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Let s(k) be the first derivative of -k**7/1470 + k**6/630 + 2*k**3 + 18. Let r(f) be the third derivative of s(f). Factor r(n).
-4*n**2*(n - 1)/7
Suppose -1/6*l + 5/6*l**2 + 0 - 2/3*l**3 = 0. Calculate l.
0, 1/4, 1
Let o(c) be the second derivative of -c**7/42 + 7*c**6/30 - 4*c**5/5 + 2*c**4/3 + 8*c**3/3 - 8*c**2 - 33*c. Factor o(h).
-(h - 2)**4*(h + 1)
Solve 2/9*h**2 + 346/9*h + 0 = 0.
-173, 0
Let l be 4/27 + (-8 - -3 - -5). Let m(f) be the second derivative of 0 + 1/27*f**4 + l*f**3 - 5*f - 2/45*f**5 + 1/9*f**2 - 1/45*f**6. Let m(s) = 0. What is s?
-1, -1/3, 1
Factor 544*z + z**2 - 265*z - 271*z - 20.
(z - 2)*(z + 10)
Let w = -20 + 22. Suppose -11 = -4*j - 0*j + 3*p, w*j - 4*p = 8. Factor 1/2*r - 1/2*r**3 + 0 + 1/4*r**j - 1/4*r**4.
-r*(r - 1)*(r + 1)*(r + 2)/4
Let r(f) be the second derivative of f**4/4 - 57*f**3 + 339*f**2/2 + 311*f. What is j in r(j) = 0?
1, 113
Suppose 1998*c - 909*c**2 - 972 + 309/2*c**3 - 9*c**4 = 0. What is c?
2/3, 9/2, 6
Let g(t) = -5*t**2 - 14*t - 6. Let i(v) = -5*v**2 - 13*v - 7. Let d(c) = -c - 1. Let u be d(5). Let f(z) = u*i(z) + 7*g(z). Factor f(j).
-5*j*(j + 4)
Let z(p) be the first derivative of -p**4/48 - 5*p**3/24 - p**2/2 + 16*p - 6. Let f(w) be the first derivative of z(w). Factor f(i).
-(i + 1)*(i + 4)/4
Let z(p) = -p**3 - p. Let u be z(-1). Factor 306 - 306 + 15*n - 5*n**u.
-5*n*(n - 3)
Let t(q) = -q**2 - 5*q - 1. Let c(k) = 3*k**4 - 9*k**3 - 31*k**2 + 85*k + 149. Let j(n) = -c(n) - 5*t(n). Factor j(o).
-3*(o - 4)*(o - 3)*(o + 2)**2
Find l, given that 0 + 14/9*l**4 + 16/9*l**2 + 28/9*l**3 + 2/9*l**5 + 0*l = 0.
-4, -2, -1, 0
Let g = 143 + -141. Let y be ((-13)/(-182))/(g/8). Factor 0 + y*v**3 + 0*v - 2/7*v**4 + 0*v**2.
-2*v**3*(v - 1)/7
Let x(r) be the third derivative of 1/720*r**6 + r**2 + 0*r**4 + 0 + 4/3*r**3 + 0*r + 1/240*r**5. Let m(z) be the first derivative of x(z). Solve m(t) = 0.
-1, 0
Suppose -4*a + 14 = -34. Let c(s) = -s**3 + 13*s**2 - 11*s - 9. Let y be c(a). Factor -10*x**2 + 18 + 0 + 0*x**3 + 6*x + 3*x**y - x**3.
2*(x - 3)**2*(x + 1)
Let d(h) be the third derivative of h**6/60 - h**5/10 + h**4/6 - 16*h**2 - h. Determine f, given that d(f) = 0.
0, 1, 2
Let m(q) be the second derivative of 3*q**7/28 - 7*q**6/5 + 9*q**5/4 + 5*q**4/2 - 33*q**3/4 + 6*q**2 - 33*q + 1. Let m(y) = 0. Calculate y.
-1, 1/3, 1, 8
Let v(h) be the third derivative of -h**7/2310 + 7*h**6/660 - h**5/11 + 25*h**4/132 + 4*h**3/3 - 19*h**2. Let b(r) be the first derivative of v(r). Factor b(m).
-2*(m - 5)**2*(2*m - 1)/11
Find x, given that -13*x + 16*x**2 + 59*x - 86*x - 42 - 66*x = 0.
-3/8, 7
Let s(j) be the first derivative of 3*j**5/10 - 9*j**4/4 + 6*j**3 - 15*j**2/2 + 9*j/2 + 384. Factor s(f).
3*(f - 3)*(f - 1)**3/2
Let d(m) = -10*m**2 + 130*m - 38. Let l(w) = -18*w**2 + 260*w - 77. Let h(c) = 5*d(c) - 2*l(c). Factor h(s).
