e o(n). Solve -2/3 + 2/3*k**2 + 2/3*k - 2/3*k**m = 0.
-1, 1
Let x be 1/(-6)*(1 + (-1 - 3)). Let j(c) be the second derivative of x*c**4 + 0*c**2 - 5*c + 0 + 1/10*c**6 + 0*c**3 - 9/20*c**5. What is v in j(v) = 0?
0, 1, 2
Let u(v) be the first derivative of 5*v**3 + 55*v**2/2 + 65*v - 38. Let x(y) = 23*y**2 + 83*y + 98. Let n(w) = 8*u(w) - 5*x(w). Let n(k) = 0. Calculate k.
-3, -2
Let d(m) be the second derivative of -2*m**6/45 - 7*m**5/15 + 40*m**4/9 - 88*m**3/9 - 58*m. Determine p, given that d(p) = 0.
-11, 0, 2
Let b = -21681 - -64409/3. Let y = b + 214. Determine j so that 8*j + 14/3*j**2 - y = 0.
-2, 2/7
Let a(i) be the second derivative of -i**4/3 - 2*i**3/3 + 4*i**2 - 69*i. Find q such that a(q) = 0.
-2, 1
Solve -8/7*l + 8*l**2 - 52/7*l**4 - 4/7 - 32/7*l**3 + 40/7*l**5 = 0.
-1, -1/5, 1/2, 1
Let y(p) be the first derivative of p**4/20 - p**3/5 + 88. What is r in y(r) = 0?
0, 3
Suppose -2*s + 2 = 2*p, -2*p + 4 = -2*s + 5*s. Find r such that -s*r - 3*r - r + 0*r - 2*r**2 = 0.
-3, 0
Suppose 4*o + 0*o + 0*o = 0. Let f be o + -3 + 6 + -3. Factor 10/9*i**3 + 2/3*i + f - 14/9*i**2 - 2/9*i**4.
-2*i*(i - 3)*(i - 1)**2/9
Let d(j) be the second derivative of j**7/231 - 7*j**6/55 + 119*j**5/110 - 79*j**4/66 - 40*j**3/11 + 100*j**2/11 - 29*j. Determine n, given that d(n) = 0.
-1, 1, 10
Let v(k) be the third derivative of k**7/525 + 7*k**6/300 + k**5/10 + 13*k**4/60 + 4*k**3/15 + 2*k**2 + 52*k. Factor v(i).
2*(i + 1)**3*(i + 4)/5
Let j(a) = a**2 + 6*a - 13. Let x be j(-8). Let m be (12/18 + (-2)/x)/(-1). Solve -1/3*f**2 + 0 + m*f - 1/3*f**5 - f**4 - f**3 = 0.
-1, 0
Let w(s) = s**3 - 9*s**2 - 17*s + 12. Let j be w(-2). Solve 3/2*f + 9/4 + 1/4*f**j = 0 for f.
-3
Let h be 8/(-32) + (-34)/(-8). Suppose p - h = 0, -2*p = 5*t - 20 - 198. Factor -12 + t*u - 33*u**2 + 15/2*u**3.
3*(u - 2)**2*(5*u - 2)/2
Let r(m) be the third derivative of m**7/420 + m**6/120 + m**5/120 + 63*m**2. Let r(t) = 0. Calculate t.
-1, 0
Factor -447*u**2 - 36 + 69*u**2 - 186*u - 42*u + 17*u**2.
-(19*u + 6)**2
Factor -27/7*x**2 + 0 - 1/7*x**3 - 26/7*x.
-x*(x + 1)*(x + 26)/7
Let d = -262 + 5241/20. Let c(s) be the third derivative of 0*s + 1/10*s**6 + 0 + d*s**5 + 6*s**2 + 1/14*s**7 + 0*s**3 + 1/56*s**8 + 0*s**4. Factor c(k).
3*k**2*(k + 1)**2*(2*k + 1)
Let b(p) = -p**3 - 10*p**2 + 46*p - 66. Let z(n) = -2*n**3 - 9*n**2 + 45*n - 67. Let a be (-9)/(-6)*(-8)/6. Let g(l) = a*z(l) + 3*b(l). Factor g(w).
(w - 4)**3
Let c(k) be the first derivative of -k**5/20 + k**4/8 + k**3/3 - k**2/4 - 3*k/4 - 31. Factor c(p).
-(p - 3)*(p - 1)*(p + 1)**2/4
Factor 2/5*p**2 - 36/5*p + 0.
2*p*(p - 18)/5
Let g(p) be the first derivative of 0*p**2 - 5/24*p**6 - 9/16*p**4 + 3/5*p**5 + 28 + 1/6*p**3 + 0*p. Solve g(u) = 0 for u.
