585. Factor -2/9*u + 0 + i*u**2 - 8/9*u**3.
-2*u*(u - 1)*(4*u - 1)/9
Let x be 4 - (4 - 1) - -1. Let n(w) be the first derivative of 2/3*w**3 - 1 - 2/5*w**5 + 1/2*w**4 - w**x + 0*w. Factor n(y).
-2*y*(y - 1)**2*(y + 1)
Let w(b) be the second derivative of -b**8/1680 - b**7/840 + b**6/360 + b**5/120 - b**3/2 + b. Let c(x) be the second derivative of w(x). Factor c(h).
-h*(h - 1)*(h + 1)**2
Let o(p) be the first derivative of p**4/28 + 4*p**3/21 + 5*p**2/14 + 2*p/7 + 9. Factor o(x).
(x + 1)**2*(x + 2)/7
Let z(n) be the first derivative of -n**4/2 + 8*n**3/3 - 3*n**2 - 4. Factor z(t).
-2*t*(t - 3)*(t - 1)
Let h be 22/6 + (-3)/(-9). Determine l, given that l**3 + 2*l**5 + 14*l**4 - l**3 + 2*l**3 - 18*l**h = 0.
0, 1
Let f(n) be the first derivative of -1/18*n**4 - 2 - 2/9*n**3 - 3*n - 1/3*n**2. Let g(u) be the first derivative of f(u). Factor g(h).
-2*(h + 1)**2/3
Let b = -4/15 - -2/5. Solve b + 2/3*k**2 - 8/15*k - 4/15*k**3 = 0.
1/2, 1
Let o(c) be the second derivative of 0*c**3 + 0*c**5 - 1/45*c**6 + 1/9*c**4 + 0 - 1/3*c**2 + 2*c. Factor o(f).
-2*(f - 1)**2*(f + 1)**2/3
Let y = 313797 - 126774097/404. Let p = -2/101 - y. What is n in 0*n - 1/4*n**2 + 1/2*n**3 + 0 - p*n**4 = 0?
0, 1
Let u(m) be the second derivative of m**5/45 - 4*m**4/27 + 2*m**3/9 + m - 51. Factor u(n).
4*n*(n - 3)*(n - 1)/9
Factor 8/5*z + 8/5 + 2/5*z**2.
2*(z + 2)**2/5
Let h(n) be the first derivative of n**6/105 + n**5/35 + 3*n + 4. Let q(g) be the first derivative of h(g). Solve q(t) = 0 for t.
-2, 0
Let w be 1/(-6)*4 + 14/3. Let z(p) be the second derivative of 0 + 1/20*p**5 + 0*p**3 + 0*p**w + 1/42*p**7 + 0*p**2 + 1/15*p**6 - 2*p. Factor z(k).
k**3*(k + 1)**2
Factor 49/2 - 5/2*l**3 - 69/2*l**2 - 231/2*l.
-(l + 7)**2*(5*l - 1)/2
Let v(k) = k**4 + 11*k**3 + 19*k**2 + 9*k - 9. Let d(g) = g**4 + 6*g**3 + 9*g**2 + 4*g - 4. Let b(w) = 9*d(w) - 4*v(w). Factor b(x).
5*x**2*(x + 1)**2
Let m(g) be the third derivative of g**6/320 + g**5/96 - g**4/48 - g**3/12 + 10*g**2. Factor m(h).
(h - 1)*(h + 2)*(3*h + 2)/8
Let h be 0 + 0 - 4/(-18). Suppose 0 = -3*w + 2*o, -o = -0*o. What is c in 2/9*c**3 + w - 8/9*c**2 + 8/9*c**4 - h*c = 0?
-1, -1/4, 0, 1
Suppose -10 = -y - 4*y. Let u(x) be the first derivative of -y + 1/12*x**3 + 0*x + 1/8*x**2 - 1/8*x**4. Factor u(s).
-s*(s - 1)*(2*s + 1)/4
Factor -1 + 1 + 15*p**3 - 1158*p**4 + 1146*p**4 - 6*p**2 + 3*p**5.
3*p**2*(p - 2)*(p - 1)**2
Let a(l) be the third derivative of -l**7/105 + l**6/20 - l**4/3 - 7*l**2. Factor a(y).
-2*y*(y - 2)**2*(y + 1)
Let f(w) = 2*w + 8. Let k be f(6). Factor -i**2 - 1 + 2 + k*i**3 - 19*i**3 - i.
(i - 1)**2*(i + 1)
Factor -8/5*h**4 - 12/5*h**2 + 28/5*h**3 + 0*h + 0.
-4*h**2*(h - 3)*(2*h - 1)/5
Let o(t) be the second derivative of 3*t - 1/8*t**3 + 1/80*t**5 + 1/4*t**2 + 0 + 0*t**4. Solve o(i) = 0.
