15/2*w + 15*w**4 - 7/2*w**5 + 20*w**2 + 1 = 0.
2/7, 1
Let d(b) be the third derivative of -b**5/30 + 23*b**4/6 - 15*b**3 - 14*b**2 - 9. What is l in d(l) = 0?
1, 45
Let t(f) = 20*f**3 - 68*f**2 + 48*f + 8. Let o(n) = -13*n**3 + 45*n**2 - 32*n - 5. Let x(d) = 8*o(d) + 5*t(d). Factor x(b).
-4*b*(b - 4)*(b - 1)
Let j(g) = 9*g + 2. Let d be j(5). Suppose -4*h - 2*l + 88 = 0, -5*h + 2*l + 84 = -2*l. Factor -51*c**3 + 2*c**4 - h*c**3 + 32*c**2 - 6*c**3 - 4*c + d*c**4.
c*(c - 1)*(7*c - 2)**2
Let f(q) be the second derivative of -7*q**4/12 + q**3/3 + 5*q. Let i(k) = 10*k**2 - 3*k. Let z(n) = -7*f(n) - 5*i(n). Factor z(y).
-y*(y - 1)
Let q(l) be the third derivative of l**7/2520 - l**6/90 + 2*l**5/15 + l**4/8 - 36*l**2. Let b(f) be the second derivative of q(f). Factor b(s).
(s - 4)**2
Let j(a) be the second derivative of -3/4*a**4 + 3/20*a**5 + a**3 + 0*a**2 + 0 + 12*a. Factor j(v).
3*v*(v - 2)*(v - 1)
Factor 1/4*x**4 + 802135684 + 238*x**3 + 13481272*x + 84966*x**2.
(x + 238)**4/4
Let z(p) be the second derivative of 1/60*p**5 - 7/36*p**4 + 0 - 3/2*p**2 - 12*p + 5/6*p**3. Factor z(r).
(r - 3)**2*(r - 1)/3
Let v(t) = 0 - 4*t + t**2 + 3 + 0*t**2 - 5. Let m be v(5). Find z, given that -3/5 + 3/5*z**2 - 3/5*z + 3/5*z**m = 0.
-1, 1
Factor -11*x - 75/2*x**2 + 0 + 7/2*x**3.
x*(x - 11)*(7*x + 2)/2
Let a = 49287/5 + -9855. Factor -a*j**2 + 0*j + 0 - 3/5*j**3.
-3*j**2*(j + 4)/5
Suppose h - 269 = 3*d - 4*d, d = -2*h + 533. Let t be 3 - (8/(-10) + h/80). Factor w**2 + t - 3/2*w**4 - w**3 - 1/2*w**5 + 3/2*w.
-(w - 1)*(w + 1)**4/2
Let o(q) be the second derivative of -q**6/150 + 7*q**5/50 - 17*q**4/15 + 13*q**3/3 - 15*q**2/2 - 143*q. Let o(n) = 0. What is n?
1, 3, 5
Let d(q) = 2*q + 2. Suppose 20 = -g + 6*l - l, 3*g + 12 = 3*l. Let o be d(g). Let -21*a**4 - 3*a**5 - a**5 + 9*a**3 - 3*a**o - 24*a**3 - 5*a**5 = 0. What is a?
-1, -1/3, 0
Let r(v) be the first derivative of -2*v**3/15 + 26*v**2/5 - 10*v + 199. Factor r(k).
-2*(k - 25)*(k - 1)/5
Let n(g) = 55*g**3. Let b(y) be the third derivative of y**6/15 + 4*y**2. Let u(d) = -20*b(d) + 3*n(d). Factor u(o).
5*o**3
Let n(f) be the first derivative of 3*f**5/25 + 3*f**4/2 + 37*f**3/5 + 18*f**2 + 108*f/5 + 355. Find a such that n(a) = 0.
-3, -2
Let r = 0 + -2. Let t = r + 5. Factor g**2 + g**2 + g + 0*g**3 - 3*g**t.
-g*(g - 1)*(3*g + 1)
Let m be (-90)/(-27)*(-36)/10. Let q(h) = 10*h**3 + 10*h**2 + 8*h + 20. Let y(b) = b**3 + b**2 + 1. Let s(w) = m*y(w) + q(w). Find n, given that s(n) = 0.
-2, -1, 2
Let b(v) be the second derivative of -1/4*v**4 - 29*v + 1/30*v**6 - 1/10*v**5 + 0*v**3 + 0*v**2 + 0. Let b(n) = 0. What is n?
-1, 0, 3
Let r(n) be the second derivative of -7*n**5/20 + 79*n**4/16 + 133*n**3/24 + 9*n**2/4 + 86*n. Factor r(v).
