**6/270 + c**5/45 + c**4/18 + 2*c**3/27 + c**2/18 + 12*c. Let n(p) = 0. Calculate p.
-1
Factor -8/11*c**3 + 18/11*c**2 - 12/11*c + 2/11.
-2*(c - 1)**2*(4*c - 1)/11
Suppose -p = -u + 6, -3*p + 12 = -4*u + 32. Solve -c**u + 1/2*c - 3/2*c**3 + 0 = 0 for c.
-1, 0, 1/3
Let t(a) be the first derivative of -a**5/20 + a**4/6 + a**3/6 - a**2 + a - 3. Let i(x) be the first derivative of t(x). Find g, given that i(g) = 0.
-1, 1, 2
Let a(u) be the third derivative of 1/336*u**8 + 1/35*u**7 + 1/5*u**5 - u**2 + 13/120*u**6 + 0 + 0*u + 0*u**3 + 1/6*u**4. Let a(z) = 0. What is z?
-2, -1, 0
Factor -3/2*i**2 + 0 + 0*i.
-3*i**2/2
Let j be (-8)/10*25/(-70). Let -j*w + 0 + 2/7*w**2 = 0. What is w?
0, 1
Let p(t) be the second derivative of -t**9/15120 - t**8/1680 - t**7/630 - t**4/6 - 3*t. Let v(c) be the third derivative of p(c). Factor v(g).
-g**2*(g + 2)**2
Let d(s) be the third derivative of -s**7/1050 + s**6/600 + s**5/100 - s**4/120 - s**3/15 - 3*s**2. Solve d(p) = 0 for p.
-1, 1, 2
Determine f so that 3/5*f**2 - 3/5*f**4 + 0*f + 0 + 0*f**3 = 0.
-1, 0, 1
Let n(q) = 1. Let v(h) = h**2. Let l(c) = n(c) + v(c). Let p be l(1). Factor 3*i**3 - 3 + 1 - 3*i**2 + 5 - p*i - i.
3*(i - 1)**2*(i + 1)
Let q(p) be the first derivative of p**7/2100 - p**6/900 - p**5/300 + p**4/60 - p**3/3 + 2. Let l(d) be the third derivative of q(d). Factor l(j).
2*(j - 1)**2*(j + 1)/5
Let g = 0 + 3. Factor 3*i**3 + 3*i**3 - 3*i - 3*i**g.
3*i*(i - 1)*(i + 1)
Let 28/5*n**2 + 0 + 24/5*n + 4/5*n**3 = 0. Calculate n.
-6, -1, 0
Let w be (9 + -3)/(12/8). Factor 2 - 2*g**5 - 2*g**3 + g**3 + 15*g**4 - 4*g**2 - 13*g**w + 5*g**3 - 2*g.
-2*(g - 1)**3*(g + 1)**2
Factor 3/2*v**3 + 0 + 0*v + 3/2*v**2.
3*v**2*(v + 1)/2
Let r = 238/11 - 234/11. Factor 2/11*t**2 + r*t + 0.
2*t*(t + 2)/11
Let z be (-9)/(-2) - 3/2. Let r be 20/4 - (-1 + z). Factor -1 - j**2 + 2 - j**r + j + 0*j**3.
-(j - 1)*(j + 1)**2
Let h(q) be the third derivative of q**7/1050 - q**6/300 - q**5/75 + q**4/60 + q**3/10 - 33*q**2. Factor h(y).
(y - 3)*(y - 1)*(y + 1)**2/5
Let f(b) be the first derivative of -b**7/1120 - b**6/180 - 7*b**5/480 - b**4/48 + b**3/3 - 2. Let o(v) be the third derivative of f(v). Factor o(q).
-(q + 1)**2*(3*q + 2)/4
Let f = -78 + 78. Let m(w) be the second derivative of -1/70*w**5 + f + 1/42*w**4 + 1/147*w**7 + 0*w**2 - 1/105*w**6 + 0*w**3 - 3*w. Factor m(z).
2*z**2*(z - 1)**2*(z + 1)/7
Let i = 13 + -10. Find j such that i - j**2 + 0*j - 11 - 8*j - j**2 = 0.
-2
Let o(x) = -x**2 - 6*x - 5. Let f be o(-4). Factor 1/4*y - 1/4*y**f - 1/4*y**2 + 1/4.
-(y - 1)*(y + 1)**2/4
Let p(b) = b**5 - 6*b**4 - b**3 + 6*b - 6. Let a(k) = 2*k**5 - 11*k**4 - 2*k**3 + 11*k - 11. Let i be 45/7 - 33/77. Let z(l) = i*a(l) - 11*p(l). Factor z(h).
h**3*(h - 1)*(h + 1)
Let r be 3 + 18/(-8) + (-3)/6. Factor 0 - 3/4*f**3 + 1/2*f - 1/4*f**4 + r*f**2 + 1/4*f**5.
f*(f - 2)*(f - 1)*(f + 1)**2/4
Let j(u) be the third derivative of u**7/6720 - u**6/2880 - u**5/480 + 7*u**3/6 - u**2. Let c(p) be the first derivative of j(p). Solve c(d) = 0 for d.
