14 - 6*(-2)/8. Let -x*a**2 + 20/7*a + 0 = 0. Calculate a.
0, 5
Let r(g) = -10*g + 172. Let t be r(17). Find w such that 12*w - w - 4*w + 2*w - 3 + 3*w**3 - 9*w**t = 0.
1
Suppose -3*d + 430 = 418. Determine u, given that 66*u**4 - 128*u**3 + 3*u**5 + 41*u**3 - 90*u**2 - 180*u**4 + 60*u**4 + 60*u**d = 0.
-6, -1, 0, 5
Let r(y) be the first derivative of y**6/10 - 4*y**5/25 + y**4/20 - 759. Factor r(o).
o**3*(o - 1)*(3*o - 1)/5
Let s(u) = -9*u**2 - 8*u + 1. Let f be (-1)/((-22)/(-204) + 1/(-6)). Let k(t) = 3*t**2 + 3*t. Let w(a) = f*k(a) + 6*s(a). Factor w(d).
-3*(d - 2)*(d + 1)
Let f(t) = t**2 - 396*t - 8314. Let i be f(-20). Let 3/2*j**2 + 0 + i*j**3 + 7/2*j**4 - j = 0. Calculate j.
-1, 0, 2/7
Let n(v) be the first derivative of v**5/5 - 73*v**4/4 + 93*v**3 - 207*v**2/2 + 6635. Factor n(p).
p*(p - 69)*(p - 3)*(p - 1)
Factor 0 - 128/5*y**4 + 0*y - 3136/5*y**2 + 1232/5*y**3 + 4/5*y**5.
4*y**2*(y - 14)**2*(y - 4)/5
Let p(d) be the third derivative of -13*d**7/420 - 33*d**6/16 - 173*d**5/40 - 37*d**4/48 + 32*d**2 + 5*d. Let p(z) = 0. What is z?
-37, -1, -1/13, 0
Let v = 29185/61982 + -1/3646. Let 0*b**2 - 2/17*b**5 + v*b**4 + 0*b + 10/17*b**3 + 0 = 0. Calculate b.
-1, 0, 5
Suppose -41*c - 689 = -54*c. Factor -11122*t**5 - 52*t**3 - 50*t**2 - c*t**3 - 60*t**4 + 11117*t**5.
-5*t**2*(t + 1)**2*(t + 10)
Let x(a) = -5*a**2 - 8*a - 6. Let l = -2 - -4. Let t(q) = 36*q**l + 22*q + 46*q + 42 + 63*q - 75*q. Let d(n) = -6*t(n) - 44*x(n). What is v in d(v) = 0?
-3, -1
Let a(b) be the third derivative of -b**7/315 + 7*b**6/180 - b**5/15 - 8*b**4/9 + 32*b**3/9 + 3*b**2 - 1006*b. Let a(k) = 0. Calculate k.
-2, 1, 4
Let r(q) be the second derivative of -5/3*q**4 + 0 + 2/15*q**6 + 110*q + 0*q**2 + 2*q**3 + 1/5*q**5. Factor r(b).
4*b*(b - 1)**2*(b + 3)
Let d(j) = -17*j + 106. Let r be d(6). Suppose u + r = z, 4 = -3*z - 2*u + 6. Factor 0 - 12/5*g**z - 3/5*g.
-3*g*(4*g + 1)/5
Let x(v) = -2*v**4 - v**2 - v. Let u(d) = -d**4 + 17*d**3 - 37*d**2 - 7*d. Let a(q) = -u(q) + 7*x(q). Factor a(s).
-s**2*(s - 1)*(13*s + 30)
Let 25653*d**3 - 25710*d**3 + 738 + 108*d - 395*d**2 - 399*d + 5*d**4 = 0. Calculate d.
-3, 1, 82/5
Let k(u) be the second derivative of -u**7/189 + u**6/135 + 5*u**5/18 - 85*u**4/54 + 32*u**3/9 - 4*u**2 + 860*u. Suppose k(i) = 0. What is i?
-6, 1, 2, 3
Suppose -5*y - y + 24 = 0. Factor y*z**3 - 4*z - 34*z - 36*z**2 - 32*z - 44 - 14*z.
4*(z - 11)*(z + 1)**2
Let n(v) = -88*v**2 - 460*v - 204. Let a(x) = 9*x**2 - x + 1. Let k(d) = 12*a(d) + n(d). Let k(c) = 0. What is c?
-2/5, 24
Let d(x) be the third derivative of -1/4*x**4 + 0*x + 2 - 1/120*x**6 - 23*x**2 + 0*x**3 - 1/12*x**5. Factor d(u).
