se 5*n - 6*n = -7. Let i be 0/n - (-945)/6. Suppose 1029/4*s**5 + 0 - 6*s + 57*s**2 + 147/4*s**4 - i*s**3 = 0. Calculate s.
-1, 0, 2/7
Suppose 14*n + 6*n**2 + 17*n - 2*n**3 - 31*n = 0. What is n?
0, 3
What is p in 0 - 10/13*p**2 - 6/13*p**3 - 4/13*p = 0?
-1, -2/3, 0
Let y = -22/3 + 8. Suppose -2*u + 6 = -i, -i - 4*i - 2*u = -18. Suppose -b + 1/3*b**i + y = 0. Calculate b.
1, 2
Factor -2*s**2 - 4/3*s + 2/3.
-2*(s + 1)*(3*s - 1)/3
Suppose -5*x = 11 - 46. Let g(u) = -u**2 + 5*u + 14. Let o be g(x). Find c such that 0*c + 0 - 2/5*c**3 + o*c**2 = 0.
0
Suppose -g = -3*g. Let h = g + 3. Factor -2*b**2 - 3 + h + 4*b - 2.
-2*(b - 1)**2
Factor -2/9*p**2 + 4/3*p - 2.
-2*(p - 3)**2/9
Factor -4/3*c - 2/3*c**3 + 0 - 2*c**2.
-2*c*(c + 1)*(c + 2)/3
Let x be (7 - -2) + -2 + 1. Let t be x/12*(1 + 2). Solve 2 + 0*b**2 + 15*b**2 + b**t + 8*b + 4*b = 0 for b.
-1/2, -1/4
Let z(w) be the second derivative of -w**4/18 - w**3 + 17*w. Determine p so that z(p) = 0.
-9, 0
Let x be (24/(-540))/(1/(-5)). Factor 2/9*p + 0 + 4/9*p**2 + x*p**3.
2*p*(p + 1)**2/9
Let j(v) be the second derivative of -v**9/540 + v**8/105 - 11*v**7/630 + v**6/90 + 7*v**4/12 - 6*v. Let b(k) be the third derivative of j(k). Factor b(z).
-4*z*(z - 1)**2*(7*z - 2)
Suppose 5*k = d - 15, -5*d - 15 - 2 = -2*k. Let m = d - -9. Suppose 0 - 4/3*u**m - 2/3*u**3 + 0*u**2 + 0*u - 2/3*u**5 = 0. Calculate u.
-1, 0
Let a(l) = l**3 - 5*l**2 - 3*l + 3. Let n be a(6). Let t be ((-12)/n)/(6/(-21)). Let -p**4 - p**3 + p**t + p**3 - p**3 + p**5 = 0. Calculate p.
-1, 0, 1
Let j(y) be the first derivative of -y**7/420 - y**6/60 - y**5/30 + 2*y**3 - 1. Let g(i) be the third derivative of j(i). Factor g(z).
-2*z*(z + 1)*(z + 2)
Let v(g) be the third derivative of g**8/4200 - g**7/4200 + g**3/3 + 3*g**2. Let t(a) be the first derivative of v(a). Factor t(y).
y**3*(2*y - 1)/5
Determine i, given that 2/17*i**2 - 14/17*i + 12/17 = 0.
1, 6
Let f = 1/2 - 0. Let u(y) be the first derivative of -3*y**2 + 1 - 2*y**3 - 2*y - f*y**4. Factor u(h).
-2*(h + 1)**3
Let r(p) be the first derivative of 2*p**6/3 - 4*p**5/5 - p**4 + 4*p**3/3 + 3. Factor r(m).
4*m**2*(m - 1)**2*(m + 1)
Let c(u) be the first derivative of u**4/24 + u**3/9 - u**2/12 - u/3 - 10. Factor c(n).
(n - 1)*(n + 1)*(n + 2)/6
Suppose -1 = -5*p + 19. Let w(y) be the second derivative of 0 + 1/4*y**2 + 1/48*y**p + 3*y + 1/8*y**3. Solve w(h) = 0 for h.
-2, -1
Let o(i) be the third derivative of -i**8/840 + i**7/105 - i**6/36 + i**5/30 - i**3/3 + 4*i**2. Let t(d) be the first derivative of o(d). Factor t(a).
-2*a*(a - 2)*(a - 1)**2
Suppose -3*z = -2*z - 5. Let h(q) = 6*q**3 + 4*q**2 + 4*q + 4. Let o(t) = 7*t**3 + 5*t**2 + 5*t + 5. Let y(l) = z*h(l) - 4*o(l). Factor y(m).
2*m**3
Let z(b) = b**3 + 2*b - 1. Let u(c) = -c + 15. Let y be u(14). Let t be z(y). Factor 0*a + 1/4 - 1/4*a**t.
