s) be the second derivative of 6*s**5/5 - 5*s**4/3 - 7*s**3/3 + 9*s. Let d(r) = 5*r**3 - 4*r**2 - 3*r. Let k(f) = -28*d(f) + 6*j(f). Factor k(g).
4*g**2*(g - 2)
Suppose -21 = -3*h - 0*h. Find z such that -327*z**3 - 57*z**5 + 378*z**4 - 90*z**5 - h*z + 108*z**2 - z - 4*z = 0.
0, 2/7, 1
Let o(k) be the second derivative of k**10/75600 + k**9/12600 + k**8/5600 + k**7/6300 - k**4/3 + 4*k. Let t(q) be the third derivative of o(q). Solve t(u) = 0.
-1, 0
Let j(m) be the first derivative of 3*m**5/10 - 5*m**3/2 + 6*m + 10. Find y such that j(y) = 0.
-2, -1, 1, 2
Factor 2*i**2 + 4/3*i + 0 + 2/3*i**3.
2*i*(i + 1)*(i + 2)/3
Let p(j) be the first derivative of 11/8*j**2 - 1/2*j - 5/4*j**3 - 3. Find o such that p(o) = 0.
1/3, 2/5
Let 16*x**2 - 15*x - 8 - 22*x**2 - x + 4*x**3 + 2*x**4 = 0. What is x?
-2, -1, 2
Let a(d) = -7*d**3 - 5*d. Let x(q) = -20*q**3 - 14*q. Let g(v) = 14*a(v) - 5*x(v). Solve g(l) = 0.
0
Let v(m) = -m**2 - 5*m. Let p be v(-4). Suppose -21*d + 22*d = p. Factor 1/2*c**3 - 1/2*c + 0*c**2 + 1/4*c**d - 1/4.
(c - 1)*(c + 1)**3/4
Let k = 6 - 6. Factor 0 + c**4 - 1/2*c**3 + k*c - 1/2*c**5 + 0*c**2.
-c**3*(c - 1)**2/2
Let o be 3/22*40/15. Let x be 6/(-27) - (-58)/99. Factor 2/11*c**2 + x*c**3 - o*c - 2/11.
2*(c - 1)*(c + 1)*(2*c + 1)/11
Let v(a) be the third derivative of a**6/360 + a**5/90 - a**4/24 + 4*a**2. Let v(b) = 0. Calculate b.
-3, 0, 1
Suppose -3*h + 11*h**4 - 5*h**2 + 11*h**4 - 21*h**4 - h**3 = 0. Calculate h.
-1, 0, 3
Let n(l) be the first derivative of -l**4/2 - 2*l**3 - 2*l**2 + 47. Factor n(i).
-2*i*(i + 1)*(i + 2)
Let p(o) be the second derivative of -2/21*o**4 + 0 + 1/7*o**2 + o + 2/21*o**3 - 1/35*o**5 + 1/35*o**6. Find z, given that p(z) = 0.
-1, -1/3, 1
Let c(h) be the first derivative of -2*h**6/21 - 16*h**5/35 - 25*h**4/28 - 19*h**3/21 - h**2/2 - h/7 + 12. Determine o, given that c(o) = 0.
-1, -1/2
Suppose 0 = 5*u + 2*u + 14*u. Let 0*t - 4/7*t**4 - 4/7*t**2 + 8/7*t**3 + u = 0. Calculate t.
0, 1
Let u(t) be the third derivative of 2*t**6/5 - 7*t**5/15 + t**4/6 + 7*t**2. Factor u(o).
4*o*(3*o - 1)*(4*o - 1)
Let w be ((-6)/20)/(6/(-8)). Let l = -18 + 92/5. Factor 0 - w*f**4 + 2/5*f**2 + 2/5*f - l*f**3.
-2*f*(f - 1)*(f + 1)**2/5
Let r(h) = -9*h - 372. Let x be r(-42). Factor -9/2 - 3/2*v**2 + x*v.
-3*(v - 3)*(v - 1)/2
Let x be (-2)/(-4) - 6/8*-2. Factor 4/9*s**x + 0 + 2/9*s + 2/9*s**3.
2*s*(s + 1)**2/9
Let y(q) = 2*q - 7. Let g be y(5). Let b(i) = 3*i**2 - 53*i + 77. Let o(w) = -w**2 + 27*w - 39. Let l(a) = g*b(a) + 5*o(a). Find d such that l(d) = 0.
3
Suppose 3*s - 2*a - 8 = 0, 3*a - a = 2*s - 6. Factor -14/3*l**s + 4/3*l + 0 + 10/3*l**3.
2*l*(l - 1)*(5*l - 2)/3
Suppose 0 = 2*l - 3*l + 5. Suppose l = -w + 9. Let 0 + 0*t + 1/2*t**w - 1/2*t**2 + 0*t**3 = 0. What is t?
