1/3, 0
Let n = 19490 - 19487. Determine t, given that -3*t + 3/2*t**2 + 1/2*t**n - 4 = 0.
-4, -1, 2
Let g(f) be the third derivative of 0 + 0*f + 1/840*f**7 + 0*f**6 + 1/1344*f**8 + 0*f**5 + 0*f**4 - 2*f**2 + 0*f**3. Factor g(x).
x**4*(x + 1)/4
Let h(a) be the first derivative of 5*a**4/9 - 208*a**3/27 + 290*a**2/9 - 200*a/9 - 146. Factor h(j).
4*(j - 5)**2*(5*j - 2)/9
Let p(t) be the first derivative of -8*t**3/9 - 121*t**2/3 - 20*t - 185. Find q such that p(q) = 0.
-30, -1/4
Let k(w) be the third derivative of -w**8/50400 + w**7/12600 + w**5/30 - 3*w**2. Let q(t) be the third derivative of k(t). Factor q(r).
-2*r*(r - 1)/5
Let j(n) = -2*n. Let a(l) = 4*l**2 - 360*l + 7056. Let d(y) = -a(y) + 12*j(y). Factor d(s).
-4*(s - 42)**2
Factor 1/5*c**2 + 4 + 9/5*c.
(c + 4)*(c + 5)/5
Let l(b) be the first derivative of -b**5 + 5*b**3 + 5*b**2 + 82. Solve l(h) = 0 for h.
-1, 0, 2
Factor -11*b + 25 - b**3 + 11 + 16 - 24*b + 22 - 38*b**2.
-(b - 1)*(b + 2)*(b + 37)
Let a = -2402 - -2405. Suppose -27/2*c**a + 21/4*c**2 - 3 + 9*c - 27/4*c**4 = 0. Calculate c.
-2, -1, 1/3, 2/3
Let l(u) be the first derivative of u**3/5 + 93*u**2/5 + 2883*u/5 - 97. Factor l(t).
3*(t + 31)**2/5
Let f = -4/77 - -137/1155. Let h(t) be the first derivative of f*t**3 - 4 - 1/25*t**5 + 1/30*t**6 - 1/20*t**4 + 0*t + 0*t**2. What is s in h(s) = 0?
-1, 0, 1
Suppose 0 = 2*p - 5*u + 16, -2*p + 20 = -0*p + 4*u. Solve 5*r + 34 + 4*r**p - r - 34 = 0 for r.
-1, 0
Let f(y) be the first derivative of y**4/12 - 19*y**3 + 3249*y**2/2 - 61731*y - 99. Factor f(b).
(b - 57)**3/3
Let v(y) be the second derivative of -11*y**4/6 - 2*y**3 - 9*y**2/11 + y + 15. Suppose v(n) = 0. What is n?
-3/11
Let i(j) be the second derivative of -1/70*j**5 + 0 + 0*j**2 + 17*j - 1/21*j**4 + 0*j**3. Solve i(z) = 0 for z.
-2, 0
Let t(m) be the first derivative of -m**6/3 + 16*m**5/15 + m**4/2 + 79. Factor t(o).
-2*o**3*(o - 3)*(3*o + 1)/3
Let d be 5/(-20)*2*-10. Determine i so that 26*i - i**5 - 20 + 26*i**2 - 25*i**3 - 6*i - 5*i**4 - i**2 + 6*i**d = 0.
-2, -1, 1, 2
Let i be 50/18 - (3 - 87/27). Suppose 0*d - 12 = -4*d. Find x, given that -3*x**5 - x**5 + 6*x**d - 2*x**i = 0.
-1, 0, 1
Let q(u) = -19*u + 6*u - 5*u**2 - 2*u + 56. Let b(s) = 45*s**2 + 135*s - 505. Let i(w) = 6*b(w) + 55*q(w). Factor i(a).
-5*(a - 2)*(a + 5)
Let w(f) be the first derivative of f**4/54 + 4*f**3/27 + f**2/3 + 15*f + 11. Let x(q) be the first derivative of w(q). Find u such that x(u) = 0.
-3, -1
Let z = 69/94 - 11/47. Let c(h) be the third derivative of 0*h + z*h**4 + 0*h**3 - 1/15*h**5 + 3*h**2 + 0. Factor c(k).
-4*k*(k - 3)
Let r be 56/(-42) - 26/(-6). Solve -4*j + 10*j**2 + 8*j**2 - 14*j**2 - j**r = 0.
0, 2
Let a(x) be the third derivative of 13*x**2 - 1/30*x**3 + 1/120*x**4 + 1/300*x**5 - 1/600*x**6 + 0*x + 0. Let a(t) = 0. Calculate t.