-(a - 1)*(a + 1)/4
Let i(g) be the second derivative of 5*g**7/42 - g**5/2 + 5*g**3/6 + 15*g. Let i(u) = 0. Calculate u.
-1, 0, 1
Suppose 7*w - 3*w - 33 = -5*v, -1 = 2*w - v. Let a be ((7 - 4) + -3)/w. Factor a + 4/3*i - 2/3*i**2.
-2*i*(i - 2)/3
Let b be 51/21 + -2 - 346/840. Let l(a) be the third derivative of -1/12*a**4 + 2*a**2 + 0*a**3 + 0 + 0*a + b*a**5. Find y such that l(y) = 0.
0, 2
Let g(f) be the second derivative of 3/2*f**2 + 1/20*f**5 + 0 + 3/40*f**4 - 1/5*f**3 + f. Let w(h) be the first derivative of g(h). Factor w(l).
3*(l + 1)*(5*l - 2)/5
Let m(i) = 11*i**4 + 11*i**3 - 6*i**2 + 6. Let y(l) = 32*l**4 + 32*l**3 - 17*l**2 + 17. Let r(t) = 17*m(t) - 6*y(t). Factor r(u).
-5*u**3*(u + 1)
Let o = 1/23 - -111/92. Let l(i) = -i - 2. Let c be l(-5). Determine t so that 0 + 0*t + o*t**5 - 1/2*t**2 - 5/4*t**c + 1/2*t**4 = 0.
-1, -2/5, 0, 1
Determine g, given that -40/11*g**2 - 4/11 + 18/11*g**3 + 26/11*g = 0.
2/9, 1
Factor 28/9*t**2 + 0 + 4/9*t**5 + 8/9*t + 20/9*t**4 + 4*t**3.
4*t*(t + 1)**3*(t + 2)/9
Let a(z) = -z**3 - 6*z**2 - 5*z + 4. Let q(i) = -2*i**3 - 5*i + 0*i + 12 - 11*i**2 - 4*i - 5. Let d(s) = 7*a(s) - 4*q(s). Factor d(c).
c*(c + 1)**2
Suppose -2*l = -8 - 2. Factor 1/2*m**l + 0*m**2 + 1/2*m + 0 + 0*m**4 - m**3.
m*(m - 1)**2*(m + 1)**2/2
Suppose 3*b - 5*b = -y - 13, -4*y + 2 = b. Factor -8*j + 10*j + 2*j**4 + 6*j**2 + b*j**3 - 5 + 5.
2*j*(j + 1)**3
Let j(i) be the first derivative of i**3 + 39*i**2 + 507*i + 33. Factor j(o).
3*(o + 13)**2
Let v(q) be the first derivative of q**4/8 - 2*q**3 + 12*q**2 - 32*q - 3. Factor v(a).
(a - 4)**3/2
Let k(j) = j**4 - 41*j**3 + 51*j**2 + 11*j + 11. Let x(f) = -8*f**3 + 10*f**2 + 2*f + 2. Let h(y) = 4*k(y) - 22*x(y). Factor h(b).
4*b**2*(b - 1)*(b + 4)
Suppose 5*f - 1 = -2*w, -2*f + 11 + 5 = 2*w. Let q(b) = b**2 - 14*b + 13. Let o be q(w). Suppose o*d**3 + 0*d - 1/4 - 1/4*d**4 + 1/2*d**2 = 0. What is d?
-1, 1
Let f = -21/109 + -33467/545. Let u = f - -62. Factor 2/5 - 4/5*g + u*g**2.
2*(g - 1)**2/5
Let -3 + 5*b - 11 + 9*b**2 + b**2 - 5*b**3 + 4 = 0. Calculate b.
-1, 1, 2
Let q(z) be the second derivative of -6*z + 2/3*z**2 + 1/60*z**5 + 0 + 4/9*z**3 + 5/36*z**4. Factor q(b).
(b + 1)*(b + 2)**2/3
Determine i, given that -51*i + 41*i + 2*i**5 - i**2 - 3*i**2 + 7*i**3 + i**3 + 8*i**4 - 4 = 0.
-2, -1, 1
Let j(y) be the third derivative of 0*y + 0 + 1/42*y**5 - 2*y**2 + 0*y**3 - 1/84*y**4 - 1/105*y**6. Factor j(h).
-2*h*(h - 1)*(4*h - 1)/7
Let u(q) be the second derivative of -q**5/80 - 7*q**4/48 - 39*q. Factor u(c).
-c**2*(c + 7)/4
Let i(q) be the first derivative of -q**6/240 - q**5/40 - q**4/16 - q**3/12 + q**2 + 2. Let f(a) be the second derivative of i(a). Factor f(r).
-(r + 1)**3/2
Let m(n) be the first derivative of n**4/2 + 28*n**3/9 + 17*n**2/3 + 4*n + 55. Let m(y) = 0. Calculate y.
