4/3*q**2 - 2/3*q**5 - 8/3*q**4 - 8/3*q**3 = 0. What is q?
-2, -1, 1
Let d(m) be the third derivative of m**6/360 + 7*m**5/720 + m**4/144 + m**3/2 - m**2. Let o(t) be the first derivative of d(t). Factor o(b).
(b + 1)*(6*b + 1)/6
Let p = -39 + 43. Factor 0*y**2 + 0*y**p - 2/5*y**5 - 2/5*y + 0 + 4/5*y**3.
-2*y*(y - 1)**2*(y + 1)**2/5
Let g be 7/(-2) + 2 + (-159)/(-53). Factor 0 + 3/2*j**3 - g*j**2 + 0*j.
3*j**2*(j - 1)/2
Let j(c) be the third derivative of -1/3*c**3 - 7/24*c**4 + 0*c + 2*c**2 + 0 - 1/12*c**5. What is b in j(b) = 0?
-1, -2/5
Let t(s) be the first derivative of 3*s**4/26 + 10*s**3/39 + 2*s**2/13 - 5. Factor t(o).
2*o*(o + 1)*(3*o + 2)/13
Let l(w) be the third derivative of -w**7/945 + w**5/135 - w**3/27 + w**2. Factor l(f).
-2*(f - 1)**2*(f + 1)**2/9
Let l(z) be the first derivative of -3*z**5/100 + z**4/10 + 2*z**3/5 - z**2 - 5. Let g(h) be the second derivative of l(h). Determine k so that g(k) = 0.
-2/3, 2
Let r(t) = t**2 - 2*t. Let m be r(2). Let v(j) be the first derivative of -1 + 1/6*j**3 + m*j**2 - 1/8*j**4 + 0*j. Solve v(n) = 0.
0, 1
Suppose 2 = -2*v + 3*v. Solve -4*p + 4*p + 2*p**v - 2*p + 0*p = 0.
0, 1
Let s(z) be the second derivative of -z**6/60 + z**5/30 + z**4/12 + z**3/2 - z. Let w(a) be the second derivative of s(a). Find d, given that w(d) = 0.
-1/3, 1
Let j be (-2)/(-52)*(-2390)/(-225). Let l = j + -1/117. Factor 2/5*s**3 - 2/5*s**2 - 2/5*s + l.
2*(s - 1)**2*(s + 1)/5
Let d be (835/210 - 4)*-1. Let k(g) be the second derivative of -1/20*g**5 + 0*g**3 - d*g**7 + 0*g**2 - 1/15*g**6 - 2*g + 0*g**4 + 0. Factor k(p).
-p**3*(p + 1)**2
Let w(f) = -f**2 - 3 - f + 19 + 13*f - f. Let m be w(12). Factor -2*p + 1/2 + 1/2*p**m + 3*p**2 - 2*p**3.
(p - 1)**4/2
Let a = -6 - 4. Let g = -8 - a. Solve 1/5*t**g - 4/5*t + 4/5 = 0 for t.
2
Let z(l) be the second derivative of -3*l**6/10 + 3*l**5/20 + 9*l. Factor z(u).
-3*u**3*(3*u - 1)
Factor 2*w + 1 + 5/4*w**2 + 1/4*w**3.
(w + 1)*(w + 2)**2/4
Suppose 3*z = 2*d - 0*z + 6, -d + 6 = 3*z. Factor 1/3*o**5 + d*o - o**4 - 1/3*o**2 + 0 + o**3.
o**2*(o - 1)**3/3
Let b(j) = 11*j**5 + 20*j**4 + 31*j**3 + 16*j**2 - 6. Let n(u) = 155*u**5 + 280*u**4 + 435*u**3 + 225*u**2 - 85. Let o(z) = 85*b(z) - 6*n(z). Factor o(m).
5*m**2*(m + 1)**2*(m + 2)
Let r(f) be the second derivative of -f**4/36 - f**3/18 + 5*f. Factor r(t).
-t*(t + 1)/3
Let f be 2 - (-1 - -2)*-1. Factor -4*q**f + 22*q - q**3 + 3*q**3 - 4 - 24*q**2 + 8*q**4.
2*(q - 1)**2*(q + 2)*(4*q - 1)
Let m(t) = t + 1. Let g(u) = -3*u**3 - 2*u**2 - 2*u - 1. Let x be g(-1). Let a be m(x). Let h**a + 0*h**3 + 0*h**3 + 3*h**4 - 2*h**2 = 0. What is h?
-1, 0, 2/3
Factor 6*q**2 + 0*q**2 - 2*q**2 - 2*q**2 - 9*q**3.
-q**2*(9*q - 2)
Let f(z) be the first derivative of -z**6/3 + 2*z**5/5 + z**4/2 - 2*z**3/3 - 5. Solve f(m) = 0 for m.