-u*(u + 2)*(u + 3)
Let j(n) be the first derivative of -37 - 8/7*n**2 - 3/7*n**4 + 0*n - 10/7*n**3 + 2/35*n**5. Let j(f) = 0. Calculate f.
-1, 0, 8
Let g be 57/380*32/(-72)*-48. Factor 144/5 + 88/5*n**2 + 1/5*n**4 - 192/5*n - g*n**3.
(n - 6)**2*(n - 2)**2/5
Suppose 48*x**2 + 17*x**3 + 62*x**2 - 15*x**2 + 540 - 12*x**3 - 5*x**2 + 405*x = 0. What is x?
-12, -3
Let s be (((-399)/(-28))/(-19))/(-3). Let c(j) be the second derivative of 4*j + 11/24*j**3 - s*j**2 - 13/48*j**4 + 0 + 1/20*j**5. Solve c(l) = 0 for l.
1/4, 1, 2
Let d(j) be the third derivative of j**8/784 + 43*j**7/490 - 3*j**6/280 - 131*j**5/140 - 43*j**4/28 + 6999*j**2. Let d(n) = 0. Calculate n.
-43, -1, 0, 2
Let 1/2*z**2 - 316 - 157*z = 0. What is z?
-2, 316
Let a(t) be the first derivative of -t**6/30 - t**5/20 + t**4/12 + t**3/6 - 41*t + 43. Let m(f) be the first derivative of a(f). Let m(h) = 0. Calculate h.
-1, 0, 1
Let u(t) be the first derivative of -9*t**5/10 + 15*t**4/16 + 2*t**3 - 21*t**2/8 + 4752. Factor u(l).
-3*l*(l - 1)**2*(6*l + 7)/4
Suppose -12508*m - 2865 = -13081*m. Determine h, given that -616/15*h**m - 134/15*h**4 + 142/15*h**2 - 8/15 - 8/3*h + 656/15*h**3 = 0.
-1, -2/7, -2/11, 1/4, 1
Let q(x) be the first derivative of -9*x**4/4 + 160*x**3/9 - 77*x**2/2 - 6*x - 2629. Suppose q(k) = 0. Calculate k.
-2/27, 3
Let d be (7 + -29 + 23)*(-2)/(-28). Let h(a) be the first derivative of 0*a - 4/21*a**3 + 1/7*a**2 - 43 + d*a**4. Factor h(q).
2*q*(q - 1)**2/7
Solve -12*c**4 - 363*c - 1/4*c**5 - 663/4*c**3 - 517*c**2 + 0 = 0.
-22, -3, -1, 0
Let y(l) = -l**3 + 8*l**2 - 13*l + 8. Let c be y(6). Suppose 3*k + 2*r = 8, 3*k + r - 5 = c*r. Factor -4 + 4*z - z**2 + 2*z - 3*z + k*z.
-(z - 4)*(z - 1)
Let q(o) = -14*o**2 - 393*o + 191. Let g(p) = p**2 + 2*p + 1. Suppose -19*w + 19 + 0 = 0. Let y(x) = w*q(x) + 4*g(x). Factor y(i).
-5*(i + 39)*(2*i - 1)
Factor 250*k**2 + 405/2 + 450*k.
5*(10*k + 9)**2/2
Let d = 733539 - 733537. Let 1/6*c**d - 1/2*c**3 + 1/6*c**5 + 0 - 1/6*c**4 + 1/3*c = 0. Calculate c.
-1, 0, 1, 2
Let f(h) be the first derivative of -2*h**3/27 + 377*h**2/9 - 752*h/9 - 2015. Factor f(v).
-2*(v - 376)*(v - 1)/9
Let u = 684078 + -684078. Determine i, given that u - 4/3*i**5 + 7/3*i**3 - 11/3*i**2 + 11/3*i**4 - i = 0.
-1, -1/4, 0, 1, 3
Let q(y) be the second derivative of y**7/840 + y**6/40 + 9*y**5/40 + y**4/6 + 2*y**2 + 2*y - 34. Let o(w) be the third derivative of q(w). Factor o(g).
3*(g + 3)**2
Let g(w) be the first derivative of -w**3/3 + 1525*w**2/2 + 1526*w - 5361. Factor g(p).
-(p - 1526)*(p + 1)
Suppose -2*o = -2*n + 42, -323*o + 327*o - 96 = -5*n. Factor 200*s - n*s**2 - 2000/3 + 2/3*s**3.