-3, -1, -2/3
Factor -1/3*u**2 + 1/3*u**4 + 0 + 1/6*u**3 - 1/6*u.
u*(u - 1)*(u + 1)*(2*u + 1)/6
Let w be ((-53)/38 + 2)/2. Let b = w - 1/19. Factor -3/4*r + b - 1/4*r**3 + 3/4*r**2.
-(r - 1)**3/4
Let m be (-6)/(-9)*9/3. Let f(q) be the first derivative of -3/8*q**m - 1/4*q**3 + 3 - 1/16*q**4 - 1/4*q. Factor f(r).
-(r + 1)**3/4
Let g(f) be the third derivative of -f**5/40 + 7*f**4/8 - 49*f**3/4 - 14*f**2. Let g(x) = 0. Calculate x.
7
Suppose n = 2*n. Let y(c) be the second derivative of 1/2*c**2 - 3/20*c**5 + 1/2*c**3 + n - c - 1/12*c**4. Factor y(z).
-(z - 1)*(z + 1)*(3*z + 1)
Let s = 91/10 - 15/2. Factor 8/5*x - 6/5*x**2 - 4/5*x**3 + s + 2/5*x**4.
2*(x - 2)**2*(x + 1)**2/5
Factor 2/15*a**2 + 0*a + 0.
2*a**2/15
Let f(m) = -m**3 - 7*m**2 - 5*m + 8. Let l be f(-6). Factor 2*u**2 + l*u**2 + 0*u**2 + 2*u + 4*u**3 - 2*u**3.
2*u*(u + 1)**2
Factor 2/15*t**2 + 0*t + 0 + 2/5*t**3 - 8/15*t**4.
-2*t**2*(t - 1)*(4*t + 1)/15
Let u(t) be the first derivative of -1 + 2/15*t**3 + 3/2*t**2 - 1/30*t**4 + 1/300*t**5 + 0*t. Let x(h) be the second derivative of u(h). Factor x(y).
(y - 2)**2/5
Let -1/6*k**2 - k - 3/2 = 0. Calculate k.
-3
Suppose -2*s - 2*m = -s - 4, s + 3 = 5*m. Let h be (-98)/10 + -36 + 46. Factor -12/5*p**s + 7/5*p - h.
-(3*p - 1)*(4*p - 1)/5
Suppose 4*z = 6*z - 5*h + 20, -h + 4 = 0. Suppose -g = -z*g. Factor 1/2*w + 2*w**2 + g + 3/2*w**3.
w*(w + 1)*(3*w + 1)/2
Let f(y) be the third derivative of 1/36*y**4 + 0*y - 2/45*y**5 - 1/90*y**6 + 1/504*y**8 - 5*y**2 + 2/9*y**3 + 0 + 2/315*y**7. Let f(w) = 0. What is w?
-2, -1, 1
Let w(z) be the first derivative of 2*z**3/51 + 3*z**2/17 + 10. Factor w(j).
2*j*(j + 3)/17
Let p(r) = 88*r + 178. Let w be p(-2). Find h such that 1/3*h**w - 1/3*h + 1/3*h**3 - 1/3 = 0.
-1, 1
Let i(l) be the first derivative of -1/4*l**4 + 0*l - 4/5*l**5 + 0*l**2 + 1 + 0*l**3 - 1/2*l**6. Factor i(o).
-o**3*(o + 1)*(3*o + 1)
Let d = 29 - 4. Suppose 4*a = 2*j + j - d, -3 = -5*j - 3*a. Factor 0 + 1/3*y**j + 1/3*y - 2/3*y**2.
y*(y - 1)**2/3
Let f be -10*(0 + (-4)/(-5)). Let t = 11 + f. Factor -5*m + 0*m**4 + 4*m + 6*m**2 - 4*m**4 - t*m**5 + 4 - 6 + 4*m**3.
-(m - 1)*(m + 1)**3*(3*m - 2)
Factor 0*q**2 + 0 - 3/4*q**3 + 1/4*q**5 + 1/2*q**4 + 0*q.
q**3*(q - 1)*(q + 3)/4
Factor 1 + s**2 - 2 + 5 - 6 - s.
(s - 2)*(s + 1)
Let w(a) be the third derivative of a**8/560 + a**7/840 - a**6/120 - a**5/120 + 2*a**3/3 - 6*a**2. Let b(o) be the first derivative of w(o). Factor b(t).
t*(t - 1)*(t + 1)*(3*t + 1)
Let h(l) = 2*l**4 - 2*l**3 + 2*l**2 - 6*l + 6. Let p(o) = 3*o**3 - 7*o**4 + 6*o**4 + 5*o - o**2 + 2 - 7. Let x(r) = 5*h(r) + 6*p(r). Solve x(j) = 0 for j.
-1, 0
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