-1, 0, 1
Let c(a) be the first derivative of -1 - 1/4*a - 1/12*a**3 - 1/4*a**2. Factor c(z).
-(z + 1)**2/4
Let p(i) be the first derivative of -i**6/30 - 3*i**5/25 - i**4/10 + 2*i**3/15 + 3*i**2/10 + i/5 + 14. Factor p(c).
-(c - 1)*(c + 1)**4/5
Let j(x) be the first derivative of 0*x - 3/16*x**4 + 4 + 1/8*x**6 + 0*x**5 + 0*x**3 + 0*x**2. Solve j(h) = 0.
-1, 0, 1
Let x(q) = -6*q**5 - 5*q**4 + q**3 - 5*q - 5. Let a(r) = -5*r**5 - 4*r**4 + r**3 - 4*r - 4. Let m(t) = -5*a(t) + 4*x(t). Find f, given that m(f) = 0.
-1, 0, 1
Let i be 29/9 - 4/18. Let x(a) be the third derivative of 0*a**4 + 0*a**i + 2*a**2 - 1/300*a**6 + 1/525*a**7 - 1/150*a**5 + 1/840*a**8 + 0*a + 0. Factor x(m).
2*m**2*(m - 1)*(m + 1)**2/5
Suppose -30 = -11*o + 6*o. Let b be (3/(-10))/(o/(-4)). Factor -1/5 + 0*p + b*p**2.
(p - 1)*(p + 1)/5
Let q(m) be the third derivative of 0*m**3 + 0 + 1/8820*m**7 + 0*m**6 - 1/12*m**4 + 0*m**5 - m**2 + 0*m. Let k(a) be the second derivative of q(a). Factor k(d).
2*d**2/7
Suppose 0 = -3*f, -4*g + 5*f = 20 - 4. Let u be 2*(-2)/g - 1. Suppose -1/5*i**2 + u - 1/5*i = 0. Calculate i.
-1, 0
Suppose -5*i + 3*i = -15*i. Let g(c) be the second derivative of 0 + 3/20*c**5 + i*c**2 - 1/3*c**3 + c - 5/12*c**4. Factor g(x).
x*(x - 2)*(3*x + 1)
Let y(c) be the third derivative of 0*c**3 + 0 + 3/160*c**6 + 0*c + 1/16*c**4 - 2*c**2 + 1/16*c**5. Factor y(a).
3*a*(a + 1)*(3*a + 2)/4
Let x(b) = 5*b**4 - b**3 - 5*b**2 - 3*b. Let t(s) = s**4 - s**2 - s. Let l(y) = 12*t(y) - 3*x(y). Solve l(p) = 0 for p.
-1, 0, 1
Factor 5/2*i - 5/2 + 5/2*i**5 + 5*i**2 - 5*i**3 - 5/2*i**4.
5*(i - 1)**3*(i + 1)**2/2
Suppose -3*i = -5*i + l + 44, 5*l = 0. Suppose -3*m + 10 = -2. Factor -i*w + 35*w**2 + m - 25/2*w**3.
-(w - 2)*(5*w - 2)**2/2
Let x = -8 + 10. Factor 0 + 8*b**3 + 2*b**5 + 2*b**x + 0*b + 2 + 7*b**4 - 2*b - 3.
(b + 1)**4*(2*b - 1)
Factor -2/17*c**2 + 0*c + 0.
-2*c**2/17
Suppose 0*s = -2*s - 4*k + 20, 5*k - 20 = 0. Find o, given that -2/5 + 2*o**s - 6/5*o**3 + 6/5*o - 8/5*o**4 = 0.
-1, 1/4, 1
Let k(r) be the third derivative of r**5/15 - 8*r**3/3 + 8*r**2. Determine m so that k(m) = 0.
-2, 2
Suppose -4*b + 4 + 12 = 0. Suppose 38*l = 44*l - 12. Factor -1/2 - c**2 + 3/2*c**b + 2*c**3 - l*c.
(c - 1)*(c + 1)**2*(3*c + 1)/2
Let w = -21509/90 - -239. Let z(o) be the second derivative of -2/3*o**3 + 0 + 2/3*o**2 + 13/36*o**4 - 3*o + w*o**6 - 1/10*o**5. Factor z(i).
(i - 2)**2*(i - 1)**2/3
Let p(i) be the second derivative of -i**4/21 - 8*i**3/21 - 6*i**2/7 - 8*i. Factor p(x).
-4*(x + 1)*(x + 3)/7
Let n(f) be the first derivative of f**7/756 - f**6/135 + f**5/60 - f**4/54 - f**3/3 - 1. Let z(q) be the third derivative of n(q). Suppose z(g) = 0. What is g?
2/5, 1
Let a(j) be the second derivative of -j**4/9 - 22*j**3/9 + 8*j**2 + 10*j. Factor a(b).
