 1)**3/9
Let p(o) be the second derivative of 4*o + 0*o**3 + 6 + 0*o**2 + 5/3*o**4 - 1/20*o**5. Find x, given that p(x) = 0.
0, 20
Let a be 22/5*(-55)/(-22). Factor 178 + 160 + a*u + 2*u**2 + 41*u + 0*u.
2*(u + 13)**2
Let o(j) be the second derivative of j**7/1260 - j**5/90 + j**2/2 - 54*j - 2. Let x(f) be the first derivative of o(f). Factor x(r).
r**2*(r - 2)*(r + 2)/6
Let o(n) be the third derivative of n**5/180 + 119*n**4/3 + 113288*n**3 - 119*n**2 + 2*n + 1. Find u such that o(u) = 0.
-1428
Let z(j) = j**3 - 11*j**2 - 44*j - 3. Let l be z(-3). Factor 0 + 0*a + 1/4*a**l + 3/2*a**2.
a**2*(a + 6)/4
Let o(b) be the first derivative of -b**8/840 + b**7/180 - b**6/270 - b**3/3 + 30*b**2 + 42. Let d(y) be the third derivative of o(y). Factor d(x).
-2*x**2*(x - 2)*(3*x - 1)/3
Let l = 524 + -496. Suppose -154*w**4 + 10*w**3 + w**2 + 123*w**4 - 14*w**5 - l*w**3 + 2*w = 0. What is w?
-1, -1/2, 0, 2/7
Let b(d) be the first derivative of -d**6/1980 - 17*d**5/165 - 289*d**4/33 - 2*d**3/3 + 15*d**2 + 210. Let r(v) be the third derivative of b(v). Factor r(z).
-2*(z + 34)**2/11
Let t be (-2016)/616 + 580/110. Factor -32/5*v**3 + 126/5*v**t + 32/5*v - 128/5 + 2/5*v**4.
2*(v - 8)**2*(v - 1)*(v + 1)/5
Let j(x) be the first derivative of -2*x**3/15 - 2958*x**2/5 - 4374882*x/5 - 3582. Let j(r) = 0. What is r?
-1479
Let a(n) = 6*n**3 - 2*n**2 - 4. Let b(r) = 10*r**3 + 22*r**2 - 20*r - 56. Let k(l) = -2*a(l) + b(l). Suppose k(y) = 0. Calculate y.
-1, 2, 12
Let z(w) be the first derivative of -9*w**4/2 + 10*w**3/3 + 14*w**2 - 576. Factor z(q).
-2*q*(q + 1)*(9*q - 14)
Let v = 1174 - 1213. Let c be (-6)/(-34)*(442/v - -14). Factor 0*r + c*r**3 + 0 + 6/17*r**4 + 2/17*r**2.
2*r**2*(r + 1)*(3*r + 1)/17
Suppose -164/3*g**4 - 1408/3*g**3 + 5792/3*g**2 - 7744/3 - 4/3*g**5 - 704/3*g = 0. Calculate g.
-22, -1, 2
Solve 167 + 170 + 1363 + u**2 - 32*u - 5*u**2 = 0.
-25, 17
Let y(h) be the first derivative of 5*h**4/4 + 80*h**3/3 + 45*h**2/2 - 450*h + 849. Factor y(s).
5*(s - 2)*(s + 3)*(s + 15)
Let f(k) be the first derivative of 0*k**3 + 0*k + 3/16*k**4 + 1/5*k**5 + 0*k**2 + 1/24*k**6 + 3. Factor f(m).
m**3*(m + 1)*(m + 3)/4
Let d(l) = -2*l**3 - 26*l**2 - 3*l - 51. Let u be d(-13). Let x be 1*(-4)/16 + (-27)/u. Find z such that 2/9*z**3 + 14/9*z + 10/9*z**x + 2/3 = 0.
-3, -1
Let a(i) be the third derivative of 2*i**7/105 + 7*i**6/30 + 7*i**5/15 - 5*i**4/2 - 934*i**2. Factor a(l).
4*l*(l - 1)*(l + 3)*(l + 5)
Let c(k) = -k**3 - 4*k**2 - k + 9. Let m be c(-4). Suppose 37 = 8*y + m. Solve -61*j**5 + 3*j**3 - 2*j**2 + 0*j**y + 60*j**5 = 0.
-2, 0, 1
Factor -1/5*z**2 + 3818/5*z - 3644281/5.
-(z - 1909)**2/5
Factor 16456/7*f + 0 + 4/7*f**4 + 48/7*f**3 - 2508/7*f**2.
4*f*(f - 11)**2*(f + 34)/7
Let y(m) = -4*m - 4*m**2 + 2*m**2 - 17*m - 3*m**2. Let t(d) = -d. Suppose 0 = -9*g + 1 - 10. Let i(a) = g*y(a) + 6*t(a). What is j in i(j) = 0?