-2*(s - 9)*(7*s - 2)
Let u be 1/3 + 215/(-15). Let i = -40/3 - u. Factor 1/3*s**5 + 1/3 - s**4 - s + 2/3*s**3 + i*s**2.
(s - 1)**4*(s + 1)/3
Let u(b) be the second derivative of b**7/14 - 31*b**6/120 + 27*b**5/80 - 3*b**4/16 + b**3/24 + 108*b. Determine r so that u(r) = 0.
0, 1/4, 1/3, 1
Let r(w) = 2*w**2 - 13*w - 9. Let d(y) = 5*y**2 - 26*y - 19. Let x(k) = -6*d(k) + 13*r(k). What is u in x(u) = 0?
-3, -1/4
Suppose 90*i = -49*i + 45*i + 282. Find c, given that 6/7*c**i - 16/7*c + 20/7*c**2 + 0 = 0.
-4, 0, 2/3
Suppose 5*m - 33 = -4*f + 55, -f = 3*m - 50. Determine r, given that 26*r**4 - 6*r**5 - 38*r**2 - 2*r**2 - 4*r**5 + 12*r**3 - m*r = 0.
-1, -2/5, 0, 2
Suppose -27*g + 12*g + 150 = 0. Suppose -16*n = -g*n. Factor 0*a**2 + n - 2/7*a**3 - 2/7*a**4 + 0*a.
-2*a**3*(a + 1)/7
Let l be (7 + -8)/((-2)/6). Suppose 2 + 4*f**3 - 2*f + 4*f - 3*f**l + 4*f**2 + 3*f = 0. What is f?
-2, -1
Factor 22*b + 1 + 80*b - 162*b + 900*b**2.
(30*b - 1)**2
Let w(z) be the second derivative of z**6/15 - 3*z**5/2 + 25*z**4/2 - 125*z**3/3 + 16*z. Factor w(n).
2*n*(n - 5)**3
Let t be 0 + (-2)/7 + (-46)/(-14). Let c(o) be the first derivative of t*o**3 + 0*o - 3/2*o**2 - 7 - 3/2*o**4. Let c(l) = 0. Calculate l.
0, 1/2, 1
Let v(n) be the second derivative of n**6/420 + n**5/105 - n**4/28 - 5*n**2 - 7*n. Let a(q) be the first derivative of v(q). Let a(w) = 0. Calculate w.
-3, 0, 1
Let z(a) be the first derivative of a**6/40 - a**5/20 - a**4/8 + a**3/2 - 7*a**2/2 - 2. Let i(b) be the second derivative of z(b). Find f such that i(f) = 0.
-1, 1
Find p, given that -2/3*p**3 + 0 + 148*p**2 - 8214*p = 0.
0, 111
Find h such that 0 - 2/3*h**4 - 2*h**3 + 4/3*h + 2/3*h**5 + 2/3*h**2 = 0.
-1, 0, 1, 2
Let x(u) be the first derivative of u**4 - 4*u**3/3 - 4*u**2 - 229. Factor x(w).
4*w*(w - 2)*(w + 1)
Let i(n) be the second derivative of -1/231*n**7 + 0*n**2 + 0*n**3 - 17*n + 0*n**5 + 0 - 2/33*n**4 + 1/55*n**6. Factor i(x).
-2*x**2*(x - 2)**2*(x + 1)/11
Let t(z) be the first derivative of -z**6/630 - z**5/35 - 3*z**4/14 + 20*z**3/3 + 13. Let j(r) be the third derivative of t(r). Factor j(p).
-4*(p + 3)**2/7
Determine g so that -91*g - 5*g**2 - 75*g - 105*g - 75 + 311*g = 0.
3, 5
Suppose 38 = 60253*j - 60234*j. Factor -2/5*n**2 + 8/5*n + j.
-2*(n - 5)*(n + 1)/5
Let v(g) = 33*g**3. Let k be v(1). Let y be ((-12)/66 - 5/k)*-6. Let 0 - 2/13*m**4 + 0*m - 4/13*m**3 - 2/13*m**y = 0. What is m?
-1, 0
Let j(c) be the second derivative of -c**5/60 - c**4/2 - 17*c**3/18 + 6*c + 23. Solve j(g) = 0.
-17, -1, 0
Factor 36990/7*d**2 + 36450/7*d + 0 + 2/7*d**4 + 542/7*d**3.
2*d*(d + 1)*(d + 135)**2/7
Let h be 128/(-56) + (-90)/(-21). Determine z, given that -8/7 - 16/7*z**h + 4/7*z**3 + 20/7*z = 0.