0, 2/5, 1
Let v(r) be the third derivative of -r**6/420 + 4*r**5/105 - 4*r**4/21 - 171*r**2. Solve v(s) = 0.
0, 4
Let f(t) = -10*t + 210. Let n be f(21). Let p(k) be the first derivative of 1 + n*k - 2*k**4 - 2/5*k**5 + 0*k**2 - 2*k**3. Factor p(u).
-2*u**2*(u + 1)*(u + 3)
Let c(b) be the second derivative of -b**8/3360 - b**7/630 - b**6/360 - 7*b**4/12 - 5*b. Let d(q) be the third derivative of c(q). Solve d(u) = 0.
-1, 0
Let j(k) be the second derivative of k**8/2100 - k**6/225 + k**4/30 + 7*k**3/3 + 16*k. Let a(g) be the second derivative of j(g). Solve a(p) = 0 for p.
-1, 1
Let r(z) = -z**2 + 7*z + 15. Let s be r(7). Factor 184*l + s + 185*l + 5*l**2 - 349*l.
5*(l + 1)*(l + 3)
Suppose -4*w + 2 = -10. Suppose -d - 36 = -4*i - w*d, -5*d = -4*i + 22. Suppose -6*p**3 + 0*p + 3*p**2 + 15*p**2 - 4*p - i*p**3 = 0. Calculate p.
0, 2/7, 1
Factor -16/11*a + 0 - 30/11*a**2 - 12/11*a**3 + 2/11*a**4.
2*a*(a - 8)*(a + 1)**2/11
Let y(v) be the third derivative of v**7/210 - v**6/150 - 7*v**5/100 + 2*v**4/15 + 2*v**3/15 - v**2 - 15*v. Solve y(d) = 0.
-2, -1/5, 1, 2
Let q = 1766/55 + -340/11. Factor 8/5 - q*x - 2/5*x**2.
-2*(x - 1)*(x + 4)/5
Let a(n) be the first derivative of 0*n**2 + 6 + 1/12*n**4 + 2*n + 0*n**3 - 1/20*n**5. Let l(m) be the first derivative of a(m). Let l(o) = 0. Calculate o.
0, 1
Let i(t) be the third derivative of t**9/18900 - t**8/2800 + t**7/1050 - t**6/900 + t**4/3 - 11*t**2. Let o(z) be the second derivative of i(z). Factor o(d).
4*d*(d - 1)**3/5
Let x = 14533 - 14531. Find y such that 54/19 - 2/19*y**4 - 16/19*y**3 - 36/19*y**x + 0*y = 0.
-3, 1
Suppose 7*j + 15 = 10*j. Solve 6*k**5 - 6*k**3 - 9*k**3 - 3*k**4 + 6*k + 3*k**2 + 0*k**j + 3*k**5 = 0.
-1, -2/3, 0, 1
Let r = 64 + -60. Let 8*m**4 - r*m**4 + 28*m**3 + 146*m**2 + 36*m - 86*m**2 = 0. Calculate m.
-3, -1, 0
Let g be ((-4)/8)/(0 + 1/(-10)). Let n be 2/g*(-115)/(-276). Factor n*m**3 + 0 + 1/6*m + 1/3*m**2.
m*(m + 1)**2/6
Let b(p) = p**3 - 5*p**2 + p. Let w be b(5). Let -6*o + 0*o - 25*o**2 - 78*o**3 - 20*o**2 + 59*o**w + 45*o**4 + 25*o**5 = 0. What is o?
-1, -2/7, -1/4, 0, 1
Let y(c) = -32*c**4 - 28*c**3 - 12*c**2 + 8*c - 8. Let i(a) = 11*a**4 + 9*a**3 + 4*a**2 - 3*a + 3. Let t(w) = 8*i(w) + 3*y(w). Factor t(u).
-4*u**2*(u + 1)*(2*u + 1)
Let o(q) be the second derivative of -q**6/90 - q**5/6 - 2*q**4/3 - 2*q**3 - 19*q. Let w(b) be the second derivative of o(b). Factor w(k).
-4*(k + 1)*(k + 4)
Let g(d) = 12 + 28*d - 13*d - 16*d. Let w be g(6). Determine t, given that 0*t**2 - 3*t - 3 + 6*t**2 + 0*t - w = 0.
-1, 3/2
Let t(f) = -55*f**3 - 137*f**2 - 75*f - 27. Let c(h) = 28*h**3 + 68*h**2 + 38*h + 13. Suppose 27 = m - 4*m. Let k(o) = m*c(o) - 4*t(o). Let k(x) = 0. What is x?
-3/4, -1/2
Factor 8*k**3 + 64/3*k**2 + 0*k + 0 - 4/3*k**4.
