**4 - 1/6*x**2 - 1/15*x**5 + 0*x + 1. Determine w so that o(w) = 0.
-1, 0
Let t(g) be the first derivative of -g**6/540 + g**5/54 - 2*g**4/27 + 4*g**3/27 + g**2/2 - 1. Let n(q) be the second derivative of t(q). Factor n(y).
-2*(y - 2)**2*(y - 1)/9
Find o such that -99/4*o - 15/4*o**3 + 27/2 - 21*o**2 = 0.
-3, 2/5
Suppose -4*a + 5*g = -2, 4 = g + 2. Find h, given that 6/11 + 2/11*h**a + 10/11*h**2 + 14/11*h = 0.
-3, -1
Factor -8/5 - 6/5*y**2 + 1/5*y**3 + 12/5*y.
(y - 2)**3/5
Suppose -7*n = 21*n - 56. Solve 5/4*t**n + 1 - 2*t - 1/4*t**3 = 0.
1, 2
Suppose 3*u - 2*u = 4. Let t(v) = v**3 - v**2 - 1. Let j(s) = -3*s**3 + 4*s**2 + 4. Let o(l) = u*t(l) + j(l). Factor o(f).
f**3
Let i = 1193/1332 - 1/148. Factor 2*h**2 - 8/3*h + i.
2*(3*h - 2)**2/9
Let y(g) = g**2 - 3*g - 6. Let h be y(5). Factor 0*i**4 - 7*i - 2*i**h + 6*i**2 + 3*i.
-2*i*(i - 1)**2*(i + 2)
Suppose 2*h - 3 = 5*m, -5*h + 0*h = -2*m - 18. Suppose 0 = -2*g + h, 0*g = -q - 2*g + 6. Factor 0*d - 2*d**4 + 3*d - 7*d + 0 + 4*d**3 + q.
-2*(d - 1)**3*(d + 1)
Solve 14/3*d - 1/3*d**2 - 49/3 = 0 for d.
7
Let t(k) be the second derivative of k**6/33 - 14*k**5/55 + 8*k**4/11 - 16*k**3/33 - 16*k**2/11 + 14*k. Factor t(l).
2*(l - 2)**3*(5*l + 2)/11
Let n(w) be the first derivative of 2/35*w**5 + 0*w + 1 - 4/21*w**3 + 0*w**2 + 1/14*w**4. Factor n(l).
2*l**2*(l - 1)*(l + 2)/7
Let q(g) = g**3 + 8*g**2 + 5*g - 8. Let o be q(-7). Let c be (-4)/(-12) - (-10)/o. Factor 9*n**2 + 1 + n**2 + 4*n**3 - 4*n**c + 4*n + n**4.
(n + 1)**4
Let r(l) be the first derivative of 6*l**2 - 12*l + 3/5*l**5 + 5 + 3*l**3 - 3*l**4. Factor r(o).
3*(o - 2)**2*(o - 1)*(o + 1)
Let c(n) be the third derivative of n**8/168 - 7*n**6/240 + n**5/120 + n**4/16 - n**3/12 - 6*n**2. What is s in c(s) = 0?
-1, 1/2, 1
Suppose -4*i + 12 = -n, 15 = 4*n - i + 6*i. Let o(q) = q - 8. Let l be o(10). Factor -u**2 - l*u**4 + n*u**4 + 3*u**4.
u**2*(u - 1)*(u + 1)
Let g = 4 + 1. Suppose 2*n + 2 - 4 = 4*p, -g*n = 2*p - 5. Factor 1/4 - 1/2*w**2 + 0*w**3 + 1/4*w**4 + p*w.
(w - 1)**2*(w + 1)**2/4
Factor 3/7*w**2 - 3/7*w - 6/7.
3*(w - 2)*(w + 1)/7
Let z be 7/(224/(-188)) - -9. Factor 3/4 - 9/8*o**2 + z*o.
-(o - 3)*(9*o + 2)/8
Let m(l) = -l**3 - 6*l**2 - l - 8. Let j be m(-6). Let x(f) = -2*f - 2. Let t be x(j). Factor r - 1/2 - 1/2*r**t.
-(r - 1)**2/2
Let p(k) be the second derivative of -k**7/105 + k**6/75 + k**5/50 - k**4/30 - 8*k. Find g, given that p(g) = 0.
-1, 0, 1
Factor 0 + 0*d - 1/2*d**4 + 1/2*d**5 + 0*d**2 - d**3.
d**3*(d - 2)*(d + 1)/2
Let n(v) be the third derivative of -v**7/2100 - v**6/400 - v**5/200 - v**4/240 + 11*v**2. Factor n(a).
-a*(a + 1)**3/10
Let d(n) be the second derivative of -n**6/90 + n**5/20 + n**4/6 - 14*n**3/9 + 4*n**2 - 3*n + 17. Factor d(f).