-1, 1
Let r(l) be the second derivative of l**4/6 + 8*l**3/3 + 27*l**2/2 - 4*l. Let i(t) = -6*t**2 - 48*t - 80. Let b(x) = -5*i(x) - 16*r(x). Factor b(d).
-2*(d + 4)**2
Let d(p) = -p**2 - 8*p + 4. Let o = -14 + 7. Let r be d(o). Suppose 11 - r + w - w**2 = 0. Calculate w.
0, 1
Let v(k) be the first derivative of 57/8*k**2 + 11/2*k - 6*k**3 - 13 - 7/16*k**4. Determine j so that v(j) = 0.
-11, -2/7, 1
Let k(j) be the first derivative of j**5 - 5*j**4/4 - 10*j**3 + 10*j**2 + 40*j + 54. Find h such that k(h) = 0.
-2, -1, 2
Let m(r) be the first derivative of r**5/4 - r**4/2 - r**3/2 + 23*r**2 - 25. Let v(b) be the second derivative of m(b). Determine g, given that v(g) = 0.
-1/5, 1
Let l(v) be the third derivative of -v**7/70 + 3*v**6/40 + 11*v**5/20 - 3*v**4/8 - 5*v**3 + 10*v**2 + 28*v. Solve l(o) = 0 for o.
-2, -1, 1, 5
Let f(y) = y - 1. Let i(d) = -2*d**2 + 83*d - 803. Let t(x) = -3*f(x) + i(x). Find p, given that t(p) = 0.
20
Solve -152100/7*r - 1560/7*r**2 - 4/7*r**3 + 0 = 0.
-195, 0
Let b(n) be the first derivative of 384*n + 1/2*n**3 + 43 + 24*n**2. Factor b(z).
3*(z + 16)**2/2
Let b(h) be the second derivative of -h**4/32 + 13*h**3/2 - 507*h**2 - 2*h + 298. Factor b(t).
-3*(t - 52)**2/8
Factor 23*o**2 - 78*o + 49*o - 3 - 2 - 2 + 5*o**3 + 8*o**2.
(o - 1)*(o + 7)*(5*o + 1)
Let m(h) = -h**2 + 2*h + 1. Let r be m(2). Let y(l) = -l. Let t(f) = -40*f**3 + 10*f**2 + 30*f + 5. Let g(i) = r*t(i) + 5*y(i). Factor g(n).
-5*(n - 1)*(2*n + 1)*(4*n + 1)
Factor 15*d**3 + 32*d**2 + 43*d + 64*d**2 - 29*d + 22*d.
3*d*(d + 6)*(5*d + 2)
Suppose -5*c + 27 = -3*c + 3*a, 4*a = 2*c + 8. Let d be (4/c)/((1 - -2)/18). Factor 2/9*u**2 - 2/9*u**d + 0*u**3 + 0 + 0*u.
-2*u**2*(u - 1)*(u + 1)/9
Find n such that -3/7*n**3 + 6/7*n**2 - 6/7 + 3/7*n = 0.
-1, 1, 2
Let y(i) be the first derivative of -i**4/8 + 6*i**3 - 285*i**2/4 - 361*i + 461. Find j, given that y(j) = 0.
-2, 19
Let z = 5597 - 11655/2. Let h = z + 231. Solve -3/4*w**3 - w**4 + 0 - h*w + 9/4*w**2 = 0 for w.
-2, 0, 1/4, 1
Let n be (-2 + -1)*(-2 + 1). Let l be n/(-12) + 33/36. Determine j so that -2/3*j**2 + l*j**3 - 4/3*j + 0 = 0.
-1, 0, 2
Let o(r) = -4*r**2 + 4*r + 11. Let p be o(2). What is h in 0*h + 3/2*h**4 - 3/2*h**2 - 3/2*h**p + 3/2*h**5 + 0 = 0?
-1, 0, 1
Let m(x) be the first derivative of -x**5/30 - x**4/3 - x**3/3 + 10*x**2/3 - 25*x/6 + 17. What is a in m(a) = 0?
-5, 1
Suppose 1356 = -10*c + 4*c. Let j = c - -229. Factor 8/13*r**4 + 2/13*r**5 + 2/13*r + 12/13*r**j + 8/13*r**2 + 0.
2*r*(r + 1)**4/13
Let g(t) be the second derivative of -t**4/32 + t**3/12 + t**2/4 - 3*t - 21. Factor g(o).
-(o - 2)*(3*o + 2)/8
Suppose -7 - 5 = -4*k. Find x such that 2*x**3 + 5*x**3 - 4*x**3 - 2*x - x**k = 0.