-3, 0
Let m(b) be the third derivative of b**8/168 - 43*b**7/105 - 89*b**6/60 - 3*b**5/2 - 35*b**2 + 22. Find d such that m(d) = 0.
-1, 0, 45
Let d(z) be the first derivative of -z**5/210 + 3*z**4/28 - 8*z**3/21 + 2*z**2 + z + 15. Let q(l) be the second derivative of d(l). Factor q(g).
-2*(g - 8)*(g - 1)/7
Let d(a) = 6*a**2 + 4*a - 10. Let y(t) = -9 - 2 + 7*t**2 + 5*t - t. Suppose v + 8 = 3. Let o(r) = v*d(r) + 4*y(r). Factor o(u).
-2*(u - 1)*(u + 3)
Suppose -332*o + 23*o = -182*o - 1058 - 1228. Factor -94/5 - o*u**2 + 2/5*u**3 - 186/5*u.
2*(u - 47)*(u + 1)**2/5
Let i = -325461 - -2603751/8. Factor -5/8*z**3 - 33/8*z**2 - 27/8 - i*z.
-(z + 3)**2*(5*z + 3)/8
Let r(d) be the third derivative of d**6/40 - 591*d**5/20 - 74*d**4 + 26*d**2 - 39*d. Find z, given that r(z) = 0.
-1, 0, 592
Let f = 17529 - 4207039/240. Let s = 1/240 - f. Factor 0*x**2 + s*x**3 + 0 - 2/3*x**4 + 0*x + 1/3*x**5.
x**3*(x - 1)**2/3
Suppose 3*r + 4 = k, 15 = -4*r + 19. Suppose k = 5*w + y, -10*y + 8 = w - 12*y. Find l, given that -l**3 - 6/5*l**w + 1/5*l**4 + 0 + 0*l = 0.
-1, 0, 6
Let h = -310 + 486. Let j be 0 + h/170 - 12/15. Let 18/17*a**3 + 14/17*a**2 + 2/17*a**5 + 0 + j*a + 10/17*a**4 = 0. Calculate a.
-2, -1, 0
Let z be 18/45*1 - 86/215. Let j be (-2)/(-3) - 2/12. Solve 3/2*d - j*d**2 + z = 0.
0, 3
Let y(u) be the second derivative of 14 + 0*u**2 - 1/6*u**4 + 8/3*u**3 - u. Factor y(r).
-2*r*(r - 8)
Let s = -107594 - -107600. Factor 2/7*x**2 - 44/7*x + s.
2*(x - 21)*(x - 1)/7
Let c = -1957533/5 - -391509. Factor -2/5*d**2 - 18/5 + c*d.
-2*(d - 3)**2/5
Factor -75/4*z**2 + 561/8*z + 3/8*z**3 - 207/4.
3*(z - 46)*(z - 3)*(z - 1)/8
Let r(a) be the second derivative of -a**5/80 - 35*a**4/48 - 407*a**3/24 - 1573*a**2/8 + 7*a + 19. Factor r(z).
-(z + 11)**2*(z + 13)/4
Determine g so that 360*g - 650 - 394 + 115*g**2 - 119*g**2 = 0.
3, 87
Let y(k) be the second derivative of k**4 - 286*k**3/3 + 188*k**2 - 782*k - 3. Factor y(u).
4*(u - 47)*(3*u - 2)
Let k be 2 + 8 + (1 - 9). Determine o so that o**2 - 3271 - 1837 + 19153 + 4*o**k - 530*o = 0.
53
Let l(q) = 3*q**4 + 6*q**3 + 27*q**2 + 12*q - 6. Let g(x) = -5*x - x**2 - 1 + 2 + 5*x - x**3 - x**4 + x. Let f(n) = 6*g(n) + l(n). Factor f(s).
-3*s*(s - 3)*(s + 1)*(s + 2)
Let s(d) = 67*d**2 + 8*d - 9. Let x be s(1). Suppose 131*o - 37*o**2 - 71*o + x*o**3 + 3*o**4 + 160*o**2 = 0. Calculate o.
-20, -1, 0
Suppose 0 + 28/5*o**3 + 64/5*o**2 + 4/5*o**4 + 48/5*o = 0. What is o?
-3, -2, 0
Let q(y) = 3159*y - 12633. Let l be q(4). What is b in 8/9*b**l - 2/3*b**4 + 0*b - 2/9*b**2 + 0 = 0?
0, 1/3, 1
Suppose 2*d = -3 - 1, -5*l = d - 18. Let q(w) be the second derivative of -3/2*w**5 - 3/2*w**2 + 23/8*w**l - 1/4*w**3 + 0 + 15*w. Let q(h) = 0. What is h?