-(f - 2)**3*(f + 3)/3
Let c = -5 + 7. Factor -s + 0*s**2 + s**2 + 2*s**2 - 2*s**c.
s*(s - 1)
Let m(l) be the first derivative of l**4/2 + 5*l**3/9 - l**2/6 + 21. Factor m(s).
s*(s + 1)*(6*s - 1)/3
Let f(s) be the third derivative of 0 - 1/27*s**3 - 1/540*s**6 + 0*s + 1/108*s**4 + 6*s**2 + 1/270*s**5. Factor f(q).
-2*(q - 1)**2*(q + 1)/9
Let t(g) = 4*g**5 + 7*g**4 - 6*g**3 - 5*g**2 - 5*g. Let x(i) = 3*i**5 + 6*i**4 - 5*i**3 - 4*i**2 - 4*i. Let y(s) = 4*t(s) - 5*x(s). Solve y(v) = 0.
0, 1
Factor -48/7*r + 0 + 4/7*r**2.
4*r*(r - 12)/7
Suppose z + 8 = 2*s, 33 = 4*z + 4*s + 5. Factor -2/5 - 2/5*y + 2/5*y**z + 2/5*y**3.
2*(y - 1)*(y + 1)**2/5
Factor -16 + 3*b**2 - 19 + 9*b + 35.
3*b*(b + 3)
Suppose 4*l = 2*q - 0 - 16, -3*q - 6 = 4*l. Suppose -359 + 2*w**2 - 2*w - 2*w**4 + q*w**3 + 359 = 0. Calculate w.
-1, 0, 1
Let i(d) be the second derivative of d**4/12 + d**3/6 + 11*d. Find m, given that i(m) = 0.
-1, 0
Suppose 1 + 35 = 3*l. Let 6*s + 9*s**2 - 6*s + 3*s**3 - l = 0. Calculate s.
-2, 1
Solve -38/5*o**3 - 66/5*o**4 + 48/5*o + 66/5*o**2 - 18/5*o**5 + 8/5 = 0.
-2, -1/3, 1
Factor 0 - 21*t**4 + 2/3*t + 14/3*t**2 + 13/6*t**3 + 27/2*t**5.
t*(t - 1)**2*(9*t + 2)**2/6
Factor 7*h**3 - 2*h - 3*h**3 - 5*h**3 + 3*h**2.
-h*(h - 2)*(h - 1)
Factor 5*j**4 + 6*j**5 - 10*j**3 - j**5 + 5 + 5*j - 10*j**2 + 0*j.
5*(j - 1)**2*(j + 1)**3
Let t = 2/567 + 52/567. Let g(y) be the first derivative of 1/7*y**4 + 0*y + 0*y**2 - t*y**3 + 2. Let g(s) = 0. Calculate s.
0, 1/2
Suppose -3*m + 6 = 0, 2*g + 0*m - 3*m = -2. Solve 6/5*o - 4/5 - 2/5*o**g = 0.
1, 2
Let v be -2 - (1 + 4)*(-5)/5. Let i(k) be the third derivative of -1/60*k**5 + 0*k - k**2 + 1/3*k**v + 0 - 1/24*k**4. Let i(a) = 0. Calculate a.
-2, 1
Let x(w) be the first derivative of w**4/12 + 7*w**3/9 + 8*w**2/3 + 4*w + 4. Find g such that x(g) = 0.
-3, -2
Let h = -29 + 49. Suppose 0 = 3*f - 8*f + 20, -4*t + h = 5*f. Factor 0*q + 4/3*q**3 + t + 2/3*q**4 + 2/3*q**2.
2*q**2*(q + 1)**2/3
Let l(z) = z**2 + z - 126. Let f be l(0). Let u be (-8)/f - 16/(-72). Solve 2/7 - u*d**2 + 0*d = 0 for d.
-1, 1
Let n be ((-28)/21)/(4/(-18)). Suppose -n = -2*d, d = -4*s + 5*d - 4. What is b in b + 2*b - 3 + b**s + b + 6 = 0?
-3, -1
Let a(i) be the third derivative of -i**7/2940 + i**5/420 - i**3/2 - 3*i**2. Let m(v) be the first derivative of a(v). Factor m(r).
-2*r*(r - 1)*(r + 1)/7
Suppose -2*z - 1 = v + 3, -v - 4*z - 10 = 0. Let p be 2/(-4) + 5/v. Factor 5*f - 3*f + 2*f**2 + 0*f**p.
2*f*(f + 1)
Let u(r) be the second derivative of -r**10/15120 + r**9/7560 + r**8/3360 - r**7/1260 - r**4/4 + 2*r. Let m(g) be the third derivative of u(g). Factor m(f).
-2*f**2*(f - 1)**2*(f + 1)
Let f(p) = p - 7. Let q be f(8). Let n(y) be the first derivative of -1/3*y**3 - y**2 - q - y. Suppose n(h) = 0. Calculate h.
