 + 2/385*d**7. Let k(s) = 0. Calculate s.
0, 1, 2
Suppose 2*k + 339 = -k. Let f = -789/7 - k. Factor -6/7*t**3 + 2/7*t**4 + 0 - f*t + 6/7*t**2.
2*t*(t - 1)**3/7
Suppose 1/2*m**2 + 2*m - 2 - 1/2*m**3 = 0. Calculate m.
-2, 1, 2
Let l(b) = -b. Let j be l(-4). Let u be (11 - 12)/((-10)/j). Factor -12/5*f**4 - u*f**2 + 9/5*f**3 + 0*f + 0 + f**5.
f**2*(f - 1)**2*(5*f - 2)/5
Factor -f**3 + 0*f**2 + f + 1/2 - 1/2*f**4.
-(f - 1)*(f + 1)**3/2
Suppose b + 31 + 1 = 0. Let l be 14/21 + b/(-15). Factor 0*a - 4/5*a**3 - l*a**4 + 0 + 0*a**2 - 2*a**5.
-2*a**3*(a + 1)*(5*a + 2)/5
Let c(k) be the third derivative of k**9/20160 - k**8/10080 - k**7/5040 - 2*k**5/15 - 4*k**2. Let f(q) be the third derivative of c(q). Factor f(h).
h*(h - 1)*(3*h + 1)
Let n(x) = -4*x**2 - 1 + 3 - x**3 - 3*x**2 + 8*x. Let m be n(-8). Determine a so that -3*a**m - 4*a**4 - 3 + 3 + 16*a**4 + 9*a**3 = 0.
-1, 0, 1/4
Determine z so that 32*z**4 - 2*z**3 + 2*z - 30*z**4 - 2*z**2 + 4 - 4 = 0.
-1, 0, 1
Factor -3/2*o**3 + 9/2*o - 3 + 0*o**2.
-3*(o - 1)**2*(o + 2)/2
Let y(x) be the first derivative of -3*x**4/4 + 9*x**2/2 + 6*x + 1. Factor y(i).
-3*(i - 2)*(i + 1)**2
Solve -89*q + 47*q - 4*q**2 + 62*q - 24 = 0.
2, 3
Let u = -90/47 - -8687/4512. Let l(n) be the third derivative of 0*n + u*n**4 + 2*n**2 + 1/12*n**3 + 1/840*n**7 + 0 - 1/80*n**5 - 1/480*n**6. Factor l(t).
(t - 2)*(t - 1)*(t + 1)**2/4
Let b(y) = y**2 - 3*y - 1. Let p(z) = -4*z**2 + 10*z + 4. Let s(h) = 7*b(h) + 2*p(h). Let j(v) = 5*v**2 - v - 2. Let r(u) = -j(u) - 2*s(u). Factor r(w).
-3*w*(w - 1)
Let a(p) be the third derivative of p**8/8960 - p**7/2016 + p**6/1440 + p**4/6 - 4*p**2. Let q(u) be the second derivative of a(u). Factor q(g).
g*(g - 1)*(3*g - 2)/4
Let n(b) = b**3 - 6*b**2 + 12*b - 33. Let f be n(5). Suppose -3/5*y - 1/5*y**3 + 1/5 + 3/5*y**f = 0. What is y?
1
Let a = 1595/492 - -1/123. Let p(w) be the first derivative of 1/2*w**2 + w**5 + 4 - a*w**4 + 3*w**3 - 2*w. Factor p(m).
(m - 1)**3*(5*m + 2)
Let j = -35/36 + 11/9. Suppose -6*h + 42 = 18. What is u in 1/4*u**3 + 1/2 + 1/4*u**h - 3/4*u**2 - j*u = 0?
-2, -1, 1
Suppose 2*v + 4*t - 8 = 5*t, 2*v = 4*t + 2. Factor -10*b**3 + 4*b**2 + 8*b**4 + 32*b**3 - 12*b**3 + 2*b**v.
2*b**2*(b + 1)**2*(b + 2)
Let i(r) be the first derivative of 6*r - 3/2*r**5 - 1 - 3/4*r**4 + 15/2*r**3 + 12*r**2. Determine j so that i(j) = 0.
-1, -2/5, 2
Let t = -3421/108 - -127/4. Let u(x) be the second derivative of t*x**3 - 2*x - 4/189*x**7 + 4/27*x**4 - 1/9*x**2 + 1/45*x**5 + 0 - 7/135*x**6. Solve u(l) = 0.
-1, 1/4, 1
Suppose -2*u - f + 6 = 0, 7*u - 2*u - 3*f = -7. Suppose u = p - 3. Determine k so that 2*k**p + 2/3*k + 0 - 2/3*k**3 - 2*k**2 = 0.
-1, 0, 1/3, 1
Let r be 15/10*(-8)/(-6). Factor -3*g**r - 2*g**3 - g**3 - 3*g**4 + 9*g**3 + 0*g**4.
