(z) be the second derivative of -1/10*z**5 - 1/15*z**6 + 0 + 1/6*z**4 + 1/21*z**7 + 2*z + 0*z**3 + 0*z**2. Solve j(a) = 0.
-1, 0, 1
Let a(z) = 2*z**3 + 8*z**2 - 2*z - 8. Let c(u) = -u**3 - 5*u**2 + u + 5. Let t(j) = 5*a(j) + 8*c(j). Factor t(m).
2*m*(m - 1)*(m + 1)
Suppose 4*p + 7*c - 5*c = 8, 16 = -4*p + 4*c. Let i(s) be the third derivative of p + 0*s - 1/12*s**4 + 0*s**3 - 1/15*s**5 + 1/20*s**6 + 2*s**2. Factor i(l).
2*l*(l - 1)*(3*l + 1)
Let w(o) be the first derivative of o**7/105 + o**6/30 + 2*o**2 + 4. Let n(c) be the second derivative of w(c). Find d such that n(d) = 0.
-2, 0
Suppose 14 = 2*c + 2*y, 5 = 4*c + c - y. Let m be ((-14)/(-70))/(3/5). Determine n so that 1/3*n + 0*n**c + 0 - m*n**3 = 0.
-1, 0, 1
Let t = -83 - -85. Solve -10/3*n**4 + 38/9*n**t - 8/9*n**3 - 8/9 + 8/9*n = 0.
-1, -2/3, 2/5, 1
Let l be (-2 - -3)*(-2 + -1). Let v be l*6/9*-1. Factor 2*j**3 - 2 - 4*j - 2*j**v + 0 + 2.
2*j*(j - 2)*(j + 1)
Suppose -3*j + 62 = 5*h + 21, 8 = 4*j. Find w such that w**3 + 3*w**3 + h*w**4 - 3*w**4 = 0.
-1, 0
Let b = 214 - 212. Factor -1/4 + 0*p + 1/4*p**b.
(p - 1)*(p + 1)/4
Let k be ((-6)/8)/(4/(-112)). Suppose -3 + k = 9*z. Factor -2/5*b**z - 2/5*b + 4/5.
-2*(b - 1)*(b + 2)/5
Suppose -42*y**2 + 21*y**2 - 1 + 22*y**2 = 0. Calculate y.
-1, 1
Let n(j) be the first derivative of 2*j**3/33 - j**2/11 - 4*j/11 + 48. Find c, given that n(c) = 0.
-1, 2
Let g(p) be the third derivative of -p**8/2100 - p**7/350 - p**6/150 - p**5/150 + p**3 + 5*p**2. Let a(l) be the first derivative of g(l). Factor a(r).
-4*r*(r + 1)**3/5
Let q = 266/1255 - 3/251. Let v(l) = l**3 + 3*l**2 - l - 3. Let o be v(-3). Determine y so that -q*y**3 + o - 1/5*y**2 + 1/5*y + 1/5*y**4 = 0.
-1, 0, 1
Let y(u) be the third derivative of 0 + 1/24*u**4 + 1/3*u**3 + 1/210*u**7 - 1/120*u**6 - u**2 - 1/20*u**5 + 0*u. Factor y(f).
(f - 2)*(f - 1)*(f + 1)**2
Suppose o**4 - 7*o**2 - 29*o + 18 + 53*o + 3*o**3 - 39*o = 0. Calculate o.
-3, 1, 2
Suppose 0 = 4*c - 5*n - 5, 4*c - 11 = -n - 36. Let k = c - -5. Let k - 4/7*d**2 + 2/7*d + 2/7*d**3 = 0. What is d?
0, 1
Let b(t) = -3*t**2 + 2. Let z be b(-2). Let r = z + 16. Find n, given that 9*n**3 + 7 + r*n**2 + 3*n**4 - 7 = 0.
-2, -1, 0
Let d(h) = h**4 + 2*h**3 - h**2 - 2*h + 2. Let t be (-4)/(4 - 3) - 5. Let u(x) = 5*x**4 + 9*x**3 - 5*x**2 - 9*x + 9. Let i(s) = t*d(s) + 2*u(s). Factor i(b).
b**2*(b - 1)*(b + 1)
Let k = 1549/618 - 2/309. Factor -1 + 5/2*n + n**2 - k*n**3.
-(n - 1)*(n + 1)*(5*n - 2)/2
Let y(s) be the second derivative of -s**7/840 + s**6/360 + s**3/3 + 4*s. Let u(v) be the second derivative of y(v). Factor u(f).
-f**2*(f - 1)
Suppose -5/4*t**3 + 5/4*t**2 + 0*t + 5/4*t**5 - 5/4*t**4 + 0 = 0. What is t?
-1, 0, 1
Let k(l) be the first derivative of -3/2*l**4 + 3/4*l**2 - l**3 + 3/5*l**5 + 0*l - 3 + 3/4*l**6. Find j, given that k(j) = 0.
