 be ((-3)/(-6))/(66 + -65). Factor 5*z**4 + 0 + b*z + 6*z**3 + 3*z**2 + 3/2*z**5.
z*(z + 1)**3*(3*z + 1)/2
Suppose 8*q**3 - q**5 - 12*q**4 + 4*q**5 + q**5 = 0. What is q?
0, 1, 2
Let r(h) be the second derivative of -2*h + h**2 - 5/24*h**4 + 0 + 2/3*h**3. Factor r(g).
-(g - 2)*(5*g + 2)/2
Let p(c) = c**3 - 10*c**2 - 12*c + 13. Let o be p(11). Let g = -3/17 - -43/51. Factor 0 - 1/3*a - 2/3*a**4 + 1/3*a**5 + g*a**o + 0*a**3.
a*(a - 1)**3*(a + 1)/3
Solve 4/11*i**5 + 10/11*i**2 - 6/11*i**4 + 24/11*i - 16/11*i**3 + 8/11 = 0.
-1, -1/2, 2
Let i(z) be the third derivative of z**10/108000 - z**9/151200 - z**5/20 + 2*z**2. Let u(d) be the third derivative of i(d). Factor u(l).
l**3*(7*l - 2)/5
Let a = -7 + 10. Let b**2 - 3*b**a + b**3 + 4*b**3 - b**3 = 0. What is b?
-1, 0
Let h be (-5)/(-2)*(-1)/(-35). Let w = h - -3/7. Factor 1/2 - w*u**2 + 0*u.
-(u - 1)*(u + 1)/2
Factor -2/7*z**3 - 2/7*z**2 + 18/7*z + 18/7.
-2*(z - 3)*(z + 1)*(z + 3)/7
Let w be 1 + (-4*2)/(-2). Suppose w*u = 4*u. Determine x so that u - 2*x**2 - 2*x**2 - 1 + 5*x**2 = 0.
-1, 1
Let a(h) = 16*h**5 + 36*h**4 + 20*h**3 + 8*h**2 - 8*h - 8. Let k(b) = -11*b**5 - 24*b**4 - 13*b**3 - 5*b**2 + 5*b + 5. Let f(c) = -5*a(c) - 8*k(c). Factor f(q).
4*q**3*(q + 1)*(2*q + 1)
Let x = 5 + -3. Let g be 28/(-49)*(-14)/4. Factor x*t + 1 - 3*t**2 + 3*t**2 + t**g + 0.
(t + 1)**2
Let h be ((-3)/(-9))/((-12)/(-144)). Solve -2/7*n**5 + 2/7*n**3 - 2/7*n**h + 0*n + 0 + 2/7*n**2 = 0 for n.
-1, 0, 1
Let q(u) be the second derivative of -2*u**6/15 + u**4/3 + u. What is s in q(s) = 0?
-1, 0, 1
Suppose 5*d + 5*d = 2*d. Factor 0 + 1/5*s**4 + 1/5*s**2 + d*s - 2/5*s**3.
s**2*(s - 1)**2/5
Let v = 1120/3133 + -12/241. What is n in -2/13*n**2 + 0 - v*n = 0?
-2, 0
Let t = -5 + 5. Suppose -7*g = -2*g. Solve 6/5*j**4 + 2/5*j**5 + 2/5*j**2 + g + 6/5*j**3 + t*j = 0.
-1, 0
Let q be 4 - 0 - (-30)/(-9). Suppose 6 - 2 = 2*u. Solve 0*v**u + q*v**3 - 2*v - 4/3 = 0.
-1, 2
Let i(p) = -p**4 - p**3 - p**2 + 1. Let v(m) = 18*m**4 - 114*m**3 + 195*m**2 - 132*m + 27. Let o(t) = -3*i(t) + v(t). Factor o(q).
3*(q - 2)**2*(q - 1)*(7*q - 2)
Let n(j) be the second derivative of -j**4/84 - j**3/21 - j**2/14 + 12*j. Factor n(k).
-(k + 1)**2/7
Let h(c) = -5*c**4 - 3*c**3 + 9*c**2 + 4*c + 3. Let v(t) = -24*t**4 - 14*t**3 + 44*t**2 + 20*t + 14. Let z(x) = 28*h(x) - 6*v(x). Factor z(y).