2*(s - 10)**3/3
Suppose -31*b = 690 - 225. Let j be (5 - (-174)/(-30)) + (-17)/b. Factor 1/3*m**4 + 0*m**2 - j*m**3 + 0 + 0*m.
m**3*(m - 1)/3
Let a = 24503/5 + -4900. Let q(n) be the second derivative of -a*n**2 - 28*n + 0 - 17/30*n**4 - 6/25*n**5 - 4/75*n**6 - 1/210*n**7 - 23/30*n**3. Factor q(z).
-(z + 1)**3*(z + 2)*(z + 3)/5
Let f(x) be the first derivative of x**6/2 + 3*x**5 + 9*x**4/4 - 9*x**3 - 5612. Factor f(y).
3*y**2*(y - 1)*(y + 3)**2
Suppose 5*x - 11*x + 24 = 0. Solve 18*i**3 + x*i**3 + 0*i - 6*i**3 - 12*i + 4 = 0.
-1, 1/2
Determine i, given that 563444*i - 40*i**3 + 532989*i - 186433*i - i**4 + 130*i**3 - 29100*i**2 + 3000000 + 207*i**3 = 0.
-3, 100
Let t(l) be the first derivative of -2*l**6/3 + 1332*l**5/5 - 41666*l**4 + 9313928*l**3/3 - 99490938*l**2 + 189833284*l + 629. Factor t(u).
-4*(u - 83)**4*(u - 1)
Suppose 615 - 1683 = -t - 4*u, -4*t + u + 4306 = 0. Determine z so that -3 - 532*z + t*z - 3*z**2 - 538*z = 0.
1
Let r(k) be the second derivative of k**4/48 - 47*k**3/12 + 765*k**2/8 + 6291*k. Factor r(n).
(n - 85)*(n - 9)/4
Let g(z) be the second derivative of z**4/30 - 31*z**3/15 - 312*z**2/5 - 2*z - 727. Factor g(u).
2*(u - 39)*(u + 8)/5
Let n be (-1 + (-16)/(-28))/((-22)/154). Let l(z) be the third derivative of 2/3*z**n + 7/12*z**4 + 19*z**2 + 0*z + 0 - 7/15*z**5 + 1/12*z**6. Factor l(q).
2*(q - 2)*(q - 1)*(5*q + 1)
Suppose 9*o - 40 = 77. Let t be (o - (-24)/(-3)) + 29/(-6). Determine v so that 1/6*v**3 - t*v**2 + 0 - 1/6*v + 1/6*v**4 = 0.
-1, 0, 1
Let b be 374990/40 + 1/4. Solve -5*y**3 + 54*y**2 + 78125 - b*y + 165*y**2 + 156*y**2 = 0 for y.
25
Let r = -1676 + 1445. Let z be ((1/(-2))/((-66)/r))/(-1). Factor 1/4*g**4 + 1/4 + z*g**2 + 9/8*g + 9/8*g**3.
(g + 1)**2*(g + 2)*(2*g + 1)/8
Let a(w) be the second derivative of -w**8/1680 + w**7/210 - w**6/72 + w**5/60 + 21*w**3 - w. Let b(s) be the second derivative of a(s). Solve b(j) = 0 for j.
0, 1, 2
Let u(x) be the third derivative of -1/105*x**7 + 0 - 1/336*x**8 - 6*x + 1/120*x**6 + 0*x**4 + 0*x**3 + x**2 + 1/30*x**5. Factor u(p).
-p**2*(p - 1)*(p + 1)*(p + 2)
Let g(s) be the first derivative of 28 + 0*s**4 + 37/2*s**2 + 1/7*s**3 + 0*s - 1/70*s**5. Let d(h) be the second derivative of g(h). What is u in d(u) = 0?
-1, 1
Determine c, given that -124265208 + 12091*c - 405123*c - 934458*c - 3*c**3 + 0*c**3 + 250046*c - 3114*c**2 = 0.
-346
Suppose 7 = 5*v - 108. Let c be v + -22 - -1*1. What is a in 4*a + 4*a**3 - 3*a**4 + c*a**3 - 4*a = 0?
0, 2
Let g(d) = -53*d**2 - 13350*d + 40481. Let n(u) = 9*u**2 + 2225*u - 6748. Let m(q) = -4*g(q) - 23*n(q). Solve m(c) = 0.
-448, 3
Let z = 1458 + -1456. Let a(v) be the second derivative of 0*v**3 + 4/7*v**z + 0 + 24*v - 1/42*v**4. Determine g, given that a(g) = 0.
-2, 2
Let y(w) = -9*w**3 - 30*w**2 - 114*w +