1, 2
Let u(r) be the first derivative of -r**8/140 + r**7/280 - 19*r**3/3 - 9. Let l(i) be the third derivative of u(i). Suppose l(p) = 0. What is p?
0, 1/4
Let d(s) = -9*s**3 + 67*s**2 - 242*s + 178. Let r(g) = -2*g**3 + g**2 - g - 1. Let m(t) = -d(t) + 2*r(t). Factor m(b).
5*(b - 6)**2*(b - 1)
Let g(f) be the third derivative of f**5/240 + 17*f**4/96 + 2*f**3/3 - 33*f**2 - 1. Find v such that g(v) = 0.
-16, -1
What is t in -12/5*t**3 + 9/5*t**2 + 24/5 - 3/5*t**4 + 42/5*t = 0?
-4, -1, 2
Factor 6/5 - 2/5*q**2 + 4/5*q.
-2*(q - 3)*(q + 1)/5
Let t(f) = 2*f**3 - 26*f**3 - 2 + 2*f**2 - 19*f**2 + 6*f + f**4. Let d(z) = z**4 - z**3 + z - 1. Let h = 4 - 10. Let c(q) = h*d(q) + t(q). Factor c(s).
-(s + 1)**2*(s + 2)*(5*s - 2)
Factor 1/3*j**3 - 1/3*j + 1/3*j**2 + 0 - 1/3*j**4.
-j*(j - 1)**2*(j + 1)/3
Let x(r) be the second derivative of r**4/90 - 4*r**3/15 + 4*r**2/3 + 143*r. Let x(w) = 0. Calculate w.
2, 10
Let s be (1 + -27)/(2 - 4). Let 8 - 16*l**4 - 21*l**4 - s*l**4 + 12*l + 49*l**4 + 2*l**2 - 3*l**3 = 0. What is l?
-2, -1, 2
Let d(m) = 106*m**4 - 149*m**3 + 36*m**2 + 5*m - 4. Let b(v) = 211*v**4 - 299*v**3 + 73*v**2 + 9*v - 9. Let j(q) = 2*b(q) - 5*d(q). Let j(c) = 0. What is c?
-2/9, 1/4, 1/3, 1
Let l(t) be the third derivative of 5*t**7/42 + t**6/24 - t**5/3 - t**2 + 3. Determine a, given that l(a) = 0.
-1, 0, 4/5
Factor 4*i**2 - 2*i**3 - 15*i**5 + 36*i**5 - 19*i**5 - 4*i**4.
2*i**2*(i - 2)*(i - 1)*(i + 1)
Suppose -2*f - 14 = -3*x, -9*x = -11*x + 12. Suppose 2/3*o**f + 0 - 2/3*o - 1/6*o**3 = 0. Calculate o.
0, 2
Let n = -667/40 + 84/5. Let x(r) be the first derivative of 1/4*r - 1/8*r**2 - 1/24*r**6 + n*r**4 - 1 - 1/6*r**3 + 1/20*r**5. Solve x(p) = 0 for p.
-1, 1
Let s = 75 + -71. Let s*q**3 - 6*q**3 - 2*q + 2*q + 2*q**2 = 0. What is q?
0, 1
Let z(u) = u - 6. Let s(j) = j**2 - 3*j + 11. Let b(m) = 2*s(m) + 5*z(m). Let w(d) = -3*d**2 + 9. Let v(q) = 6*b(q) + 5*w(q). Factor v(l).
-3*(l + 1)**2
Let q be (147/196)/((-30)/(-8)). Let y = 487/795 - 2/159. Factor 4/5 - 4/5*t**3 + 4/5*t - q*t**4 - y*t**2.
-(t - 1)*(t + 1)*(t + 2)**2/5
Suppose -1 = -y + 28. Let h = -24 + y. Factor -f**2 + h*f**3 - 3 - f + f**4 + 3 - 4*f**3.
f*(f - 1)*(f + 1)**2
Let y(u) = 15*u**5 - 51*u**3 + 15*u - 7. Let f(b) = -10*b**5 + 35*b**3 - 10*b + 5. Let n(t) = 7*f(t) + 5*y(t). Factor n(w).
5*w*(w - 1)**2*(w + 1)**2
Let y be (-2)/(6/21 - (-598)/(-182)). Solve 2/9*c**4 + 0 + 4/9*c + y*c**3 - 2/9*c**5 - 10/9*c**2 = 0 for c.
-2, 0, 1
Let c(s) be the second derivative of -s**5/180 - s**4/36 + s**3/6 - 13*s**2/2 - 6*s. Let w(v) be the first derivative of c(v). Factor w(g).
-(g - 1)*(g + 3)/3
Let x(y) be the third derivative of -y**10/756000 - y**9/302400 + y**8/50400 - 2*y**5/15 + 2*y**2. Let h(s) be 