-2, 1
Suppose 0 = -0*c - c - 5*h + 1, -5*h + 5 = 0. Let l be (-3 - c) + 1/1. Solve -1/2 + a - 1/2*a**l = 0 for a.
1
Let v(u) = u**3 - u**2. Let c(y) = -10*y**3 - 17*y**2 + 69*y + 18. Let z(m) = c(m) - 2*v(m). Solve z(p) = 0.
-3, -1/4, 2
Suppose 2*o - 4 = -2*o. Suppose 5 = -2*h + 2*f + o, -2*h - 3*f = -21. Find m, given that -1/4*m**h + 0 - 1/4*m**2 + 0*m = 0.
-1, 0
Let v(x) be the second derivative of 3*x + 0 + 1/12*x**4 + 5/24*x**3 + 1/8*x**2. Determine b, given that v(b) = 0.
-1, -1/4
Let y(c) = -26*c**3 + 32*c**2 + 13*c - 1. Let j(n) = -9*n**3 + 11*n**2 + 4*n. Let p(b) = -11*j(b) + 4*y(b). Factor p(r).
-(r - 2)*(r + 1)*(5*r - 2)
Let h(p) = -p + 6. Let m be h(5). Let o(r) be the first derivative of 1/3*r**3 - m + r - r**2. Factor o(w).
(w - 1)**2
Factor -6/5*t**3 + 0 + 6/5*t**2 - 2/5*t + 2/5*t**4.
2*t*(t - 1)**3/5
Let u(v) be the second derivative of -2*v + 0*v**2 + 0 + 3/20*v**5 + 0*v**4 + 0*v**3. Factor u(y).
3*y**3
Let q = 89/924 + -1/77. Let s(o) be the second derivative of 0 + 0*o**2 - q*o**4 - 1/6*o**3 + 3*o. Let s(k) = 0. What is k?
-1, 0
Let p(o) = -12*o**4 + 2*o**3 - 8*o**2 + 8*o + 8. Let x(n) = -n**4 - n**2 + n + 1. Let l(m) = -p(m) + 8*x(m). Factor l(i).
2*i**3*(2*i - 1)
Let m(t) = 7*t**2 + 15*t + 11. Suppose 0 = -q + 8*q + 21. Let v(o) = 15*o**2 + 31*o + 23. Let r(s) = q*v(s) + 7*m(s). Suppose r(c) = 0. Calculate c.
-2, -1
Let y be 120/16*(52/(-20) - -3). Factor 2*m + 8/5*m**2 + 4/5 + 2/5*m**y.
2*(m + 1)**2*(m + 2)/5
Let k be (-126)/(-24) - 5 - 1/(-4). Let m(f) be the first derivative of -f**3 + 0*f + 9/4*f**4 - 3 + 0*f**2 - 9/5*f**5 + k*f**6. Solve m(v) = 0 for v.
0, 1
Let z(o) = o**2 - 16*o + 51. Let k be z(12). Let 3/5*d**2 - 3/5*d - 3/5 + 3/5*d**k = 0. Calculate d.
-1, 1
Suppose 8/5*c**3 + 4/5*c**4 + 0*c + 0 + 0*c**2 = 0. Calculate c.
-2, 0
Let i(n) = n**3 - 8*n**2 - 8*n - 6. Let d be i(9). Let t(s) be the third derivative of 0*s + 0 - 1/60*s**5 + 0*s**d + 2*s**2 + 1/24*s**4. Factor t(q).
-q*(q - 1)
Factor 18*j**2 - 39*j**4 - 2*j**3 - j**3 + 29*j**4 - 3*j**3 - 2*j**5.
-2*j**2*(j - 1)*(j + 3)**2
Let c = 4 - 2. Solve -4*z + 7*z**2 - 2*z**4 - 16*z**2 - c*z**5 + 6*z**3 + 11*z**2 = 0 for z.
-2, -1, 0, 1
Let p = 28 - 28. Let j(o) be the second derivative of -3/20*o**5 + 0 + 1/30*o**6 + 1/4*o**4 - 1/6*o**3 + 3*o + p*o**2. Let j(r) = 0. What is r?
0, 1
Let b(r) = 3*r**3 + 3*r**2 + 3*r - 3. Let w(j) = -6*j**3 - 5*j**2 - 6*j + 7. Let i(g) = -7*b(g) - 3*w(g). Factor i(q).
-3*q*(q + 1)**2
Let q be ((-3)/2)/(3/(-58)). Determine a so that -q*a + 1 - 4*a**2 + 3*a**2 + 29*a = 0.
-1, 1
Let z(t) be the first derivative of t**3/3 - 5*t**2/2 - 3*t + 2. Let o(k) = 2*k**2 - 6*k - 4. Let f(j) = 3*o(j) - 4*z(j). Determine s so that f(s) = 0.
