/9 + 4/(-12). Suppose 0 = 9*w - c - 16. Factor w*f - 2/3 - 2*f**2 + 2/3*f**3.
2*(f - 1)**3/3
Let x(a) be the second derivative of a**4/36 + a**3/9 + a**2/6 - 8*a. Factor x(q).
(q + 1)**2/3
Let o be (1 + 1/(-2))*1. Factor -1/2*m**2 + 1/2*m**4 + 0*m + o*m**3 - 1/2*m**5 + 0.
-m**2*(m - 1)**2*(m + 1)/2
Let z(l) be the second derivative of l**4/21 + 2*l**3/7 + 4*l**2/7 - 9*l. Factor z(p).
4*(p + 1)*(p + 2)/7
Let w be -2 + (1 - -2) - -1. Suppose 0 = 2*j - 0*j - 2*a, 0 = 2*j - 3*a + w. Factor 4*t**3 + 2*t - j*t**4 - 2*t + 2*t + 2*t**3 - 6*t**2.
-2*t*(t - 1)**3
Let i(r) = -r**4 + r**3 + r**2 + r - 1. Let d(z) = -4 + 20*z**3 + 4*z**4 + 16*z + 6*z**3 + 26*z**2 + 2*z**5 + 0*z**5. Let a(f) = -d(f) + 6*i(f). Factor a(k).
-2*(k + 1)**5
Let n(g) be the first derivative of -1/2*g**4 - 3 + 1/3*g**3 + 0*g**2 + 0*g + 1/5*g**5. Suppose n(h) = 0. What is h?
0, 1
Let a(s) be the first derivative of -s**4 + 20*s**3/3 - 8*s**2 - 7. Find v, given that a(v) = 0.
0, 1, 4
Let o(c) = -2*c**3 - c**2 + c - 1. Let r be o(1). Let d be (-99)/(-15) + (r - 0). Determine j, given that -16/5*j - 8/5 + d*j**3 + 6/5*j**2 = 0.
-2/3, 1
Let r = -8 + 13. Let 2*s**3 - 2*s + 0*s**3 - 2*s**r + 2*s**3 = 0. What is s?
-1, 0, 1
Let h(l) be the third derivative of l**6/180 + l**5/45 + l**4/36 + 9*l**2. Let h(o) = 0. Calculate o.
-1, 0
Let o(u) = -u**3 - u**2 - u + 1. Let r be o(1). Let l = 0 - r. Find c, given that c**5 + c - 1 + 2*c**l + c**4 + 5*c**3 + 0*c**4 - 7*c**3 - 2*c**4 = 0.
-1, 1
Suppose 4*r + n = 12, 2*n + 0*n = -r + 3. Let -3*q**3 - q**r - 132*q**2 + 120*q**2 = 0. What is q?
-3, 0
Suppose -i + 2 = i. Let t(x) = 4*x**3 - x + 1. Let z be t(i). Factor -25*o - z*o**3 + 25*o + 6*o**2 - 2.
-2*(o - 1)**2*(2*o + 1)
Let j(p) be the second derivative of -p**9/3780 + p**7/315 - p**5/30 - 7*p**4/12 - p. Let t(o) be the third derivative of j(o). Factor t(n).
-4*(n - 1)**2*(n + 1)**2
Let h(s) be the second derivative of 2*s - 1/11*s**2 - 1/110*s**5 - 1/22*s**4 - 1/11*s**3 + 0. Suppose h(v) = 0. Calculate v.
-1
Suppose -2*w = -w. Let g = 3 + w. Factor -2*l - l**2 + 3*l + g*l - 3*l.
-l*(l - 1)
Suppose 2*i - 4*p + 16 = 0, 5*i = -4*p + 9*p - 15. Find s, given that 1/4*s**3 - 1/4*s**i - 1/4*s + 1/4 = 0.
-1, 1
Let i(p) be the second derivative of -p**5/40 + p**4/8 - p**2 + 7*p. Solve i(z) = 0.
-1, 2
Let m(h) = 260*h**4 + 125*h**3 - 35. Let w(v) = 29*v**4 + 14*v**3 - 4. Let j(l) = -4*m(l) + 35*w(l). Suppose j(u) = 0. Calculate u.
-2/5, 0
Let a = -481 + 481. Suppose a + 2/5*k + 4/5*k**2 + 2/5*k**3 = 0. What is k?
-1, 0
Find k, given that -33*k + 6*k**4 + k**5 + 3*k**4 - 3*k**5 + k**5 + 46*k**2 + 9 - 30*k**3 = 0.
1, 3
Let g(l) be the second derivative of -l**9/30240 + l**8/5376 - l**7/2520 + l**6/2880 + l**4/4 + l. Let d(i) be the third derivative of g(i). Factor d(o).
