0 + y**8/10080 + y**4/24 + 4*y**2. Let j(r) be the second derivative of k(r). Suppose j(h) = 0. What is h?
-1, 0, 1
Let n(z) be the first derivative of -3*z**2 - 2/3*z**3 - 4*z - 3. Factor n(j).
-2*(j + 1)*(j + 2)
Let x be (-4)/8 + 5/2. Let s be 4/(-18)*(-3)/x. Factor -1/3*l**2 + s*l**4 + 0 - 1/3*l + 1/3*l**3.
l*(l - 1)*(l + 1)**2/3
Factor -6/11*s**4 + 2/11*s**5 + 0*s + 0*s**3 + 0 + 8/11*s**2.
2*s**2*(s - 2)**2*(s + 1)/11
Let m(i) be the first derivative of -2*i**3/3 + 7*i**2/5 - 4*i/5 - 6. Factor m(p).
-2*(p - 1)*(5*p - 2)/5
Let r = -27/4 + 29/4. What is w in -1/2*w**2 + 1/4 - r*w**3 + 1/4*w**4 + 1/4*w + 1/4*w**5 = 0?
-1, 1
Let s(f) be the first derivative of f**6/45 - f**5/15 - 5*f - 2. Let w(n) be the first derivative of s(n). What is h in w(h) = 0?
0, 2
Let y(g) be the third derivative of 0*g**5 + 0 + 0*g**4 + 1/420*g**6 - 2*g**2 + 0*g**3 + 0*g + 1/1176*g**8 - 2/735*g**7. Factor y(q).
2*q**3*(q - 1)**2/7
Determine v, given that 13*v**2 + 3 - 3*v + 6*v**2 + 3*v**3 - 22*v**2 = 0.
-1, 1
Let k(q) be the third derivative of -q**8/6720 - q**7/420 - q**6/60 + q**5/12 - 3*q**2. Let v(m) be the third derivative of k(m). Find d, given that v(d) = 0.
-2
Let r be ((-2)/(-36))/(133/21 - 6). Solve -r*p**2 - 1/3*p - 1/6 = 0 for p.
-1
Let m = 32977 + -1682021/51. Let t = -42/17 - m. Solve 2/3*g**2 - t*g + 2/3*g**3 + 0 = 0 for g.
-2, 0, 1
Suppose -2*z = -3*w + 8, -3*w + 13 - 1 = 0. Suppose 3 + 4*m**3 + z*m**4 + 2*m**2 - 3 = 0. What is m?
-1, 0
Let z(m) be the third derivative of -m**6/120 - m**5/60 + m**4/12 + 6*m**2. Factor z(d).
-d*(d - 1)*(d + 2)
Let r = 97/377 - 3/29. Find o, given that -4/13*o**2 - r*o + 0 - 2/13*o**3 = 0.
-1, 0
Let y = 4592/15 + -306. Determine r so that 0 + 0*r - y*r**4 - 4/15*r**2 + 2/5*r**3 = 0.
0, 1, 2
Let i = -80/9 - -9. Let x(p) be the first derivative of 1/3*p**2 + i*p**3 + 1 + 1/3*p. Let x(w) = 0. Calculate w.
-1
Suppose -5*t + 39 = -6. Let q(o) = -o**3 + 9*o**2 + o - 6. Let p be q(t). Factor -3/4 + 3/4*k**5 - 15/4*k**4 + 15/2*k**p - 15/2*k**2 + 15/4*k.
3*(k - 1)**5/4
Let d = -358/5 + 72. Suppose -d*y**4 + 0 + 2/5*y - 6/5*y**2 + 6/5*y**3 = 0. Calculate y.
0, 1
Let y be (-2)/(-12) - 51/(-18). Suppose -12 + 42*d**3 - 21*d**4 - 11*d**3 - 4*d**y + 3*d**5 + 48*d + 30*d**3 - 75*d**2 = 0. What is d?
1, 2
Factor 0*m**2 - 3*m**3 - 2*m**2 + 2*m**2 - 3*m**4.
-3*m**3*(m + 1)
Suppose -2*v - v + 9 = 0. Let u be v*21/18 + -3. Factor -7/4*n**2 + u*n + 7/4*n**4 - 1/2*n**3 + 0.
n*(n - 1)*(n + 1)*(7*n - 2)/4
Let y be 2/6*2/8. Let s(h) be the second derivative of -1/4*h**2 - 1/8*h**3 - 1/60*h**6 + 0 - 3*h - 1/56*h**7 + y*h**4 + 3/40*h**5. Let s(g) = 0. Calculate g.
-1, -2/3, 1
Let x(c) be the third derivative of 0*c**5 - 1/112*c**8 + 0*c**4 + 0*c**3 + 1/35*c**7 - 1/40*c**6 + 0*c + 0 - c**2. Factor x(t).