-1, 0, 1
Suppose -3*p - 3*o = 39, -2*p - 10 = -o + 7. Let s = p + 21/2. Factor 0 - s*n**3 + 0*n + 1/2*n**2.
-n**2*(n - 1)/2
Let f = 356/217 - 42/31. Factor -2/7*d + f*d**2 + 0.
2*d*(d - 1)/7
Solve -1/3*a**2 + 1/3*a**4 - 2/3*a + 2/3*a**3 + 0 = 0.
-2, -1, 0, 1
Let m(k) = -k - 10. Let g be m(-13). Let r(q) be the first derivative of 0*q - 1/2*q**g - 1 + 3/4*q**2. What is f in r(f) = 0?
0, 1
Let g(i) be the third derivative of i**9/362880 - i**7/10080 + i**6/2160 + i**5/20 - 9*i**2. Let w(b) be the third derivative of g(b). Factor w(v).
(v - 1)**2*(v + 2)/6
Factor 21/8*d - 3/8*d**4 + 15/8*d**3 - 27/8*d**2 - 3/4.
-3*(d - 2)*(d - 1)**3/8
Let f(t) be the second derivative of t**7/420 - t**5/60 - 3*t**3/2 + 6*t. Let j(g) be the second derivative of f(g). Let j(z) = 0. What is z?
-1, 0, 1
Let a be -4 + 77/15 + (-1)/(-5). Factor 2*o - 4/3*o**3 + 2/3 + a*o**2 - 2/3*o**5 - 2*o**4.
-2*(o - 1)*(o + 1)**4/3
Let x(v) be the first derivative of -1 + 0*v - 1/2*v**2 + 1/150*v**5 - 1/15*v**4 + 4/15*v**3. Let b(q) be the second derivative of x(q). Factor b(a).
2*(a - 2)**2/5
Let a be 3/((-12)/10)*-2. Factor 3*w**2 + 4*w - 6 + 12 + a*w.
3*(w + 1)*(w + 2)
Factor 6/7*a - 4/7 - 2/7*a**2.
-2*(a - 2)*(a - 1)/7
Suppose -2/3 + 2/3*v**2 + v = 0. What is v?
-2, 1/2
Factor 1/5*k - 1/5*k**2 + 0.
-k*(k - 1)/5
Let h be 8/(-9)*73/(-292). Suppose 2/9*g - 2/9*g**3 + h*g**2 - 2/9 = 0. Calculate g.
-1, 1
Determine a so that -1 - 4 + a**3 - 12*a**2 - 6*a**3 - 3*a**2 - 15*a = 0.
-1
Let t(c) be the first derivative of 7*c**5 - 65*c**4/2 + 45*c**3 - 10*c**2 - 20*c + 11. Solve t(g) = 0.
-2/7, 1, 2
Let i = -2 - -5. Factor -1 - 12*v - 12*v**2 + 8 + i - 13.
-3*(2*v + 1)**2
Let a = 1509 - 4526/3. Solve -l**3 + 2/3 - a*l**4 + l - 1/3*l**2 = 0 for l.
-2, -1, 1
Let r(f) be the second derivative of f**8/840 - f**7/420 - f**6/180 + f**5/60 + 7*f**3/6 - 3*f. Let i(o) be the second derivative of r(o). Factor i(m).
2*m*(m - 1)**2*(m + 1)
Let i(s) be the third derivative of -s**6/40 - s**5/20 + s**4/4 - 11*s**2. Factor i(d).
-3*d*(d - 1)*(d + 2)
Let i(o) be the third derivative of -o**8/6720 - o**7/504 - o**6/240 + 3*o**5/40 - o**4/24 + 3*o**2. Let v(r) be the second derivative of i(r). Factor v(m).
-(m - 1)*(m + 3)**2
Determine n, given that -162/13*n**3 + 0 - 8/13*n + 72/13*n**2 = 0.
0, 2/9
Suppose -3*q + 0 = -9. Let u(b) be the third derivative of 0*b**q + 1/60*b**4 + b**2 + 0*b + 1/150*b**5 + 0. Factor u(t).
2*t*(t + 1)/5
Let o(x) = x**3 - 11*x**2 + 21*x - 27. Let r be o(9). Suppose -3/7*q**2 + 6/7*q + r = 0. Calculate q.
0, 2
Suppose 9 = -5*x - 11. Let a be 0/(-6) - x/3. Factor a*m**3 - 5/3*m**2 + 1/3*m + 0.
m*(m - 1)*(4*m - 1)/3
Let l(b) be the third derivative of 1/420*b**6 + 0 + 0*b - b**2 + 0*b**5 + 0*b**3 - 1/84*b**4. Let l(y) = 0. What is y?