-1
Suppose 0 + 1/2*v**2 - 1/2*v**4 - 1/3*v + 1/3*v**3 = 0. Calculate v.
-1, 0, 2/3, 1
Let l = -6/85 + 193/1530. Let x(s) be the second derivative of -4/9*s**3 - l*s**4 + 0 - 4/3*s**2 - 3*s. Factor x(r).
-2*(r + 2)**2/3
Suppose 0 = 2*c - 25 - 7. Factor -c + d + 16 + d**2.
d*(d + 1)
Suppose 3*i - 4 - 8 = 0. Let w be (6/(-24))/((-3)/i). Solve w*y**2 + 1/3 - 2/3*y = 0 for y.
1
Suppose 1 = 5*d - 9. Factor 3/2*l - 3/2*l**d - 1/2 + 1/2*l**3.
(l - 1)**3/2
Let h(y) be the first derivative of y**6/45 - y**5/60 - y**4/18 + y**3/18 + 3*y - 2. Let a(t) be the first derivative of h(t). What is s in a(s) = 0?
-1, 0, 1/2, 1
Let k = 1/103 - -512/309. Factor 0 - k*b**2 - 1/3*b**4 + 4/3*b**3 + 2/3*b.
-b*(b - 2)*(b - 1)**2/3
Let k be (-1)/(-3) - 1/3. Suppose 3*d - 2 = 4. Factor k*o + 1/2*o**3 + 1/2*o**d + 0.
o**2*(o + 1)/2
Suppose -21*s + 11*s + 30 = 0. Let r(g) be the first derivative of 2 - 2/3*g**s + 2*g + 0*g**2. Solve r(p) = 0.
-1, 1
Factor -100/7*m**2 - 4/7*m**5 + 20/7*m**4 + 20/7*m**3 - 64/7 - 160/7*m.
-4*(m - 4)**2*(m + 1)**3/7
Let p be 6/(-84)*(2 + -8). Factor 6/7*w**3 - p + 6/7*w**2 - 3/7*w - 3/7*w**4 - 3/7*w**5.
-3*(w - 1)**2*(w + 1)**3/7
Let u(v) be the second derivative of 0*v**5 + 1/6*v**2 + 1/90*v**6 + 0 - 1/18*v**4 + 5*v + 0*v**3. Factor u(p).
(p - 1)**2*(p + 1)**2/3
Let z(j) be the second derivative of j**5/50 - j**4/6 + 8*j**3/15 - 4*j**2/5 + 4*j. Factor z(p).
2*(p - 2)**2*(p - 1)/5
Let u(t) = t**2 + 25*t**3 - 12*t - 12*t**2 - 19*t**2. Let d(i) = 4*i**3 - 5*i**2 - 2*i. Let s(l) = -34*d(l) + 6*u(l). Factor s(g).
2*g*(g - 1)*(7*g + 2)
Let a(v) = 16*v**2 + 12*v. Let u(x) be the first derivative of -x**4/4 + 17*x**3/3 + 6*x**2 - x - 8. Let m(q) = -5*a(q) + 4*u(q). Factor m(t).
-4*(t + 1)**3
Let w(f) be the second derivative of 0*f**3 + 0 + 2/15*f**5 - 3*f + 1/189*f**7 + 2/45*f**6 + 4/27*f**4 + 0*f**2. Factor w(r).
2*r**2*(r + 2)**3/9
Factor -49/3 - 1/3*y**2 - 14/3*y.
-(y + 7)**2/3
Let f(d) be the first derivative of 0*d - 1/480*d**6 - 1/160*d**5 + 0*d**2 + 1/3*d**3 + 1 + 0*d**4. Let s(t) be the third derivative of f(t). Factor s(z).
-3*z*(z + 1)/4
Let i(j) be the first derivative of j**7/280 + j**6/360 - j**5/40 - j**4/24 - 2*j**3/3 - 2. Let n(l) be the third derivative of i(l). Solve n(r) = 0 for r.
-1, -1/3, 1
Let l(p) be the third derivative of -p**6/24 + p**5/12 - 12*p**2. Suppose l(v) = 0. Calculate v.
0, 1
Let n be 234/54 - (-2)/(-6). Let g be (n/(-2))/(4/(-3)). Factor 3/2*o - g + 3*o**2.
3*(o + 1)*(2*o - 1)/2
Let s(u) = -u**3 - 7*u**2 - 5*u + 9. Let i be s(-6). Solve 0 + 2/9*r**4 - 4/9*r**2 - 2/9*r**i + 0*r = 0.
-1, 0, 2
Let d be (3 - 2)*(-134)/(-4). Let p = -33 + d. Factor p - 1/2*z**2 + 0*z.
-(z - 1)*(z + 1)/2
Let r(v) be the third derivative of v**7/210 - v**6/60 - v**5/15 + v**4