-(v - 9)*(4*v + 1)*(7*v + 2)/4
Let p(w) be the second derivative of -w**6/6 + w**5/2 + 5*w**4/3 - 5*w**3/3 - 15*w**2/2 - 9*w + 3. Solve p(x) = 0 for x.
-1, 1, 3
Let c(d) be the third derivative of d**7/70 - d**6/5 - d**5/20 + d**4 + d**2 + 29. Solve c(q) = 0 for q.
-1, 0, 1, 8
Suppose 10 = -2*u, -2*y + 8 + 2 = -2*u. Suppose 31*d - 58 = 66. Determine t so that -t**d + 0 - 8/3*t**3 + 3*t**5 + y*t + 4/3*t**2 = 0.
-1, 0, 2/3
Let t = -14 - -21. Let s(n) = 9*n**3 + 2*n + 1 - 2 + t*n**3 - 6*n. Let b(y) = -3*y**3 + y. Let i(d) = 33*b(d) + 6*s(d). Suppose i(l) = 0. Calculate l.
-2, 1
Let j(p) = p**3 - 4*p**2 - 3*p - 7. Let k be j(5). Suppose 3 = 4*o + 5*c, -44*c + 9 = 3*o - 47*c. Factor -1/4*h**k + 3/4*h**o - 1/2*h + 0.
-h*(h - 2)*(h - 1)/4
Let t(u) = -8*u**3 + 32*u**2 - 81*u + 81. Let o(z) be the first derivative of 0*z**2 + 0*z + 1 - 1/3*z**3 + 1/4*z**4. Let d(q) = 5*o(q) + t(q). Factor d(n).
-3*(n - 3)**3
Let z(y) be the first derivative of y**5/15 - 7*y**4/6 + 13*y**3/9 + 598. Factor z(g).
g**2*(g - 13)*(g - 1)/3
Let j be 34/(1122/363) + 21/(-2). Determine p so that 2*p**3 + 0 - 5/2*p + j*p**2 = 0.
-5/4, 0, 1
Let k(m) be the third derivative of -3/8*m**4 + 1/20*m**5 + 0 + 0*m**3 + 26*m**2 + 0*m. Factor k(v).
3*v*(v - 3)
Let t(m) be the third derivative of -m**6/120 + m**5/10 - 3*m**4/8 + 2*m**3/3 + 7*m**2 + 2. Factor t(k).
-(k - 4)*(k - 1)**2
Find z such that 0 - 8/3*z - 22/9*z**2 + 2/9*z**3 = 0.
-1, 0, 12
Let r(x) = -2*x**2 + 3*x - 5. Let s(k) be the first derivative of k**3/3 - k**2 + 3*k + 14. Let i(f) = 3*r(f) + 5*s(f). Determine u, given that i(u) = 0.
-1, 0
Let b = 351/175 - -7/25. Factor 0*l - b*l**3 + 16/7*l**2 + 0 + 4/7*l**4.
4*l**2*(l - 2)**2/7
Let o be (-26)/91*(-3 + (-296)/(-108)). Let x(r) be the first derivative of -o*r**3 + 2/9*r + 0*r**2 + 6. Factor x(l).
-2*(l - 1)*(l + 1)/9
Let i(t) = -t**5 + t**4 - t**3 - t. Let v(w) = -4*w**5 + 17*w**4 - 27*w**3 - 3*w. Let a(l) = 6*i(l) - 2*v(l). Solve a(n) = 0.
0, 2, 12
Let o(c) = c**3 + 8*c**2 + 8*c + 7. Let m be o(-7). Let p be (9 - 0) + m + 0. Let -9*z**4 + p*z - 9*z**3 + 0*z**4 - 3*z**2 + 6 + 6*z**4 = 0. What is z?
-2, -1, 1
Let j(r) be the second derivative of -r**5/60 - 25*r**4/36 + 53*r**3/18 - 9*r**2/2 + 21*r - 2. Determine k, given that j(k) = 0.
-27, 1
Let i(s) = 2*s - 5. Let j(g) = 3*g - 11. Let l(y) = -5*i(y) + 2*j(y). Let t be l(-7). Factor t*c**2 - c**3 - 2*c - 4*c**3 - 24*c**2.
-c*(c - 1)*(5*c - 2)
Let i(c) be the third derivative of -c**6/300 + c**5/150 + c**4/30 + 107*c**2. Let i(a) = 0. What is a?
-1, 0, 2
Let t(v) be the second derivative of -v**4 - 2*v**2 - 2*v**3 + 0 + 12*v - 1/5*v**5. Find y such that t(y) = 0.
-1
Let d(n) = -20*n**3 - 14*n**2 + 6*n + 14. Let u(s) = -4*s**3 - 3*s**2 + s + 3. Let f = 42 - 28. Let r(b) = f*u(b) - 3*d(b). Factor r(o).
