et w(c) be the second derivative of -c**9/15120 + c**8/6720 + c**7/504 + c**6/240 + 8*c**4/3 - 18*c. Let y(j) be the third derivative of w(j). Factor y(n).
-n*(n - 3)*(n + 1)**2
Let t(x) = -8*x**3 - 10*x**2 + 70*x + 162. Let j(y) = 10*y**3 + 9*y**2 - 69*y - 163. Let p(z) = 2*j(z) + 3*t(z). Factor p(m).
-4*(m - 4)*(m + 2)*(m + 5)
Let m(i) be the second derivative of i**6/60 + i**5/20 - i**4/8 - 2*i**3/3 - i**2 + 373*i. Suppose m(o) = 0. What is o?
-2, -1, 2
Let w(k) be the third derivative of -k**5/12 - 5*k**4/12 + 20*k**3/3 + 2*k**2. Factor w(a).
-5*(a - 2)*(a + 4)
Let q(l) be the first derivative of 4*l**3/15 - 256*l**2/5 + 16384*l/5 + 160. Determine f, given that q(f) = 0.
64
Let o(k) be the third derivative of 0 - 1/360*k**6 + 5/6*k**3 + 0*k - 6*k**2 + 1/12*k**4 + 1/120*k**5. Let b(y) be the first derivative of o(y). Solve b(l) = 0.
-1, 2
Let p(m) be the first derivative of -m**7/168 + m**5/24 - 2*m**3 - 5. Let f(g) be the third derivative of p(g). Factor f(v).
-5*v*(v - 1)*(v + 1)
Let j be 2/10 - 6963/(-7385). Factor -2/7*h**2 - j*h - 8/7.
-2*(h + 2)**2/7
Suppose -3*v + u + 27 = 7, 4*v - 40 = 4*u. Factor 0 + 2/7*r**4 + 0*r + 1/7*r**v - 2/7*r**2 - 1/7*r**3.
r**2*(r - 1)*(r + 1)*(r + 2)/7
Let n = 99 - 94. Suppose -2*i + n*i + 2 = -4*m, -m + 4 = 3*i. Factor 0 + 2/9*j**i - 2/9*j.
2*j*(j - 1)/9
Let v(n) be the second derivative of -2*n**6/5 + 61*n**5/5 - 85*n**4 - 374*n**3 - 484*n**2 - 136*n. Suppose v(k) = 0. What is k?
-1, -2/3, 11
Factor -3/7*u**3 + 66/7*u**2 - 225/7*u + 162/7.
-3*(u - 18)*(u - 3)*(u - 1)/7
Suppose -b + 0*b = -3*j + 12, -4*j - b + 23 = 0. Suppose 2*s**4 + s**5 - 3*s**j - 4*s**4 = 0. What is s?
-1, 0
Let j be (2 - 1 - -3) + 2. Suppose 11 = 4*x + 3*r - 0*r, -j = -5*x + 4*r. Factor q + 13*q**3 - 2*q**4 - 6*q**4 - 8*q**2 + q + x*q**5 - q**3.
2*q*(q - 1)**4
Let k be (-2 + 10)*(-1)/(-2). Factor -9*v**2 - 11*v**3 + 2*v**3 + 0*v**2 - 3*v - v**k - 2*v**4.
-3*v*(v + 1)**3
Let j = -16 + 21. Suppose -4*w - 5*i + 14 = -w, -j = -w - 2*i. Factor -2/3*r - 10/3*r**w + 0 - 4/3*r**4 - 8/3*r**2.
-2*r*(r + 1)**2*(2*r + 1)/3
Let l(u) be the second derivative of -3*u**6/20 + 69*u**5/40 - 37*u**4/8 - 15*u**3/4 + 6*u. Let l(h) = 0. Calculate h.
-1/3, 0, 3, 5
Solve 48/5 + 24/5*f**2 - 14*f - 2/5*f**3 = 0.
1, 3, 8
Let o = -2815 - -2817. Find u, given that -2/7*u**5 - 4/7*u**o + 0*u + 4/7*u**4 + 0 + 2/7*u**3 = 0.
-1, 0, 1, 2
Let h = -1701 + 1701. Suppose 0 + 0*j**2 - 12/7*j**5 + h*j - 3/7*j**3 + 15/7*j**4 = 0. Calculate j.
0, 1/4, 1
Let v(j) = -85*j**2 - 65*j + 1310. Let d(i) = 5*i**2 + 4*i - 77. Let z(r) = -35*d(r) - 2*v(r). Suppose z(a) = 0. What is a?
-5, 3
Let g = 3 - 3. Let a be 15 + -4 + -4 + (-30)/6. Factor g*q - 2/7*q**a + 0.