-3*g**2*(g - 1)**2
Let a(m) = -2*m**2 + 3*m. Let o be a(4). Let s be ((-16)/o)/((-6)/(-10)). Factor -s*r**2 + 4/3 - 2/3*r + 2/3*r**3.
2*(r - 2)*(r - 1)*(r + 1)/3
Let i(w) = -w**4 - 4*w**3 + 5*w**2 + 12*w - 12. Let t(n) = n**2 - 1. Let b(k) = -i(k) + 3*t(k). Factor b(j).
(j - 1)**2*(j + 3)**2
Factor -12/5*h + 2/5*h**2 + 18/5.
2*(h - 3)**2/5
Let r(l) be the first derivative of -5*l**9/3024 - l**8/560 + l**7/420 - 5*l**3/3 + 6. Let b(c) be the third derivative of r(c). Factor b(f).
-f**3*(f + 1)*(5*f - 2)
Let b(h) be the second derivative of h**5/35 - h**4/7 + 4*h**3/21 + 5*h. What is d in b(d) = 0?
0, 1, 2
Let p(j) = -7*j**3 + 8*j**2 - 11*j + 10. Let q(a) = 6*a**3 - 9*a**2 + 12*a - 9. Let x(o) = -3*p(o) - 4*q(o). Find i such that x(i) = 0.
1, 2
Let o(a) = a**3 - 6*a**2 + 3*a - 7. Let y be o(6). Factor 3 - c**5 + y*c**4 - 12*c**4 - 3.
-c**4*(c + 1)
Let z = 10 - 6. Factor -3 + 0*g**3 + 0 + 3*g**2 - z*g**3 + 3*g + g**3.
-3*(g - 1)**2*(g + 1)
Factor 2*f**3 - 10*f**5 + 7*f**5 - 4*f**3 - 4*f**4 + f**5.
-2*f**3*(f + 1)**2
Let s(a) = -a**5 - 7*a**3 - 8*a**2 + 8*a - 8. Let p(n) = n**3 + n**2 - n + 1. Let i(v) = -24*p(v) - 3*s(v). Factor i(c).
3*c**3*(c - 1)*(c + 1)
Let w(l) = -l**3 + 7*l**2 + l - 7. Let f be w(7). Factor -3/5*y**2 - 3/5*y**3 + 3/5*y + 3/5*y**4 + f.
3*y*(y - 1)**2*(y + 1)/5
Let b = -8 - -10. Let n(l) = l**4 + 4*l**3 - l**2 - 4*l. Let v(c) = c**4 + 3*c**3 - c**2 - 3*c. Let k(a) = b*n(a) - 3*v(a). Factor k(x).
-x*(x - 1)*(x + 1)**2
Let p(h) be the first derivative of 0*h + 0*h**3 + 0*h**2 - 9 + 1/16*h**4 + 1/20*h**5. Determine a, given that p(a) = 0.
-1, 0
Let h(k) be the third derivative of -k**7/490 - 3*k**6/140 - 13*k**5/140 - 3*k**4/14 - 2*k**3/7 - k**2. Factor h(z).
-3*(z + 1)**2*(z + 2)**2/7
Let g(i) be the third derivative of -1/112*i**8 - 7/120*i**6 + 0*i**3 + 0*i**4 - 4/105*i**7 + 0 - 1/30*i**5 - 2*i**2 + 0*i. Factor g(s).
-s**2*(s + 1)**2*(3*s + 2)
Factor 107*g + 1850 - 5*g**4 + 25*g**3 + 8*g - 1810 + 53*g**2 + 52*g**2.
-5*(g - 8)*(g + 1)**3
Let k(d) be the third derivative of d**8/168 - 16*d**7/105 + 21*d**6/20 + 8*d**5/15 - 16*d**4/3 + 26*d**2. Factor k(c).
2*c*(c - 8)**2*(c - 1)*(c + 1)
Let i = -9/4 + 35/12. Let r(u) be the second derivative of -1/2*u**2 + 2*u + 0 - 1/4*u**4 + i*u**3. Factor r(x).
-(x - 1)*(3*x - 1)
Suppose 3 = a - 0. Determine x so that 2 + 5*x + x**2 + a*x - 5*x = 0.
-2, -1
Let m be (-12)/9*(-9)/(-2). Let z = m - -8. Let -1/4 + 0*s + 1/4*s**z = 0. Calculate s.
-1, 1
Suppose -4*n + 24 + 4 = 4*k, -2*k + 2 = -n. Let a(s) be the second derivative of s + 0 - 3/10*s**4 + 2/5*s**2 - 7/15*s**k. Factor a(r).
-2*(r + 1)*(9*r - 2)/5
Let r be (8/448)/(8/64). Determine j, given that -3/7 + 3/7*j**2 + r*j - 1/7*j**3 = 0.