4*y*(y - 2)*(y + 1)**2
Factor 35 - 9*t**2 + 5*t**2 - 25 + 25*t - 31*t**2.
-5*(t - 1)*(7*t + 2)
Let u = -34 - -38. Let p(i) be the third derivative of -2*i**2 + 0 + 0*i**u + 0*i**3 + 0*i - 1/180*i**5. Factor p(z).
-z**2/3
Determine a so that -21*a**4 - 5*a**5 + 21*a**4 = 0.
0
Let y(j) be the second derivative of j**7/14 + 13*j**6/20 + 9*j**5/4 + 4*j**4 + 4*j**3 + 9*j**2/4 + 17*j. Let y(a) = 0. Calculate a.
-3, -1, -1/2
Let j be ((-114)/18)/((-2)/(-4)). Let s = 13 + j. Let -s*h + 1/3*h**2 + 0 = 0. Calculate h.
0, 1
Factor -4/3*z + 0 + 1/3*z**2.
z*(z - 4)/3
Let y(v) be the third derivative of -v**8/168 + v**7/21 - v**6/20 - 3*v**5/10 - 2*v**2. Let y(l) = 0. Calculate l.
-1, 0, 3
Let n = 20 - 17. Suppose -2*v + 15 = n*v. Factor 0 + 1/2*z**2 + 1/2*z**4 + 0*z - z**v.
z**2*(z - 1)**2/2
Let v(r) = -r**3 + 11*r**2 - 11*r + 6. Let y be v(10). Let j(w) = -4*w**2 + w - 2. Let p(g) = -g**2 - 1. Let q(m) = y*j(m) + 14*p(m). Let q(x) = 0. What is x?
-1, 3
Let q be 14/4*(-4)/(-7). Let b(w) be the first derivative of 1/4*w**4 + 0*w - 1 - 1/5*w**5 + 0*w**q - 1/6*w**6 + 1/3*w**3. Factor b(j).
-j**2*(j - 1)*(j + 1)**2
Let q = 1122 - 1122. Suppose 1/5*v + q + 1/5*v**2 = 0. What is v?
-1, 0
Determine f, given that 3*f**2 + 2*f + 2*f**3 + 1/2*f**4 + 1/2 = 0.
-1
Let y(l) be the third derivative of -2*l**2 + 4/21*l**3 + 3/28*l**4 + 1/420*l**6 + 0*l + 1/35*l**5 + 0. Factor y(f).
2*(f + 1)**2*(f + 4)/7
Let f(v) be the second derivative of v + 0 - 3/20*v**5 + 1/5*v**6 + 0*v**2 + 1/14*v**7 - 1/2*v**4 + 0*v**3. Let f(d) = 0. What is d?
-2, -1, 0, 1
Let m(h) be the first derivative of -5*h**6/6 - 7*h**5 - 45*h**4/2 - 110*h**3/3 - 65*h**2/2 - 15*h - 15. Suppose m(l) = 0. Calculate l.
-3, -1
Let l(h) be the third derivative of 11/15*h**5 + 0*h - 3/28*h**8 - 22/105*h**7 + 7/30*h**6 + 0*h**3 + 0 + 1/3*h**4 - 2*h**2. Solve l(d) = 0 for d.
-1, -2/9, 0, 1
Suppose -6*s - 18 = -12*s. Factor -3/4 - 3/4*y**4 + 0*y + 0*y**s + 3/2*y**2.
-3*(y - 1)**2*(y + 1)**2/4
Suppose -3 = -5*p + 2. Let y be (-3 - -8)*p/25. Factor 1/5*g**4 + 1/5 - 2/5*g**2 - 2/5*g**3 + y*g**5 + 1/5*g.
(g - 1)**2*(g + 1)**3/5
Suppose 2*z - 5*i = -32, z + 4*i - 14 = -i. Let f(s) = -s - 6. Let q be f(z). Suppose o**3 + q*o**2 - 2*o**4 + 3*o**2 + 5*o**3 + 2*o - 9*o**2 = 0. What is o?
0, 1
Let l(h) be the first derivative of 3*h**4/28 + h**3/3 + 5*h**2/14 + h/7 + 26. Factor l(r).
(r + 1)**2*(3*r + 1)/7
Let o(w) be the third derivative of w**7/70 + 3*w**6/8 + 15*w**5/4 + 125*w**4/8 + 33*w**2. Suppose o(l) = 0. Calculate l.