-1, 0, 1
Find t such that -3*t + 1 - 3/4*t**4 + 1/4*t**5 + 11/4*t**2 - 1/4*t**3 = 0.
-2, 1, 2
Let t(i) = -i**5 + i**4 + i**3 - i**2 + 1. Let r(y) = -y**5 + 16*y**4 + 75*y**3 + 170*y**2 + 176*y + 66. Let l(f) = -3*r(f) + 6*t(f). Let l(n) = 0. What is n?
-4, -1
Let x(m) be the third derivative of -m**6/80 + 7*m**5/40 - m**4 + 3*m**3 + 17*m**2. Factor x(u).
-3*(u - 3)*(u - 2)**2/2
Let y(u) be the first derivative of -u**4/2 + 4*u**3/3 + u**2 - 4*u + 12. Factor y(n).
-2*(n - 2)*(n - 1)*(n + 1)
Let x be (18/(-24))/((-18)/32). Let c(p) be the first derivative of -1/2*p**4 - 1/2*p**2 + 1 - 4/5*p**5 + 0*p + x*p**3 + 1/2*p**6. Factor c(w).
w*(w - 1)**2*(w + 1)*(3*w - 1)
Let i = 23735/4 + -126691/20. Let r = i - -402. Solve -2/5*a**2 + 2/5*a**5 - r*a**4 + 0*a + 6/5*a**3 + 0 = 0 for a.
0, 1
Let i(b) be the third derivative of 0 - 4*b**2 - 11/105*b**7 + 1/6*b**4 + 0*b - 3/10*b**5 + 0*b**3 + 1/4*b**6 + 1/56*b**8. Determine h, given that i(h) = 0.
0, 2/3, 1
Determine o, given that 0*o + 0 - 2/5*o**3 - 2/5*o**4 + 0*o**2 = 0.
-1, 0
Let g(x) = -x - 1. Let w(p) = p**2. Let b = 3 - 5. Let v be w(b). Let q(a) = -2*a**3 - 5*a**2 + 3. Let u(k) = v*g(k) + q(k). Factor u(d).
-(d + 1)**2*(2*d + 1)
Let n(j) be the first derivative of -j**6/600 - j**5/300 + j**4/120 + j**3/30 - 7*j**2/2 + 2. Let b(q) be the second derivative of n(q). Factor b(i).
-(i - 1)*(i + 1)**2/5
Let b(r) = -3*r**3 - 5*r**2 - 5*r + 1. Let k = 7 + -9. Let j(z) = z**2 + 1. Let c(p) = k*j(p) + b(p). Let c(l) = 0. Calculate l.
-1, -1/3
Let w be (-2)/(-5) - 91/(-35). Solve -3*f + 3*f - 12 - 2*f**w + 4 + 6*f**2 = 0.
-1, 2
Let -45*x**4 - 113*x**2 + 6*x**5 - 150*x**3 - 11*x**5 - 165*x - 117*x**2 - 45 = 0. What is x?
-3, -1
Let f be (5 + 35/(-3))/(-2). Suppose -4/3*x - 14/3*x**4 + 0 + f*x**5 + 14/3*x**2 - 2*x**3 = 0. What is x?
-1, 0, 2/5, 1
Let w = 34 + -34. Let y(n) be the second derivative of 0*n**2 + 1/60*n**4 + 2*n + w + 0*n**3 + 3/100*n**5 - 1/150*n**6 - 1/70*n**7. Find z, given that y(z) = 0.
-1, -1/3, 0, 1
Suppose 0 = 2*y + 5*x - 6 + 45, 0 = -2*y - 4*x - 34. Let q = y + 15. Let q*a**5 - 6*a**5 - 2*a**3 - 2*a**4 + a + 2*a**2 - a = 0. Calculate a.
-1, 0, 1
Let a(k) be the first derivative of -3*k**4/8 - 3*k**3 - 27*k**2/4 - 6*k - 1. Factor a(j).
-3*(j + 1)**2*(j + 4)/2
Let y(x) be the first derivative of -x**3/6 - x**2/2 + 3*x/2 - 11. Suppose y(q) = 0. What is q?
-3, 1
Let c(v) = -3*v**4 + v**2. Let t be (-8 - 1) + 1 + -3. Let a(k) = -3*k**3 - 3*k**3 - 6*k**2 + 7*k**3 + 16*k**4. Let y(q) = t*c(q) - 2*a(q). Factor y(b).
b**2*(b - 1)**2
Determine i, given that 10*i**5 - 3*i - 28*i**2 + 52*i**3 + 5*i - 7 - 38*i**4 + 9 = 0.
-1/5, 1
Let l be 0 + 0 + 10 + -9. Factor q - 2*q - 1 + l - q**2 + 2.
-(q - 1)*(q + 2)
Let s(z) be the third