4*o*(o - 1)*(o + 1)
Let j be 130/(-40)*-20*1. Let g = 391/6 - j. Suppose -1/6*o + 1/6*o**3 - g*o**2 + 1/6 = 0. What is o?
-1, 1
Let x(b) be the third derivative of -b**7/1470 + 11*b**6/840 - 41*b**5/420 + 61*b**4/168 - 5*b**3/7 + 2*b**2 + 25. Suppose x(p) = 0. Calculate p.
1, 2, 3, 5
Let y(d) be the first derivative of 8*d**3 + 12/5*d**5 + 0*d - 4*d**2 - 13/2*d**4 - 1/3*d**6 - 33. Determine j, given that y(j) = 0.
0, 1, 2
Let w(p) = 2*p**4 + 252 + 2*p**2 - 5*p**4 - 255. Let u(d) = d**4 + 1. Let x(n) = 6*u(n) + 3*w(n). Suppose x(i) = 0. Calculate i.
-1, 1
Let t be (-44)/286 + -2 + 108/26. Let z(v) be the first derivative of v**t - 1/3*v**3 - v - 4. Factor z(q).
-(q - 1)**2
Factor -6/7*d**3 + 0*d + 2/7*d**4 - 20/7*d**2 + 0.
2*d**2*(d - 5)*(d + 2)/7
Let c(v) = v**3 - 47*v**2 - 155*v - 162. Let o(a) = 16*a**2 + 52*a + 54. Let m(h) = 2*c(h) + 7*o(h). Determine t so that m(t) = 0.
-3
Factor -40 - 4/7*r**2 - 68/7*r.
-4*(r + 7)*(r + 10)/7
Let u(g) = 2*g**3 + 4*g**2 + 10*g - 4. Let r(b) = b. Let l = 3 - -9. Let t = l + -11. Let w(p) = t*u(p) - 12*r(p). Factor w(h).
2*(h - 1)*(h + 1)*(h + 2)
Let v = -3/211 - -1495/1266. Let p = v + -5/6. Factor 0*c + p - 1/3*c**2.
-(c - 1)*(c + 1)/3
Solve -843*u**2 + 2*u**3 - 129 - 510*u - 127 + 591*u**2 = 0 for u.
-1, 128
Let n = -1/2034 - -46799/34578. Let i = n - -5/34. Let -8/3*v**2 + 0 + 7/2*v**3 + 2/3*v - i*v**4 = 0. Calculate v.
0, 2/3, 1
Let n be (-4)/(-30) - (552/90 + -1). Let h be ((-4)/8)/(10/n). Factor 0 - h*u**2 + 0*u - 1/4*u**3.
-u**2*(u + 1)/4
Let a(o) be the third derivative of -o**7/42 + o**6/6 - o**5/3 - 155*o**2. Suppose a(l) = 0. What is l?
0, 2
Let m = -10 + 16. Suppose -q + m*q = 0. Suppose 2/3*y**3 + 0*y + q - 2/3*y**2 = 0. What is y?
0, 1
Let v(j) be the first derivative of -1/6*j**3 + 6*j - 4 + 1/20*j**5 - 1/6*j**4 + j**2. Let l(y) be the first derivative of v(y). Solve l(s) = 0 for s.
-1, 1, 2
Let f(v) = 19*v**3 - 72*v**2 + 432*v - 869. Let k(h) = 27*h**3 - 108*h**2 + 648*h - 1303. Let a(x) = -7*f(x) + 5*k(x). Determine c so that a(c) = 0.
6
Suppose 45 = a + 5*f, 6*a - 100 = 2*a - 4*f. Factor 10*s**2 + 0*s - 31 + 16 - 20*s**3 + a*s + 5*s**4 + 0*s**2.
5*(s - 3)*(s - 1)**2*(s + 1)
Let b(v) = 21*v**4 - 119*v**3 + 99*v**2 + 108*v - 131. Let u(w) = 11*w**4 - 59*w**3 + 49*w**2 + 53*w - 66. Let i(f) = 6*b(f) - 11*u(f). Factor i(z).
5*(z - 12)*(z - 1)**2*(z + 1)
Let n(v) be the third derivative of v**5/300 + 77*v**4/60 + 5929*v**3/30 - 462*v**2. Suppose n(b) = 0. Calculate b.
-77
Let m(u) be the third derivative of u**9/15120 + u**8/1680 + u**7/420 + u**6/180 + 13*u**5/60 - 3*u**2. Let g(h) be the third derivative of m(h). Factor g(s).
4*(s + 1)**3
Determine n, given that -10 + 1/3*n**3 + 4/3*n**2 - 11/3*n = 0.
-5, -2, 3
Let r