-1/4, 2/5, 1
Let f(b) = -110*b - 225. Let l(h) = h**2 + 111*h + 224. Let m(z) = -6*f(z) - 5*l(z). Factor m(d).
-5*(d - 23)*(d + 2)
Let -2 + 88/5*i**3 + 4/5*i**5 - 20*i**2 + 52/5*i - 34/5*i**4 = 0. What is i?
1/2, 1, 5
Suppose -83*g = -82*g - 2907. Determine b so that g*b - 3*b**2 - 12 + 5*b**2 - 2916*b + b**2 = 0.
-1, 4
Let r(u) = -11*u - 718. Let l be r(-66). Let n(a) be the second derivative of l*a + 0 + 3/40*a**5 + 1/9*a**3 + 0*a**2 - 1/6*a**4. Suppose n(z) = 0. What is z?
0, 2/3
Let j(m) be the first derivative of -m**4/30 - 4*m**3/15 - 4*m**2/5 + 19*m + 41. Let p(n) be the first derivative of j(n). Solve p(o) = 0.
-2
Let w(x) = -16*x**2 + 73*x + 83. Suppose 4*b = -4*t - 84, 5*b + 4 + 21 = 0. Let s(v) = -84*v**2 + 364*v + 416. Let j(i) = t*w(i) + 3*s(i). Factor j(p).
4*(p - 20)*(p + 1)
Factor 151*u - 216 + 10*u**3 + 446 + 204*u + 114*u**2 - 674*u**2 - 35*u**3.
-5*(u - 1)*(u + 23)*(5*u + 2)
Let c = 584 + -590. Let l(s) = 11*s**3 + 2*s**2 - 13*s + 12. Let g(w) = 24*w**3 + 3*w**2 - 25*w + 24. Let b(v) = c*g(v) + 13*l(v). Factor b(o).
-(o - 4)*(o - 3)*(o - 1)
Determine q so that 2299*q + 361/3 + 241*q**2 + 19/3*q**3 = 0.
-19, -1/19
Let x(f) be the second derivative of 6*f + 230/3*f**3 - 4 + 2645/12*f**4 + 10*f**2. Suppose x(c) = 0. Calculate c.
-2/23
Let m be (-41)/(-14) + (-327)/218. Factor 0 + 0*b - 2/7*b**3 + m*b**2.
-2*b**2*(b - 5)/7
Let w(j) = 11*j**2 + 1970*j - 1946. Let i(t) = -2*t**2 - 328*t + 324. Let x(k) = -35*i(k) - 6*w(k). Factor x(q).
4*(q - 84)*(q - 1)
Let u(m) = 14*m**3 + 11386*m**2 - 2177574*m + 2166029. Let s(t) = 3*t**3 + 2277*t**2 - 435516*t + 433206. Let v(y) = -29*s(y) + 6*u(y). Factor v(h).
-3*(h - 380)**2*(h - 1)
Suppose -2*j - 30 = 4*s, -2441*j + 9*s + 87 = -2439*j. Factor -1/6*g + 2/3 + 1/6*g**j - 2/3*g**2.
(g - 4)*(g - 1)*(g + 1)/6
Suppose 2*d + 5*c - 31 = 0, -5*d + 40 = 4383*c - 4378*c. Factor -3/2*s**d - 20736 - 108*s**2 - 2592*s.
-3*(s + 24)**3/2
Let t(b) be the first derivative of 2*b**5/35 - 11*b**4/14 - 26*b**3/7 - 41*b**2/7 - 4*b - 2006. Factor t(g).
2*(g - 14)*(g + 1)**3/7
Determine j so that 0 - 18/7*j**3 - 120/7*j**2 - 75/7*j + 24/7*j**4 - 3/7*j**5 = 0.
-1, 0, 5
Let b(p) be the second derivative of -p**6/10 - 17*p**5/5 + 119*p**4/12 + 3440*p**3/3 - 1152*p**2 + 1476*p. Solve b(g) = 0.
-16, 1/3, 9
Let r = 216 - 238. Let b be 14/(-77) + (-48)/r. Find t, given that 1/6*t**3 - 3/2 + 5/6*t**b + 1/2*t = 0.
-3, 1
Let v(d) be the second derivative of 1/25*d**5 - 1/15*d**3 + 0 - 1/105*d**7 - 33*d - 1/5*d**2 - 1/75*d**6 + 1/15*d**4. Factor v(f).
-2*(f - 1)**2*(f + 1)**3/5
Suppose 15 + 1/4*a**2 - 23/4*a = 0. Calculate a.
3, 20
Let u(d) = -d**3 - 2*d**2 - 3*d - 4. Let h be u(-2)