-1, 0, 1/3, 1
Factor -3/4*p**2 + 3/4*p + 0.
-3*p*(p - 1)/4
Factor -8*u**2 + 4*u**3 + 16/3*u - 2/3*u**4 + 0.
-2*u*(u - 2)**3/3
Factor 8*i**3 + 39*i - 45*i - 3*i**3 - 3*i**3 - 4.
2*(i - 2)*(i + 1)**2
Let u be 132/21 - 8/28. Let z(v) be the third derivative of 0 + 1/14*v**4 + 2*v**2 + 0*v + 1/105*v**u - 1/21*v**3 - 3/70*v**5. Factor z(h).
2*(h - 1)**2*(4*h - 1)/7
Suppose 0 = y + 1 + 1. Let m(k) = k**2 - 2. Let l be m(y). Factor 7*i**2 - 2*i**3 + 0*i**l - 4*i - i**2.
-2*i*(i - 2)*(i - 1)
Factor -126*h - 16*h**5 - 5*h**5 + 29*h**4 + 1632*h**2 - 258*h + 229*h**4 - 1080*h**3.
-3*h*(h - 4)**3*(7*h - 2)
Let q(x) = 5*x**4 - 4*x**3 + 5*x**2 + 6. Suppose 4*a + 1 = -3. Let i(y) = y**4 - y**3 + y**2 + 1. Let v(g) = a*q(g) + 6*i(g). Factor v(z).
z**2*(z - 1)**2
Let m(a) be the second derivative of 0*a**2 - 1/15*a**6 - 1/3*a**4 - a - 3/10*a**5 + 0*a**3 + 0. Let m(q) = 0. What is q?
-2, -1, 0
Let v = -154 + 154. Suppose -14/3*p**3 + 0*p**2 + 2*p**4 + 8/3*p + v = 0. What is p?
-2/3, 0, 1, 2
Factor -1/2*o**2 + o + 3/2.
-(o - 3)*(o + 1)/2
Let z(c) = c**4 - c - 1. Let k(h) = -15*h**4 + 15*h**3 + 5*h**2 + 5*h + 10. Let a(n) = -k(n) - 20*z(n). Suppose a(q) = 0. What is q?
-2, -1, 1
Let i(t) be the first derivative of -t**3/3 + 4*t**2 - 16*t + 8. Factor i(b).
-(b - 4)**2
Let r(g) be the first derivative of 2*g - 2/3*g**3 + 3 + 0*g**2. Factor r(n).
-2*(n - 1)*(n + 1)
Let j(q) be the second derivative of q**5/25 - q**4/5 + 2*q**3/5 - 2*q**2/5 + 9*q. Factor j(c).
4*(c - 1)**3/5
Solve 6/5 - 12/5*d + 6/5*d**2 = 0 for d.
1
Suppose -2*g + 12*g = 6*g. Factor 0*u**2 + g*u + 1/2*u**3 + 0.
u**3/2
Suppose 0 = 2*r + 6. Let f(z) = 5*z**2 + 5*z. Let u(j) = -14*j**2 - 14*j. Let s(q) = r*u(q) - 8*f(q). Factor s(d).
2*d*(d + 1)
Let w(g) be the third derivative of g**5/75 - g**4/120 - 8*g**2. Let w(r) = 0. Calculate r.
0, 1/4
Let b be 12*(-2)/(-15)*20. Let j = -27 + b. Let 0*a - 1/2*a**j + 1/2*a**3 + 0*a**4 + 0*a**2 + 0 = 0. Calculate a.
-1, 0, 1
Factor -3/5*a**2 + 1/5*a**3 + 2/5*a + 0.
a*(a - 2)*(a - 1)/5
Solve 0 - 1/4*o**5 - 1/2*o**4 + 1/4*o + 0*o**3 + 1/2*o**2 = 0 for o.
-1, 0, 1
Let p(k) be the second derivative of 3/2*k**2 + 1/150*k**5 + 0 + 2/15*k**3 + 1/20*k**4 + 3*k. Let b(i) be the first derivative of p(i). What is o in b(o) = 0?
-2, -1
Let c(i) be the first derivative of 7*i**6/360 + i**5/90 + i**2 + 7. Let a(h) be the second derivative of c(h). Factor a(z).
z**2*(7*z + 2)/3
Suppose 1 + 3 = -2*x. Let z = x + 7. Factor z*h**3 - 2 + 1 - h + h**2 - 4*h**3.
(h - 1)*(h + 1)**2
Let w = -581 - -585. Suppose -2 = 3*a - 2*p, -a - 1 = p - 7. Factor -16/3*k**3 - 2/3*k**a + 0 + 4/3*k - 10/3*k**w.
-2*k*(k + 1)**2*(5*k - 2)/3
Let o(l) be the second derivative of -8*l**6/285 + 5*l**5/38 - 9*l**4/38 + 11*l**3/57 - l**2/19 - l + 17. Solve o(y) = 0 for y.