-1, 0, 2
Let u(c) = -c**4 + 3*c**3 + 3*c**2 + 3*c + 3. Let n(q) = 16*q**2 - 6*q**4 + 15 + 10*q**3 + 6*q**3 + 1 + 16*q. Let v(b) = 3*n(b) - 16*u(b). Factor v(r).
-2*r**4
Suppose -4*j = -1 - 11. Suppose 5*v - 25 = -0*v. Factor v*x - x + 0*x**j - 2*x**3 - 2*x**2.
-2*x*(x - 1)*(x + 2)
Let p = 89 + -799/9. Factor 2/9*a**4 + 2/9*a - 2/9*a**2 - p*a**3 + 0.
2*a*(a - 1)**2*(a + 1)/9
Suppose 12 = 9*q - 3*q. Let v(f) be the first derivative of -3*f**2 + 2*f + q*f**3 - 1/2*f**4 - 1. Factor v(w).
-2*(w - 1)**3
Suppose -4*h - 2 + 14 = 0. What is o in o + 4*o**3 + o**3 - o**4 - 2*o**h - 3*o**2 = 0?
0, 1
Let y(b) be the third derivative of b**7/84 + 7*b**6/240 - b**5/40 - 7*b**4/48 - b**3/6 + b**2. Factor y(n).
(n - 1)*(n + 1)**2*(5*n + 2)/2
Suppose i = 4*i - 39. Let f be i/10 + 3/(-6). Suppose f*z + 2/5*z**2 + 2/5 = 0. Calculate z.
-1
Suppose 2*b**2 - 1 + 38*b - 19*b - 18*b + 0*b**2 = 0. What is b?
-1, 1/2
Let w(a) be the second derivative of -a**8/3360 - a**7/420 - a**6/120 - a**5/60 + a**4/12 + 2*a. Let x(c) be the third derivative of w(c). Factor x(l).
-2*(l + 1)**3
Let u = 16 + -16. Let l(c) be the third derivative of 1/270*c**5 + c**2 + u + 1/27*c**3 + 1/54*c**4 + 0*c. Factor l(j).
2*(j + 1)**2/9
Let z(k) be the first derivative of 3/2*k**4 - 5 + 0*k**2 + 1/3*k**6 + 6/5*k**5 + 2/3*k**3 + 0*k. Suppose z(d) = 0. Calculate d.
-1, 0
What is h in 27*h - 1/2*h**4 + 81/2 - 3*h**3 + 0*h**2 = 0?
-3, 3
Let w(p) be the third derivative of -8*p**7/35 - p**6/5 + 63*p**5/20 + 4*p**4 + 2*p**3 - 17*p**2 - 2*p. Let w(r) = 0. Calculate r.
-2, -1/4, 2
Let d = 357 + -9995/28. Let z(g) be the third derivative of 0*g + 0*g**5 + 0 - 2/21*g**3 - d*g**4 - g**2 + 1/420*g**6. Factor z(w).
2*(w - 2)*(w + 1)**2/7
Suppose -z**3 - 6*z**3 + 10*z**3 = 0. What is z?
0
Let v(r) be the second derivative of -r**6/60 + r**5/8 - r**4/4 - r**3/3 + 2*r**2 - r. Factor v(p).
-(p - 2)**3*(p + 1)/2
Suppose -3 = -z - 1. Let 1 + 0 - 4*j - j**z - 4*j**2 = 0. Calculate j.
-1, 1/5
Let p = -6 - -8. Factor 4*g**3 - p*g**2 + 4*g**2 - 6*g**2 - 2*g**3 + 2*g.
2*g*(g - 1)**2
Let l(t) = -2*t**2 + 3*t + 2. Let a be l(2). Factor a*b + 0 + 2/3*b**2.
2*b**2/3
Let b(x) be the first derivative of 9*x**4 + 11*x**3 + 3*x**2 + 3. Solve b(f) = 0.
-2/3, -1/4, 0
Let r(q) be the first derivative of 5*q**4/4 + 25*q**3/3 + 20*q**2 + 20*q + 1. Factor r(t).
5*(t + 1)*(t + 2)**2
Suppose -5 = -0*o - o. Suppose 0 = -o*b + 4*b + 3. Determine s, given that b*s + 4*s**2 - 3*s**2 - 2*s = 0.
-1, 0
Suppose h + 0*h - 4 = 0. Suppose h*y + 10 = -5*l, -l + 2*l + 23 = -5*y. Find m such that l*m**2 - 2*m**2 + m**2 = 0.