-4*(b - 1)*(b + 12)/3
Let w = 16 - 14. Suppose w*j = -2*j + 8. Factor -1/4*z**4 + 0*z**3 - 1/4*z**5 + 0*z + 0 + 0*z**j.
-z**4*(z + 1)/4
Let y(p) be the first derivative of -p**6/30 - 7*p**5/25 - 19*p**4/20 - 5*p**3/3 - 8*p**2/5 - 4*p/5 - 9. Factor y(t).
-(t + 1)**3*(t + 2)**2/5
Let n(h) be the first derivative of 5 + 4/3*h + 1/3*h**2 - 2/9*h**3. Factor n(l).
-2*(l - 2)*(l + 1)/3
Let t(f) = 3*f**2. Let s be t(-1). Factor 0 + 2/7*d**s - 2/7*d + 2/7*d**2 - 2/7*d**4.
-2*d*(d - 1)**2*(d + 1)/7
Factor 6*h**3 + 3*h**3 + 2*h**3 - 9*h**3.
2*h**3
Let y = -6/31 + 61/155. Factor y*x**3 + 0*x + 0 + 0*x**2 - 1/5*x**5 + 0*x**4.
-x**3*(x - 1)*(x + 1)/5
Let t(m) be the second derivative of -5*m**4/12 - 10*m**3 - 55*m**2/2 + 8*m. Factor t(i).
-5*(i + 1)*(i + 11)
Let z(y) be the second derivative of -7*y**5/10 + 11*y**4/12 + 5*y**3/6 - y**2 + 4*y. Factor z(a).
-(a - 1)*(2*a + 1)*(7*a - 2)
Let p(s) be the first derivative of 1/24*s**4 + 1/12*s**3 - 1 - 1/4*s**2 - 1/40*s**5 + s. Let y(d) be the first derivative of p(d). Factor y(z).
-(z - 1)**2*(z + 1)/2
Let h = -18 + 18. Let w(i) be the third derivative of h*i**3 + 0*i + 0*i**5 - 1/60*i**6 + 0 + 1/12*i**4 - i**2. Factor w(t).
-2*t*(t - 1)*(t + 1)
Let m(l) be the third derivative of -1/90*l**5 + 0 + 0*l**4 - 4*l**2 + 1/9*l**3 + 0*l. Factor m(q).
-2*(q - 1)*(q + 1)/3
Factor -s + 0 + 3*s**2 - 5/4*s**3.
-s*(s - 2)*(5*s - 2)/4
Let j(q) be the second derivative of 1/4*q**6 + 2*q - 3/28*q**7 + 0 + 7/20*q**5 - 1/2*q**4 + 0*q**2 - 2/3*q**3. Let j(m) = 0. What is m?
-2/3, 0, 1, 2
Let z(w) = 2*w - 18. Let i be z(9). Suppose -6*f**4 + i*f**5 + 0*f**5 + 0*f**4 - 6*f**3 - 2*f**5 - 2*f**2 = 0. Calculate f.
-1, 0
Let l = -20 + 16. Let b be l*4/(-48)*2. Factor -b*s**2 + 2/3*s - 2/9 + 2/9*s**3.
2*(s - 1)**3/9
Let y(k) = -k**2 - 4*k + 3. Let s be y(0). Let f(p) be the first derivative of 0*p - 1/4*p**4 + p**2 + 1 + 1/3*p**s. Solve f(c) = 0.
-1, 0, 2
Suppose 5*h = 7*h - 28. Let o be (-18)/(-63) - 4/h. Factor 0*d + o + 1/3*d**2.
d**2/3
Suppose -4*x = x - 10. Let t(a) be the first derivative of -1/6*a**3 + 0*a - 1/4*a**4 - 2 - 1/10*a**5 + 0*a**x. Find q, given that t(q) = 0.
-1, 0
Let z(f) = 92*f + 463. Let d be z(-5). Let g be 12/10 - 0 - 1. Solve 1/5*r**d + g*r**2 + 0 - 1/5*r**4 - 1/5*r = 0 for r.
-1, 0, 1
Let 61*k - k**2 - 59*k + 4*k**3 - 5*k**3 = 0. What is k?
-2, 0, 1
Let b = 644 - 7076/11. Suppose -2/11*s**2 + 8/11*s - b = 0. What is s?
2
Let p be (-2 + -3)*(-12)/30. Factor -1/5*z**3 + 0*z + 0 + 1/5*z**p.
-z**2*(z - 1)/5
Let c(u) be the first derivative of 1331*u**6/6 + 726*u**5/5 + 33*u**4 + 8*u**3/3 + 8. Factor c(h).
h**2*(11*h + 2)**3
Let u(o) be the first derivative of o**4/4 + 2. Let u(b) = 0. Calculat