-2*q**2/7
Suppose 24 = 22*r - 10*r. Let u(i) be the first derivative of 5/4*i**r - 2/3*i**3 + 5 - 1/2*i. Find t, given that u(t) = 0.
1/4, 1
Factor 106/7*y - 2/7*y**2 + 0.
-2*y*(y - 53)/7
Let m(t) = -t + 10. Let u be m(5). Suppose -9*j - u + 23 = 0. Let j*c + 5/4*c**2 - 1 = 0. What is c?
-2, 2/5
Let y = -85 - -70. Let u be 3/(3*(-5)/y). Factor 2/7*d**4 - 2/7*d**u + 0*d**2 + 0 + 0*d.
2*d**3*(d - 1)/7
Let f(h) = 3*h + 26. Let g be f(-6). Let s be 212/140 + g/28. Factor 9/5*n + s*n**2 + 3/5 + 3/5*n**3.
3*(n + 1)**3/5
Let r(i) be the first derivative of -4*i**3/3 - 20*i**2 - 96*i + 160. Suppose r(b) = 0. Calculate b.
-6, -4
Let f(r) be the second derivative of 1/36*r**4 + 0 - 4/9*r**3 - 18*r + 8/3*r**2. Factor f(s).
(s - 4)**2/3
Let i(p) be the second derivative of p**4/4 - 123*p**3 + 45387*p**2/2 + 333*p. Factor i(h).
3*(h - 123)**2
Let c(s) = 3*s - 22. Let d be c(8). Suppose g - 6 = -3. Suppose -43*f**d + 31*f**g + 4*f - 7*f**3 + 4*f**5 + 16*f**4 + 59*f**2 = 0. What is f?
-1, 0
Let n(z) be the first derivative of 0*z**2 - 1/7*z**3 - 9 + 0*z. Let n(d) = 0. What is d?
0
Let w be (-72)/(-7 + 3)*2/3. Suppose 4*n + 5*j = -3, 5*n + 0*j - w = -j. Determine b so that n*b**3 + 7*b**2 + 4/3 + 16/3*b = 0.
-1, -2/3
Suppose 0 = -2*f - i + 2, -2*f - f + 10 = -2*i. Factor 7*u - 10*u + 4*u**2 - u**3 + 0*u**f.
-u*(u - 3)*(u - 1)
Let j(g) be the third derivative of g**5/450 - 5*g**4/36 + 8*g**3/15 + 3*g**2 - 66. Factor j(l).
2*(l - 24)*(l - 1)/15
Suppose -i - 119 = -8*i. Suppose -i + 7 = -5*g. Factor -8*s**g + 18*s**2 - 15*s**2.
-5*s**2
Let v(u) be the first derivative of -u**6/40 + u**5/20 + 3*u**4/4 - 39*u**2/2 + 47. Let l(z) be the second derivative of v(z). Factor l(p).
-3*p*(p - 3)*(p + 2)
Suppose 0 = -2*p - 4*f + 8, -3*f + 8*f = p + 3. Find b such that -4*b**4 - b**4 + 2*b**3 + 2*b**4 + 2*b**p - 2*b + b**4 = 0.
-1, 0, 1
Let o(u) be the first derivative of -2/3*u**3 - 10*u + 14 - 6*u**2. Factor o(t).
-2*(t + 1)*(t + 5)
Let d be (-5)/(-25) - 18/(-10). Let h be (3/d)/3*6. Let 10*f**2 + 4*f**h - 24*f**3 + 2*f**2 + 48*f + 16 = 0. What is f?
-1, -2/5, 2
What is m in -30*m**2 + m**4 - 8*m + 71*m**3 + 19 + 17*m**2 - 62*m**3 - 7 - m**5 = 0?
-3, -1, 1, 2
Let n(h) be the second derivative of h**7/21 + h**6/3 + h**5 + 5*h**4/3 + 5*h**3/3 + h**2 - 90*h. Factor n(v).
2*(v + 1)**5
Determine f, given that -8/7*f**2 - 92/7*f - 204/7 = 0.
-17/2, -3
Let h be (54/8)/(((-30)/192)/(8/(-48))). Let 4/5*k**4 + h*k**3 + 24*k**2 + 96/5 + 176/5*k = 0. Calculate k.
-3, -2
Let k(y) be the first derivative of 1/15*y**3 - 1/30*y**4 + 0*y**2 + 6*y - 3. Let a(i) be the first derivative of k(i). Factor a(n).
-2*n*(n - 1)/5
Let d = -469 - -478. Let g(x) be the first derivative of d + 0*x + 1/2*x**4 + 0*x**3 - x**2. Solve g(b) = 0 for b.