-3*t**3*(t - 1)**2
Let w be 2/4 + 57/(-120). Let o(b) be the second derivative of -w*b**5 + 2*b + 0*b**4 + 0*b**2 + 0 + 1/60*b**6 + 0*b**3. Suppose o(g) = 0. Calculate g.
0, 1
Let z(d) = d**2 - 4*d + 5. Let l be z(4). Let r be 2/(l/(-2) - -3). What is o in 18/5*o**5 - 6/5*o**r + 8/5*o**2 - 16/5*o**3 + 0*o + 0 = 0?
-1, 0, 2/3
Let g = 17 - 10. Let b = g + -5. Find k, given that -2*k - 2 - 1/2*k**b = 0.
-2
Let z(f) = 5*f**4 + 7*f**3 - f**2 - 3*f + 4. Let h(y) = -y**4 + y**3 + y**2 - y + 1. Let x(s) = 4*h(s) - z(s). Factor x(m).
-m*(m + 1)*(3*m - 1)**2
Let o be ((-4)/(-15))/(54/81). Find p such that 2/5*p + 4/5*p**2 - o*p**5 + 0*p**3 + 0 - 4/5*p**4 = 0.
-1, 0, 1
Let o(k) be the first derivative of -k**6/15 - 4*k**5/25 + k**4/2 + 4*k**3/3 - 4*k**2/5 - 16*k/5 - 15. Solve o(i) = 0 for i.
-2, -1, 1, 2
Factor -30*p**3 - 20 - 21*p**2 + 6*p - 16*p**2 - 28*p**2 - 5*p**4 - 66*p.
-5*(p + 1)**2*(p + 2)**2
Let t(f) = f + 3. Let l(d) = -2*d**2 + d + 4. Let v(i) = i**2 + i. Let m(r) = -l(r) - v(r). Let q(h) = 3*m(h) + 4*t(h). Let q(g) = 0. What is g?
0, 2/3
Factor -30*k**4 + 71*k**2 + 27*k**3 + k**2 + 33*k**4 + 48*k.
3*k*(k + 1)*(k + 4)**2
Let l(v) = v**3 - 7*v**2 - 8*v + 5. Let d be l(8). Factor -7*b - 2*b - b**3 + d*b**2 + 4 + b.
-(b - 2)**2*(b - 1)
Find y such that 120*y**4 - 100*y**5 - 16*y - 19 + 44*y**3 - 48*y**2 + 19 = 0.
-2/5, 0, 1
Let o = 3/13 - 32/195. Let v(w) be the third derivative of 2*w**2 + 1/150*w**5 + o*w**4 + 0*w + 0 + 4/15*w**3. Let v(n) = 0. Calculate n.
-2
Let l(k) be the first derivative of k**4/4 + k**3/3 - 13. Determine z, given that l(z) = 0.
-1, 0
Let g = -20 - -23. Find i, given that -4*i - 6*i**2 + g*i**2 - 2 + 1 = 0.
-1, -1/3
Let y(g) = 3*g**4 - 7*g**3 - 7*g**2 - g. Let x(b) = 7*b**4 - 15*b**3 - 15*b**2 - 2*b. Let j(t) = 4*x(t) - 9*y(t). Find n, given that j(n) = 0.
-1, 0
Let j be 2 - 3/1 - -1. Let p = 4 + j. Suppose -1 - 3*d**3 + 0*d**p + d**3 + 0*d + 2*d + d**4 = 0. Calculate d.
-1, 1
Suppose 20 = -4*i, p = -3*p - 4*i - 20. Factor p*j + 0 - 1/4*j**2.
-j**2/4
Let z(b) be the first derivative of -b**6/120 + b**4/8 - 5*b**3/3 - 4. Let v(w) be the third derivative of z(w). Factor v(x).
-3*(x - 1)*(x + 1)
Let x(v) = v**4 + v**3 - v**2 - v. Let m = -12 - -11. Let l(p) = -8*p**4 - 12*p**3 + 4*p**2 + 12*p + 4. Let t(a) = m*l(a) - 6*x(a). Factor t(r).
2*(r - 1)*(r + 1)**2*(r + 2)
Let z(f) = 15*f**3 + 98*f**2 + 75*f - 8. Let q(t) = 10*t**3 + 65*t**2 + 50*t - 5. Let d(w) = 8*q(w) - 5*z(w). Factor d(r).
5*r*(r + 1)*(r + 5)
Suppose -a + 4*a = 12. Suppose 6*l - a = 4*l. Factor -4/7 - 2/7*q**l + 6/7*q.
-2*(q - 2)*(q - 1)/7
Suppose g - 12 = -g. Let q be 8/g*3/14. Find x, given that 4/7*x**2 - 2/7*x**4 - q + 2/7*x + 2/7*x**5 - 4/7*x**3 = 0.