-4*k**2*(k - 8)*(k + 2)/3
Let a(r) be the second derivative of 5*r**4/12 - 25*r**3/3 - 60*r**2 - 364*r. Factor a(c).
5*(c - 12)*(c + 2)
Suppose 52 - 70 = -6*t. Suppose -10*y + 14 = -t*y. Factor 2/5*n + n**y - 7/5*n**3 + 0.
-n*(n - 1)*(7*n + 2)/5
Let u(l) be the third derivative of 0 - 1/24*l**4 + 0*l**3 + 38*l**2 + 0*l + 1/60*l**5. Factor u(m).
m*(m - 1)
Let d(w) = w**5 + w**4 - w**3 - w**2 + w + 2. Let b(x) = -2*x**5 - 8*x**4 + 4*x**3 + 4*x**2 - 4*x - 8. Let u(m) = b(m) + 4*d(m). Suppose u(v) = 0. What is v?
0, 2
Factor -56 + 101*w - 109*w + 2*w**4 + 20*w**3 + 2*w**2 + 40*w**2.
2*(w - 1)*(w + 2)**2*(w + 7)
Let o be ((-330)/56 + 6)*(-68)/(-51). Solve 0*v**2 - 1/7*v**3 + o*v + 0 = 0 for v.
-1, 0, 1
Let w(b) be the third derivative of -5*b**2 - 1/9*b**4 + 0*b - 13/270*b**5 - 1/90*b**6 + 0 - 4/27*b**3 - 1/945*b**7. Factor w(s).
-2*(s + 1)**2*(s + 2)**2/9
Suppose 170*i**2 + 6*i**4 + i**4 - 2*i**4 - 105*i**3 - 19*i - i - 530*i**2 + 480 = 0. Calculate i.
-2, 1, 24
Suppose 0 = -664*s + 678*s. Let n(r) be the second derivative of -3*r + 0*r**4 + 1/120*r**6 + 0*r**3 + s*r**2 - 1/80*r**5 + 0. Factor n(w).
w**3*(w - 1)/4
Let o(f) be the third derivative of f**5/480 + 31*f**4/96 - 8*f**3/3 + 9*f**2 - 8*f. Factor o(t).
(t - 2)*(t + 64)/8
Let s be (10 + (-2774)/285)/((-2)/(-20)). Let a(d) = -d**3 + 3*d**2 - 1. Let z be a(2). Factor 0 - s*f - 10/3*f**z + 8*f**2.
-2*f*(f - 2)*(5*f - 2)/3
Let r = 40 + -41. Let t = r + 1. Let t*y + 0*y**4 + 0*y**2 + 0 - 3/5*y**3 + 3/5*y**5 = 0. Calculate y.
-1, 0, 1
Let o(y) be the first derivative of 3*y**4/8 - 11*y**3/3 + 5*y**2/4 + 7*y + 107. Factor o(c).
(c - 7)*(c - 1)*(3*c + 2)/2
Let t(k) be the first derivative of 5*k**6/24 - 5*k**4/8 + 5*k**2/8 - 50. Let t(q) = 0. What is q?
-1, 0, 1
Let v be 7 - 13/(104/24). Determine l, given that -2/13 + 6/13*l**5 - 2/13*l**v + 4/13*l**2 + 6/13*l - 12/13*l**3 = 0.
-1, 1/3, 1
Factor -28 + 199*g - 463*g + 8*g**2 + 212*g.
4*(g - 7)*(2*g + 1)
Factor -25*y - 130*y**2 - 21 - 138*y**2 + 278*y**2 - 9 + 5*y**3.
5*(y - 2)*(y + 1)*(y + 3)
Let v(m) be the first derivative of 6/5*m**2 + 36 - 7/25*m**5 - 28/15*m**3 - 47/20*m**4 + 0*m. Suppose v(t) = 0. Calculate t.
-6, -1, 0, 2/7
Let q(l) be the first derivative of 1/2*l**2 + 29 - 1/3*l**3 + 0*l. Solve q(k) = 0.
0, 1
Let c(b) be the first derivative of -b**6/10 + 3*b**5/25 + 3*b**4/5 - 4*b**3/5 - 87. Let c(z) = 0. What is z?
-2, 0, 1, 2
Let d be 10/8 - (76 + -76). Let c(w) be the third derivative of -3/20*w**6 - 3/2*w**3 - 3/5*w**5 - d*w**4 - 1/70*w**7 + 0 - 5*w**2 + 0*w. Factor c(n).
-3*(n + 1)**3*(n + 3)
Let w(b) be the third derivative of 0 + 5/4*b**4 + 2*b**3 + 0*b + 19*b**2 + 3/80*b**6 + 7/20*b**5. Let w(f) = 0. Calculate f.
-2, -2/3
Let q(k) be the second derivative of k**7/7 - 2*k**6/3 + 3*k*