1/8, 1
Suppose -3*l = 2*y - 5 - 4, -3*y = 3*l - 12. Factor -1/4*h**y + 1/4*h**2 + 1/4*h - 1/4*h**4 + 0.
-h*(h - 1)*(h + 1)**2/4
Suppose 0*f - 2*f + 20 = 0. Let c = f + -8. Suppose 2/5 + 6/5*d**c + 6/5*d + 2/5*d**3 = 0. What is d?
-1
Let y be (1 + (-79)/80)*84/63. Let f(v) be the third derivative of 0 + 0*v**3 + 0*v + 0*v**4 - 1/15*v**5 - y*v**6 - v**2. Factor f(h).
-2*h**2*(h + 2)
Let x = 1626/7 - 232. Let p(k) = k**3 + k + 3. Let a be p(0). Factor 0*r + 0 + 2/7*r**5 - x*r**a + 0*r**2 + 0*r**4.
2*r**3*(r - 1)*(r + 1)/7
Let z = 503/114 - -5/57. Suppose -10 = -5*s + k, -5*s + 2*s - 16 = -5*k. Factor 5*j**s + j + 0 - z*j**2.
j*(2*j - 1)*(5*j - 2)/2
Let z(q) be the second derivative of -q**5/30 - q**4/6 + 5*q. Factor z(u).
-2*u**2*(u + 3)/3
Determine g, given that -5/6*g**2 - 1/6*g**3 - 1/2*g + 3/2 = 0.
-3, 1
Let s(k) be the third derivative of -3*k**2 - 1/525*k**7 + 1/15*k**4 + 0*k - 1/15*k**3 + 1/75*k**6 - 1/25*k**5 + 0. Find q such that s(q) = 0.
1
Suppose 0 = -2*j + 2*t + 12, j - 3*t + 5*t = -3. Solve 2*d + 6*d**3 + 3*d**j - 6*d**2 - 3*d**4 - 2*d = 0.
0, 1, 2
Let m(w) be the first derivative of w**4/8 - w**3/6 - w**2/4 + w/2 + 4. Determine t so that m(t) = 0.
-1, 1
Let a(l) = -l**2 - 12*l - 9. Let k be a(-11). Suppose -t = -k*f + 16 - 7, -f + 3 = t. Factor -2/3*u**f - 8/3*u**2 + 0*u + 8/3*u**3 + 0.
-2*u**2*(u - 2)**2/3
Let x be (-3)/(-6) + ((-54)/(-12))/(-9). Let x*c + 1/5*c**4 + 0 - 1/5*c**2 - 1/5*c**5 + 1/5*c**3 = 0. Calculate c.
-1, 0, 1
Let s be (18 - -10)*6/(-8). Let f(k) = -81*k**2 + 9*k + 21. Let j(z) = -8*z**2 + z + 2. Let w(x) = s*j(x) + 2*f(x). Factor w(n).
3*n*(2*n - 1)
Let n be ((-1)/(-10) - 0)*(-51 - -55). Factor 1/5*w**2 - n*w + 1/5.
(w - 1)**2/5
Let p(l) = l - 1. Let y(u) = u**2 + u + 1. Let m(j) = 9*j**3 - 34*j**2 + 38*j - 16. Let z(h) = -m(h) - y(h). Let a(k) = -3*p(k) - z(k). Factor a(w).
3*(w - 2)*(w - 1)*(3*w - 2)
Let m(w) be the third derivative of w**5/240 + w**4/24 + w**3/8 - 12*w**2. Factor m(v).
(v + 1)*(v + 3)/4
Let p(c) be the third derivative of -1/4*c**4 + 2/15*c**5 + 0 + 0*c - c**2 - 1/3*c**3. Factor p(u).
2*(u - 1)*(4*u + 1)
Let x(v) be the third derivative of 0 + 2/15*v**3 + 1/175*v**7 - 3/20*v**4 - 11/300*v**6 - 3*v**2 + 1/10*v**5 + 0*v. Factor x(j).
2*(j - 1)**3*(3*j - 2)/5
Let n(d) = d**4 + 5*d**3 - 11*d**2 + 7*d - 4. Let p(j) = 4*j**4 + 15*j**3 - 34*j**2 + 21*j - 13. Let l(i) = -21*n(i) + 6*p(i). Let l(g) = 0. What is g?
1, 2
Let j(t) = -3*t**2 - 4*t - 5. Let u(r) = 4*r**2 + 5*r + 6. Let o(q) = -5*j(q) - 4*u(q). Find g, given that o(g) = 0.
-1, 1
Let a(w) = -4*w**3 - 16*w**2 - 2*w + 10. Let q(x) = 4*x**3 + 16*x**2 + x - 11. Let i(u) = 5*a(u) + 6*q(u). Factor