-1, 1
Factor 2/7*y**3 + 8/7*y**2 + 6/7*y + 0.
2*y*(y + 1)*(y + 3)/7
Let j be 4/45*1/28. Let n(u) be the third derivative of 0*u**3 - 1/180*u**6 - j*u**7 + 0*u + 1/90*u**5 + 1/36*u**4 - 2*u**2 + 0. Factor n(a).
-2*a*(a - 1)*(a + 1)**2/3
Let m(l) = -5*l**3 - 7*l**2. Let z(p) = -p**3 - p**2. Let f(x) = m(x) - 6*z(x). Find u, given that f(u) = 0.
0, 1
Let m(z) be the first derivative of -1/15*z**5 + 2/3*z**2 + 5/12*z**4 + 0*z - 3 - 8/9*z**3. Determine n, given that m(n) = 0.
0, 1, 2
Suppose 2*a = 4*g + 4 - 2, 2*a - 5 = g. Let c(y) be the third derivative of 0*y + 4/15*y**a + 0 - 1/15*y**4 + 1/150*y**5 - 2*y**2. Factor c(s).
2*(s - 2)**2/5
Let d(o) = 2*o - 4*o**3 - o**2 - o + 3*o**2. Let s(k) = 3*k**3 - 2*k**2 - k. Let f(p) = -4*d(p) - 5*s(p). Factor f(z).
z*(z + 1)**2
Let u(z) be the first derivative of -z**6/540 - z**5/90 - z**4/36 - 2*z**3/3 - 1. Let h(c) be the third derivative of u(c). Suppose h(f) = 0. What is f?
-1
Let d(v) = -v**2 - v + 6. Let a be d(-3). Let y(s) be the second derivative of 2/21*s**3 + a + 1/42*s**4 + 1/7*s**2 - s. Let y(j) = 0. Calculate j.
-1
Let f = 298/3 + -99. Determine t, given that -t**4 + t - 2/3*t**3 - 1/3*t**5 + f + 2/3*t**2 = 0.
-1, 1
Let p(n) = n**2 - 23*n + 44. Let x be p(21). Let -1/4*k + 1/8*k**x + 1/8 = 0. Calculate k.
1
Let y = 3/11 - 4/55. Let n = 2/15 + y. Factor -1/3*p**3 + 1/3 - 1/3*p**2 + n*p.
-(p - 1)*(p + 1)**2/3
Let s(v) = v**3 + 1. Let o be s(1). Let m = -1 + o. What is g in -25/4*g**2 - 5*g - m = 0?
-2/5
Factor 6 - 2 - 4*y**3 + 14 + 14 - 48*y + 24*y**2.
-4*(y - 2)**3
Let -4*c**2 - 1/3*c + 1/3 = 0. Calculate c.
-1/3, 1/4
Let r be (-1)/(1/(-2)*1). Factor -k**4 - 3 + 2 + k**r + k**2.
-(k - 1)**2*(k + 1)**2
Factor 40/17*k + 200/17 + 2/17*k**2.
2*(k + 10)**2/17
Let y(c) be the first derivative of 0*c**4 + 0*c - 3/25*c**5 + 3/5*c**3 + 2 + 3/5*c**2. Factor y(q).
-3*q*(q - 2)*(q + 1)**2/5
Let u(x) be the second derivative of 0 + 0*x**2 - 4*x + 1/20*x**4 - 1/5*x**3 + 6/25*x**5 + 1/10*x**6. What is i in u(i) = 0?
-1, 0, 2/5
Suppose 5*g - 21 + 6 = 0. Find o such that 9/5*o**2 + 3/5*o**g + 3/5 + 9/5*o = 0.
-1
Let d(b) = -2*b**2 + 4*b**2 + 3*b**2 + 1 - 4*b**2. Let o(u) = -u - 1. Let q(j) = -d(j) - o(j). Factor q(s).
-s*(s - 1)
Let z(h) = -7*h**3 - 2*h**2 + 9*h - 5. Let r(u) = 8*u**3 + 2*u**2 - 10*u + 6. Let y(d) = -5*r(d) - 6*z(d). Factor y(b).
2*b*(b - 1)*(b + 2)
Let a(o) be the first derivative of o**8/420 - o**7/105 - o**6/90 + o**5/15 + 2*o**3 - 1. Let p(r) be the third derivative of a(r). Let p(v) = 0. Calculate v.
-1, 0, 1, 2
Let z = -138107/171 + 18210/19. Let f = 151 - z. What is s in 2/9*s**4 - 4/9 - 10/9*s - 2/3*s**2 + f*s**3 = 0?
-1, 2
Let v(j) be the third derivative of j**5/105 - 2*j**3/21 + 10*j**2. Factor v(k).
4*(k - 1)*(k + 1)/7
Let n(j) = -3*j - 5. Let o b