-o*(o - 1)**2*(2*o - 1)/4
Let d(b) be the third derivative of -b**6/480 + b**5/120 + 9*b**2. Factor d(n).
-n**2*(n - 2)/4
Suppose -i = i - 24. Suppose 0 = -4*w - z + i, 5*w + 5*z - 38 = -8. Determine s so that -4*s**4 - 6*s**3 - s + 0*s**2 - s**5 - 4*s**w + 0*s**4 = 0.
-1, 0
Factor -20/7*u**2 + 4/7*u**5 - 8/7*u + 4/7*u**4 + 0 - 12/7*u**3.
4*u*(u - 2)*(u + 1)**3/7
Let g = -6/35 + 47/70. Suppose 1/4*d**4 + 0 + 1/4*d**2 + 0*d - g*d**3 = 0. Calculate d.
0, 1
Let o = -29/56 - -9/14. Solve 0 - 1/8*k**2 - o*k = 0 for k.
-1, 0
Let f(j) be the second derivative of -1/15*j**5 + 5/18*j**4 + 1/3*j**2 + 0 - 2/15*j**6 - 3*j - 5/126*j**7 + 1/2*j**3. What is s in f(s) = 0?
-1, -2/5, 1
Let q = 23/28 + -4/7. Let n(a) be the first derivative of -3/4*a**2 - 3/4*a + 1 - q*a**3. What is p in n(p) = 0?
-1
Let g(c) be the third derivative of -c**6/360 - c**5/90 - 6*c**2. Factor g(i).
-i**2*(i + 2)/3
Factor 28/3*g - 2/3*g**2 - 98/3.
-2*(g - 7)**2/3
Suppose -5*r = -2*o + 10, o + 1 = -3*r + 6. Factor 21*l**2 + 27*l**3 + 0*l**5 + 6*l + r*l + 3*l**5 + 15*l**4.
3*l*(l + 1)**3*(l + 2)
Let q(d) be the third derivative of -d**7/210 - 7*d**6/360 - d**5/36 - d**4/72 - d**2. Solve q(s) = 0.
-1, -1/3, 0
Let l(s) = -5*s**3 - 5*s**2 - 2*s + 2. Let c(r) = -15*r**3 - 15*r**2 - 7*r + 7. Let h(w) = -2*c(w) + 7*l(w). Factor h(o).
-5*o**2*(o + 1)
Let w(n) be the first derivative of 4*n**5/5 - 4*n**4 + 8*n**3 - 8*n**2 + 4*n + 23. Solve w(o) = 0 for o.
1
Let t be 442/208 + 2/(-16). Factor 4/9*u**4 + 10/9*u + 2/9 + 2*u**t + 14/9*u**3.
2*(u + 1)**3*(2*u + 1)/9
Let o = -109 + 439/4. Suppose -5/4*n**3 + o*n**4 + 1/2*n**2 + 0 + 0*n = 0. What is n?
0, 2/3, 1
Let z = -15 + 28. Suppose 2 = 5*x - z. Factor 0*o + 2/5*o**x + 0 + 2/5*o**5 + 0*o**2 + 4/5*o**4.
2*o**3*(o + 1)**2/5
Let h(z) be the first derivative of 42*z**4 + 51*z**3 - 33*z**2/2 - 18*z + 8. Solve h(s) = 0.
-1, -2/7, 3/8
Let w be (-170)/(-33) + 68/11 + -6. Factor -w*g - 10/3*g**2 - 8/3 - 2/3*g**3.
-2*(g + 1)*(g + 2)**2/3
Suppose -3*x + 11 = -4. Let d = x + -3. Factor t**2 + 8*t**3 + 2*t**5 + 0*t**d - t**2 + 8*t**4.
2*t**3*(t + 2)**2
Let f(a) be the second derivative of -a**6/60 - a**5/40 + a**4/24 + a**3/12 - 6*a. Suppose f(g) = 0. Calculate g.
-1, 0, 1
Let d(m) = 2*m**3 + 2*m**2 - m. Let i be d(1). Suppose -5*b + 7 = -i. Suppose p**b + 6 + 3*p**2 + 3*p + p**2 - 8*p**2 = 0. Calculate p.
-1, 2
Factor -r**3 + 2*r + 8*r**5 - 4*r**4 + 12*r**2 - r**3 + 7*r - 7*r**5.
r*(r - 3)**2*(r + 1)**2
Suppose 0 = -4*f + t - 1, 2*t = t + 1. Let m(i) be the second derivative of -1/60*i**5 + 1/18*i**4 - i - 1/3*i**2 + f + 1/18*i**3. Factor m(n).
-(n - 2)*(n - 1)*(n + 1)/3
Let d(f) be the third derivative of 0*f**4 + 0*f + 0 + 0*f**5 + 0*f**3 + 1/300*f**6 - 2*f**2. Determine q so that d(q) = 0.