-1, 0, 1
Let d(z) = -4*z**5 + 43*z**4 + 108*z**3 - 162*z - 5. Let i(f) = -15*f**5 + 150*f**4 + 378*f**3 - 567*f - 18. Let a(w) = -18*d(w) + 5*i(w). Factor a(c).
-3*c*(c - 1)*(c + 3)**3
Let j(o) be the first derivative of -o**5/5 - 3*o**4/4 + o**3/3 + 3*o**2/2 - 269. Find z such that j(z) = 0.
-3, -1, 0, 1
Let h(x) = x**2. Let l(t) be the second derivative of -11*t**4/12 + 5*t**3/6 + 15*t**2 - 18*t. Let r(j) = 6*h(j) + l(j). Solve r(o) = 0.
-2, 3
Let u(d) be the first derivative of 49/10*d**4 - 56/15*d**3 + 4/5*d**2 + 0*d - 1. Factor u(y).
2*y*(7*y - 2)**2/5
Suppose -s = -3*l + 21, -3*s + 2*l = -5*s - 18. Let x be ((-68)/s - 6/9)/1. Find n such that -6/5*n**3 + 2/5*n**x + 0 + 2/5*n**4 + 4/5*n - 2/5*n**2 = 0.
-2, -1, 0, 1
Let f(d) = 6*d**3 + 6*d - 4 - 32*d**2 + 0*d - d + 19*d. Let g(u) = u**3 + u - 1. Let n(z) = -2*f(z) - 4*g(z). What is p in n(p) = 0?
1/2, 3
Let k(v) = 3*v**2 - 114*v + 3138. Let x(t) = 4*t**2 - 115*t + 3139. Let n(g) = 3*k(g) - 2*x(g). Factor n(m).
(m - 56)**2
Suppose -70 = -2*f - 5*d, 4*f = 3*f + d + 21. Factor -15*z - 22*z - 18 - 2*z**2 + f*z.
-2*(z + 3)**2
Let d(k) = k**2 + 12*k + 14. Let a be d(-11). Let w = -9 + 11. Factor -6*t**4 + 4*t**a + 16*t**2 + 5*t + w*t**4 - 12*t - 9*t.
-4*t*(t - 2)*(t - 1)*(t + 2)
Let h(p) be the first derivative of 2/9*p + 1/54*p**6 + 0*p**5 + 1/6*p**2 - 1/9*p**4 - 2/27*p**3 - 10. Factor h(x).
(x - 2)*(x - 1)*(x + 1)**3/9
Let o = -1207/3 - -404. Determine k, given that 0 - o*k**5 + 0*k + 0*k**4 + 0*k**2 + 5/3*k**3 = 0.
-1, 0, 1
Let l(n) = n**3 + 5*n**2 - 56*n - 54. Let c be l(-10). Factor -4*k**2 + 2/3*k**3 + c*k - 8/3.
2*(k - 4)*(k - 1)**2/3
Let x(c) be the first derivative of -c**6/51 + 4*c**5/85 - c**4/34 + 53. Find u such that x(u) = 0.
0, 1
Let i = 63/2 + -31. Let m = 1/6 + i. Determine w so that m*w + 0 - 2/3*w**2 = 0.
0, 1
Let a(l) be the third derivative of l**8/1680 - l**7/336 + l**6/240 - 7*l**5/60 - 11*l**2. Let g(s) be the third derivative of a(s). Factor g(f).
3*(f - 1)*(4*f - 1)
Let b = -71109/5 - -14222. Find j, given that 4/5*j - 1/5*j**3 + 8/5 + 4/5*j**4 - b*j**5 - 2*j**2 = 0.
-1, 2
Factor -85805 + 14*c**2 - 29*c**2 + 5*c**2 + 1310*c + 5*c**2.
-5*(c - 131)**2
Let j(v) = -v**4 + 17*v**2 + 18*v + 2. Let o(y) = -2*y**4 + 33*y**2 + 36*y + 5. Let x(p) = -11*j(p) + 6*o(p). Determine b, given that x(b) = 0.
-2, -1, 4
Let b(p) be the first derivative of -2/55*p**5 - 1/22*p**4 + 0*p - 24 + 0*p**3 + 0*p**2. Factor b(a).
-2*a**3*(a + 1)/11
Let d(k) be the first derivative of 20 + 9/5*k**5 - k**3 - 21/2*k**2 - 6*k + 21/4*k**4. Find v, given that d(v) = 0.
-2, -1, -1/3, 1
Find k such that 98/11*k**4 - 472/11*k + 80/11 + 1022/11*k**3 + 372/11*k**2 = 0.
-10, -1, 2/7
Let z be (-26)/(-117)*(-2)/(-20). Let i(p) be the second derivative of 0*p**2 + 0 + 0*p**3 + z*p**6 + 4*p - 1/18*p**4 + 0*