-1, 0, 1
Let k(q) = -7*q**3 + q**2 + 18*q - 4. Let s(w) = -3*w**2 - 36*w + 39 + 20*w**3 - 30 - 5*w**3. Let t(f) = 9*k(f) + 4*s(f). Determine d so that t(d) = 0.
-3, 0, 2
What is k in -8 - 10*k**3 - 2*k**2 - 8 + 14*k**3 + 14*k**2 = 0?
-2, 1
Let r(c) be the second derivative of -5*c**4/12 + 55*c**3/6 - 75*c**2 + 51*c. Factor r(x).
-5*(x - 6)*(x - 5)
Let r(g) be the second derivative of 2*g**7/21 + 8*g**6/5 + 36*g**5/5 + 32*g**4/3 - 41*g. Factor r(o).
4*o**2*(o + 2)**2*(o + 8)
Let l(g) be the second derivative of g**7/294 - g**6/105 - 3*g**5/140 + 2*g**4/21 - 2*g**3/21 + 58*g. Factor l(d).
d*(d - 2)*(d - 1)**2*(d + 2)/7
Suppose 2*h + 257*k + 16 = 253*k, 0 = 11*h + 2*k + 8. Factor h + 3/4*s**3 - 3/4*s**2 - 3/4*s + 3/4*s**4.
3*s*(s - 1)*(s + 1)**2/4
Let u(m) = 3*m - 1. Let r be u(-1). Let c(o) = 3*o**2 + 4*o + 4. Let b(g) = -9 - 2*g**2 - 9*g - 7*g**2 + 3*g**2. Let s(x) = r*b(x) - 9*c(x). Factor s(t).
-3*t**2
Factor 4000/3 + 2/15*q**2 + 80/3*q.
2*(q + 100)**2/15
Let g(l) be the first derivative of -l**4/10 + 4*l**3/15 + 7*l**2/5 + 8*l/5 + 111. Let g(r) = 0. What is r?
-1, 4
Let b(o) be the first derivative of -2*o**3/15 - 39*o**2/5 - 171. Suppose b(a) = 0. Calculate a.
-39, 0
Let m be -3 - (1550/(-434) - (-8)/14). Factor -8/3*r**2 - 8/3*r + 2/3*r**3 + m + 2/3*r**4.
2*r*(r - 2)*(r + 1)*(r + 2)/3
Let b(j) be the second derivative of -j**7/630 + j**6/90 - 4*j**3/3 + 21*j. Let m(l) be the second derivative of b(l). What is h in m(h) = 0?
0, 3
Let c be (3 + -1)/2*0/17. Let b(t) be the third derivative of 0 + 0*t**3 + 0*t - 1/20*t**5 - 1/40*t**6 + c*t**4 - t**2. Solve b(q) = 0 for q.
-1, 0
Suppose 3*d = 4 - 1. Factor -d - 1 + 2 + 3*b**2 - 3*b.
3*b*(b - 1)
Let l(h) be the third derivative of -h**7/840 - h**6/120 - h**5/40 - 3*h**4/4 - 6*h**2. Let s(x) be the second derivative of l(x). Factor s(i).
-3*(i + 1)**2
Let f(u) be the second derivative of -u**5/5 - u**4 + 8*u**3/3 - 5*u + 1. What is w in f(w) = 0?
-4, 0, 1
Let k(l) = l**2 - 5*l - 2. Suppose 0 = 3*s + s - 20. Let h(m) = -2*m**2 + 11*m + 5. Let v(x) = s*k(x) + 2*h(x). Factor v(t).
t*(t - 3)
Let y = 81 - 61. Let j = y + -17. Let 1/5*v**j + 0 + 0*v - 1/5*v**2 = 0. What is v?
0, 1
Factor -1/4*x**2 - 5329/4 - 73/2*x.
-(x + 73)**2/4
Find u such that 4/9*u + 0 + 2/3*u**2 + 2/9*u**3 = 0.
-2, -1, 0
Factor -1 - 121/2*k**2 + 123/2*k.
-(k - 1)*(121*k - 2)/2
Let c = 1009 - 3026/3. Factor 0 - c*i + 1/3*i**2.
i*(i - 1)/3
Suppose y - 4 = 2*y. Let u = y + 6. Factor 3*c**3 + u*c**2 - 3*c - c**2 - c**4 + 0*c.
-c*(c - 3)*(c - 1)*(c + 1)
Find k such that 1/6*k**4 + 3/2*k**3 - 25/6*k + 3 - 1/2*k**2 = 0.
-9, -2, 1
Let m(d) be the third derivative of 0 + 11*d**2 + 0*d**3 + 0*d**4 + 2/315*d**7 - 1/90*d**6 + 0*d**5 + 0*d. Factor m(u).
4*u**3*(u - 1)/3
Le