0
Let d(w) = 6*w - 1. Let t be d(1). Let j(i) = -3*i - 6. Let z be j(-3). Factor 13 + y**3 - 3*y**4 + y**t - 13 - 2*y + z*y**2.
y*(y - 2)*(y - 1)**2*(y + 1)
Let k be (-14)/(-30) - 13/(-65). Let w(d) be the first derivative of k*d**3 - 1/2*d**2 - 3 - 2*d + 1/4*d**4. Factor w(s).
(s - 1)*(s + 1)*(s + 2)
Factor 0 + 0*b**4 + 1/3*b**3 - 1/6*b - 1/6*b**5 + 0*b**2.
-b*(b - 1)**2*(b + 1)**2/6
Let r(c) = -c**4 - c**2. Let n(b) = 12*b**4 + 7*b**3 + 14*b**2 + b. Let q(v) = 4*n(v) + 36*r(v). Determine w, given that q(w) = 0.
-1, -1/3, 0
Let y be ((-3)/5)/(1/(-5)). Let r(v) be the first derivative of -y - 40/9*v**3 - 4/3*v**2 - 25/6*v**4 + 0*v. Solve r(p) = 0 for p.
-2/5, 0
Let p(k) = -k**3 + k. Let l(c) = 2*c**4 + 12*c**3 + 2*c**2 - 12*c - 4. Let m(x) = l(x) + 6*p(x). What is d in m(d) = 0?
-2, -1, 1
Let j be (-2)/7*-7*1. Suppose 0 = 3*n + 2*y - 12, -n - n + 8 = -j*y. Factor 0*l + 3/2*l**n + 0*l**2 + 0 - 3*l**3.
3*l**3*(l - 2)/2
Let l(v) be the first derivative of v**9/9072 + v**8/2520 - v**7/2520 - v**6/540 - 2*v**3/3 + 6. Let k(w) be the third derivative of l(w). Solve k(g) = 0 for g.
-2, -1, 0, 1
Let u(n) = -23*n**2 + 30*n + 37. Let j(r) = -8*r**2 + 10*r + 12. Let y(z) = -8*j(z) + 3*u(z). Factor y(p).
-5*(p - 3)*(p + 1)
Let w be (-6)/3*((-4)/(-8) - 2). Factor -2/13 + 2/13*o**w - 2/13*o + 2/13*o**2.
2*(o - 1)*(o + 1)**2/13
Suppose 9/2*k**4 + 3 - 25/2*k**3 + 25/2*k - 15/2*k**2 = 0. What is k?
-1, -2/9, 1, 3
Let z(k) be the second derivative of -k**4/4 + k**3 + 9*k**2/2 - 6*k. Find l, given that z(l) = 0.
-1, 3
Factor 6/5 + 3/5*g**3 - 9/5*g + 0*g**2.
3*(g - 1)**2*(g + 2)/5
Let y be 2/(9 + (2 - 3)). Find d, given that 0*d - y*d**5 - 1/4*d**2 + 1/4*d**4 + 1/4*d**3 + 0 = 0.
-1, 0, 1
Let k be 4/(-4)*-3 - 3. Suppose k*b - 2 = -b. Find v such that -1/2*v**5 + 0 + 0*v**4 - 1/2*v + v**3 + 0*v**b = 0.
-1, 0, 1
Let n be 0 + -1 - (2 - 5). Suppose -4*h + 17 - 1 = 0, f = n*h - 5. Factor -4*c**4 + 5/2*c**f + 2*c**5 - 1/2*c**2 + 0 + 0*c.
c**2*(c - 1)*(2*c - 1)**2/2
Let w(b) be the first derivative of b**4/16 - b**3/3 + b**2/2 + 5. Factor w(v).
v*(v - 2)**2/4
Suppose -2*a + a - 3*h = 6, 0 = 4*a + 4*h - 8. Suppose a = r + 3. Factor o**r + 1 + 2*o**3 - o**2 - 4*o**3 + o.
-(o - 1)*(o + 1)**2
Let q(u) = u - 1. Let b(r) = -r**2 - 4*r + 8. Let k(x) = b(x) + 4*q(x). What is z in k(z) = 0?
-2, 2
Let x = 6 - -2. Suppose -3*y = -2*f - x, -y - f + 0 = -6. Factor -t**4 + 4*t**4 - y*t**4 - t**3.
-t**3*(t + 1)
Factor 8/13*k**2 + 0 - 2/13*k**5 + 8/13*k**4 - 12/13*k**3 - 2/13*k.
-2*k*(k - 1)**4/13
Let v be (-21 + 29)*(-2)/8*-1. Let z(x) be the first derivative of -14*x**4 + 4*x + 16/5*x**5 - v + 11*x**3 + 14*x**2. Factor z(t).
(t - 2)**2*(4*t + 1)**2
Let i(w) be the second derivative of 0*w**3 - 1/4*w*