-1, 0
Find o, given that -5*o**2 + 12*o + 3 + 4*o**2 - 10*o = 0.
-1, 3
Let h(v) = -4*v**4 + 2*v**3 - 12*v**2 + 7*v + 1. Let p(z) = 0 + z**3 - 1 + 0*z**3 + z**4 + z**2 + 0*z**4. Let t(r) = -h(r) - 3*p(r). Factor t(u).
(u - 2)*(u - 1)**3
Let d(m) be the third derivative of 0*m - 3*m**2 + 0 + 1/60*m**4 - 1/30*m**3 - 1/300*m**5. Factor d(o).
-(o - 1)**2/5
Let -2/9*k + 0 - 1/9*k**4 + 1/3*k**3 + 1/9*k**2 - 1/9*k**5 = 0. What is k?
-2, -1, 0, 1
Factor 19 - 35 - 6*p + 19 + 3*p**2.
3*(p - 1)**2
Let x(c) be the third derivative of c**6/20 + 3*c**5/20 + c**4/8 + 2*c**2. Factor x(d).
3*d*(d + 1)*(2*d + 1)
Let y(k) = -k**2. Let l(p) be the third derivative of 2*p**2 - 1/2*p**3 + 0 + 0*p + 0*p**4 - 1/10*p**5. Let w(o) = -l(o) + 9*y(o). Factor w(r).
-3*(r - 1)*(r + 1)
Let v(h) = 0*h**2 - h**2 + 0*h + h + 3*h**2 + h**3. Let y(m) = 3*m**3 + 5*m**2 + 2*m. Let s(o) = 5*v(o) - 2*y(o). Let s(x) = 0. Calculate x.
-1, 0, 1
Let i(r) be the second derivative of 3*r**5/40 + r**4/4 - r**3/4 - 3*r**2/2 + 2*r. Suppose i(z) = 0. Calculate z.
-2, -1, 1
Let m = 130 + -125. Let v(d) be the first derivative of 1/15*d**m - 1/6*d**2 - 1/9*d**3 + 0*d + 1/12*d**4 - 4. Solve v(x) = 0 for x.
-1, 0, 1
Let n(f) be the first derivative of f**6/10 - 8*f**5/15 + 2*f**4/3 - f**2 + 4. Let z(y) be the second derivative of n(y). Let z(h) = 0. What is h?
0, 2/3, 2
Let j(f) be the second derivative of -f**9/30240 - f**8/13440 + f**4/6 + 4*f. Let x(u) be the third derivative of j(u). Determine w so that x(w) = 0.
-1, 0
Let z be 11464/(-252) - (-2)/(-7). Let j = z + 46. Find y such that 2/9 + j*y**2 - 4/9*y = 0.
1
Let k be (-1 + 3)/(1/3). Find a such that 4*a - 2*a**2 + 4 - 12 + k = 0.
1
Let x(a) be the first derivative of -a**3/9 + a**2/3 + 1. Suppose x(h) = 0. What is h?
0, 2
Let q(t) be the first derivative of 0*t**3 - t**2 + 1/6*t**4 + 3*t - 2. Let d(h) be the first derivative of q(h). Factor d(o).
2*(o - 1)*(o + 1)
Let l(k) be the first derivative of -2/39*k**3 - 2/13*k + 2/13*k**2 + 3. Suppose l(g) = 0. What is g?
1
Factor 5/4*w**2 - 7/4*w + 3/4 - 1/4*w**3.
-(w - 3)*(w - 1)**2/4
Let m(b) = b**3 + 7*b**2 - 32. Let a be m(-6). Let d(z) be the second derivative of 0 - 1/18*z**3 - 1/36*z**a + 1/6*z**2 + 1/60*z**5 - 4*z. Factor d(q).
(q - 1)**2*(q + 1)/3
Let p(o) = 14*o**2 - 114*o + 11. Let t(a) = 3*a**2 - 23*a + 2. Let q(j) = -2*p(j) + 11*t(j). Factor q(d).
5*d*(d - 5)
Determine y so that 3/7*y**3 - 4/7 + y**2 + 0*y = 0.
-2, -1, 2/3
Let m(y) = -13*y**4 - 8*y**3 + 28*y**2 + 8*y - 15. Let l(x) = 25*x**4 + 15*x**3 - 55*x**2 - 15*x + 30. Let o(u) = 3*l(u) + 5*m(u). Find c, given that o(c) = 0.
-3/2, -1, 1
Let f(g) be the second derivative of -g**7/168 - g**6/30 - g**5/16 - g**4/24 + 3*g. Factor f(o).
-o**2*(o + 1)**2*(o + 2)/4
Let n(q) be the firs