0
Let v(k) be the first derivative of -2*k**5/55 + 4*k**4/11 - 12*k**3/11 + 54*k/11 - 16. Factor v(g).
-2*(g - 3)**3*(g + 1)/11
Let p(m) be the third derivative of 5*m**8/336 - m**7/42 - m**6/24 + m**5/12 + 8*m**2. Factor p(g).
5*g**2*(g - 1)**2*(g + 1)
Let l = 59 - 59. Let n(k) be the third derivative of 0*k**3 - 1/15*k**7 + 1/6*k**4 + l*k - 11/30*k**5 + 4/15*k**6 + 0 - k**2. Factor n(d).
-2*d*(d - 1)**2*(7*d - 2)
Let w(z) = 9*z + 65. Let i be w(-7). Factor -4/7 - 6/7*k - 2/7*k**i.
-2*(k + 1)*(k + 2)/7
Let j = 9 + -15. Let s be (-5)/105 + (-2)/j. Factor -2/7*x**3 + 2/7*x - s*x**2 + 2/7.
-2*(x - 1)*(x + 1)**2/7
Suppose 2*m = -5*p - 32, 4 = -p + 3*m + 1. Let i(c) = -2*c - 9. Let l be i(p). Solve 3*t**5 + 8*t**4 + 2*t**3 + 2*t**l - 2*t**4 - t**5 = 0 for t.
-2, -1, 0
Let l(x) = -x + 3. Let d be l(0). Let a = 5 - d. Solve -h**a + 3*h**2 - h - h = 0 for h.
0, 1
Let c be 40/(4 - (-20)/(-8)). Let x = c - 25. Factor -l**3 + 0 - 2/3*l + x*l**2.
-l*(l - 1)*(3*l - 2)/3
Let h(r) be the third derivative of 0*r + 1/6*r**4 + 0 - 1/70*r**7 + 0*r**3 + 5*r**2 + 11/120*r**6 - 1/5*r**5. Solve h(a) = 0 for a.
0, 2/3, 1, 2
Factor -8*g + g**2 - 12*g + 6 + 25*g.
(g + 2)*(g + 3)
Factor -6*r**4 - 439 + 2*r**5 + 439.
2*r**4*(r - 3)
Let m be (-392)/(-18) - 6/(-27). Factor -5*t**3 - 4*t**3 + 4 + 26*t**2 - m*t + t**3.
-2*(t - 2)*(t - 1)*(4*t - 1)
Let h(w) be the second derivative of w**4/12 + w**3/18 - w**2/3 + 4*w. Factor h(k).
(k + 1)*(3*k - 2)/3
Let -2*v**2 + 0 + 0*v + 2/3*v**3 = 0. What is v?
0, 3
Factor 2 + 12*w**2 - 27*w**3 - 12*w**2 - 8 + 21*w.
-3*(w + 1)*(3*w - 2)*(3*w - 1)
Let z be (-14)/(-77) + (-62)/(-22). Suppose -z*q = -5*q + 6. Factor -g**q + 39*g**2 - 40*g**2 + 0*g**3.
-g**2*(g + 1)
Let j(k) be the first derivative of 1/15*k**5 - 1/12*k**4 + 0*k + 0*k**2 - 2 - 1/9*k**3 + 1/18*k**6. Factor j(f).
f**2*(f - 1)*(f + 1)**2/3
Let n(p) be the second derivative of -p**5/110 - p**4/66 + 2*p**3/33 - 2*p. Factor n(t).
-2*t*(t - 1)*(t + 2)/11
Factor 1/4*f**3 - 1/4*f**2 - 1/4*f + 1/4.
(f - 1)**2*(f + 1)/4
Let y(l) be the second derivative of 4*l**7/105 + 31*l**6/225 + 19*l**5/150 - l**4/10 - 11*l**3/45 - 2*l**2/15 + 12*l - 4. Find t, given that y(t) = 0.
-1, -1/4, 2/3
Suppose -4*q = y - 113 + 42, 3*q + 5*y - 49 = 0. Factor -24*d**2 - q*d**4 - 36*d**3 - 20/3*d - 2/3.
-2*(d + 1)*(3*d + 1)**3/3
Let h be ((-2)/(-8))/((-1)/(-4)). Factor -h + 3 + 2 - 2*o**2 + 4*o - 2*o.
-2*(o - 2)*(o + 1)
Let d(r) = r + 2. Let p be d(-4). Let a be (-8)/28 + p/(-7). Factor 2/11 - 2/11*o**2 + a*o.
-2*(o - 1)*(o + 1)/11
Let v(m) be the first derivative of 2 - 1/6*m**3 + 1/8*m**2 + 1/16*m**4 + 0*m. Factor v(q).
q*(q - 1)**2/4
Suppose -l = 2