-1, 1, 3
Let f = -11 + 13. Suppose -4*p - 3*p**5 + 7*p**3 + 7*p**f + 5*p**2 - 8*p**4 - 4*p**3 = 0. What is p?
-2, 0, 1/3, 1
Let u(c) be the second derivative of 3*c + 1/3*c**3 + 1/3*c**4 - 1/5*c**5 - c**2 + 0 - 1/15*c**6 + 1/21*c**7. Factor u(f).
2*(f - 1)**3*(f + 1)**2
Let q = 23 + -23. Let v(n) be the first derivative of 1/15*n**6 - 1/5*n**4 + 0*n + 1/5*n**2 + 0*n**5 - 1 + q*n**3. Factor v(p).
2*p*(p - 1)**2*(p + 1)**2/5
Let x(b) be the first derivative of -b**5/25 + b**4/10 + b**3/15 - b**2/5 + 8. Factor x(u).
-u*(u - 2)*(u - 1)*(u + 1)/5
Factor 1/5*y**5 - 1/5*y**3 - 2/5*y**2 + 2/5*y**4 + 0 + 0*y.
y**2*(y - 1)*(y + 1)*(y + 2)/5
Let j(o) be the first derivative of -o**6/15 - o**5/10 + o**4/6 + o**3/3 - 3*o + 4. Let z(p) be the first derivative of j(p). Factor z(c).
-2*c*(c - 1)*(c + 1)**2
Let n(s) be the first derivative of -s**8/4200 - s**7/1050 + 2*s**3 + 7. Let w(c) be the third derivative of n(c). Factor w(q).
-2*q**3*(q + 2)/5
Factor 0*n + 2/5*n**5 + 6/5*n**4 + 0 + 6/5*n**3 + 2/5*n**2.
2*n**2*(n + 1)**3/5
Suppose 4*g - 7 = -11. Let k(l) = 3*l**2 + 2*l + 1. Let r be k(g). Factor -9*t**r + 0*t + 2*t - 23*t - 6.
-3*(t + 2)*(3*t + 1)
Let f(q) = q**3 - 9*q**2 + 8*q + 11. Let s be f(8). Let y = s + -31/3. Find z, given that 0 + 2/3*z + 4/3*z**2 + y*z**3 = 0.
-1, 0
Let q(l) be the second derivative of l**6/60 + l**5/30 + l**2/2 - 3*l. Let z(p) be the first derivative of q(p). Factor z(y).
2*y**2*(y + 1)
Let q(b) be the third derivative of b**7/630 + b**6/180 - b**4/36 - b**3/18 - 6*b**2. Factor q(j).
(j - 1)*(j + 1)**3/3
Factor -4/3 - 2/3*t**2 + 2*t.
-2*(t - 2)*(t - 1)/3
Let s = 1516/9 - 168. Let 10/9*y - s + 14/9*y**2 = 0. Calculate y.
-1, 2/7
Let u(t) = -t**4 + t**2 + 2*t + 2. Let j = 6 - 8. Let h(x) = -x**3 - x**2 - x - 1. Let y(i) = j*h(i) - u(i). Factor y(s).
s**2*(s + 1)**2
Let k(p) = -2*p**2 + 4. Let j(z) = z**3 - z**2 - z. Let s(i) = 2*j(i) + k(i). Let s(r) = 0. Calculate r.
-1, 1, 2
Let o(u) be the first derivative of 5*u**3/6 + 5*u**2/2 - 15*u/2 - 15. Factor o(r).
5*(r - 1)*(r + 3)/2
Let 8*v**2 - 5*v**3 - v**5 - 8*v**2 + 2*v**2 + 4*v**4 = 0. Calculate v.
0, 1, 2
Let o = 28 + -56. Let g be o/(-30) - (-4)/10. Factor g*z**2 - 2/3*z + 0 - 2/3*z**3.
-2*z*(z - 1)**2/3
Suppose 4*d + 4*s = -8, -2*d = s - 2*s - 2. Suppose d = 3*m - i - 12, -i = -4*m - 0*m + 15. Factor j**3 + j**m - 6*j**2 + 2*j**2.
2*j**2*(j - 2)
Let k(c) be the first derivative of 2*c**3/3 + 4*c**2 + 40. Factor k(x).
2*x*(x + 4)
Let f(r) be the second derivative of r**5/10 + 11*r**4/18 + 4*r**3/3 + 4*r**2/3 - 8*r. Let f(n) = 0. What is n?
-2, -1, -2/3
Let s = -19 - -22. Let t(m) be the first derivative of -2/5*m**2 + 2/5*m**s + 1/2*m**4 - 2 + 0*m. Factor t(v).
2*v*(v + 1)*(5*v - 2)/5
Let c(d) = 4*d + d**2 - 6*d - 4 - 11*d**2. Let p(k) = -19*k**2