-5, 0
Let c(t) be the third derivative of -t**6/48 + 23*t**5/120 - 5*t**4/24 - 2*t**3/3 + t**2. Solve c(n) = 0 for n.
-2/5, 1, 4
Find d such that -34*d**3 - d**5 - d**5 + 32*d - 16*d**2 + 32 + 2*d**3 - 14*d**4 + 0*d**4 = 0.
-2, 1
Suppose -4*s + 33 = -55. Let w be s/8 + (-3 - -1). Factor -1/2 - 1/4*p**2 + w*p.
-(p - 2)*(p - 1)/4
Let d be 4/(-22) + 252/539. Let -4/7 + 6/7*m - d*m**2 = 0. Calculate m.
1, 2
Suppose i + 4*r - 2 = 0, -4*i - 7*r + 8 = -5*r. Factor z**4 - 5 - 2*z**4 + i*z + 6 - 2*z**3.
-(z - 1)*(z + 1)**3
Let f be -4 + (0 - -3) + 1. Let c(n) = n**3 - 7*n**2 + 5*n + 8. Let d be c(6). Suppose 4/3*a**d - 2*a**3 + 2/3*a + f = 0. Calculate a.
-1/3, 0, 1
Let i(p) be the second derivative of -1/30*p**5 + 4/3*p**2 + 5/18*p**4 + 4*p - 8/9*p**3 + 0. Factor i(g).
-2*(g - 2)**2*(g - 1)/3
Let y(a) be the second derivative of a**7/63 + 2*a**6/45 - a**4/9 - a**3/9 - 7*a. Suppose y(n) = 0. Calculate n.
-1, 0, 1
Suppose -5*l - f = -9, 0*l - f = 2*l - 3. Let r(v) = -v**3 - 6*v**2 - 2*v - 6. Let i be r(-6). Factor 0*c**l + 5*c + c**2 - i*c.
c*(c - 1)
Let w(m) be the second derivative of -8/3*m**3 + 0 - 3*m + m**4 + 2*m**2. Determine c so that w(c) = 0.
1/3, 1
Let h(r) be the third derivative of -r**7/15 - r**6/5 - r**5/10 + r**4/6 + 6*r**2. Let h(b) = 0. What is b?
-1, 0, 2/7
Let n = -238/5 - -242/5. Factor n*a**2 + 16/5*a + 0.
4*a*(a + 4)/5
Let w(q) = -q**2 + 22*q + 106. Let k be w(-4). Factor -25/2*i**k - 8 + 20*i.
-(5*i - 4)**2/2
Determine c so that 3/2*c**3 + 9*c**2 + 18*c + 12 = 0.
-2
Let m(h) be the first derivative of -h**3/3 + h**2/2 - 16. Factor m(r).
-r*(r - 1)
Let t = 4 - 1. Suppose 2 = -t*j + 8. Factor -1/3 - 4/3*y**3 + 4/3*y + 1/3*y**j.
-(y - 1)*(y + 1)*(4*y - 1)/3
Let b(p) be the first derivative of -4/5*p**5 + 5/3*p**3 - 3/4*p**4 + 3/2*p**2 - p + 3. Let b(u) = 0. Calculate u.
-1, 1/4, 1
Let j(p) be the second derivative of 7*p**6/15 + 8*p**5/5 + 11*p**4/6 + 2*p**3/3 + p - 23. Determine k, given that j(k) = 0.
-1, -2/7, 0
Let c = -4/21 + 10/21. Factor c*r + 6/7*r**4 + 2*r**3 + 0 + 10/7*r**2.
2*r*(r + 1)**2*(3*r + 1)/7
Let c(q) = -2*q - 1. Let j be c(-3). Let f be 0/(-2) - (-10)/j. Factor 2/7*u**3 + 2/7*u**f + 0 + 0*u.
2*u**2*(u + 1)/7
Let c(b) be the second derivative of 2*b + 0 - 1/3*b**3 + 1/270*b**5 + 0*b**2 + 0*b**4 + 1/1620*b**6. Let z(g) be the second derivative of c(g). Factor z(h).
2*h*(h + 2)/9
Let d be (12/26 + 0)*(-263)/(-789). Find q such that 2/13*q**2 + 0*q - d = 0.
-1, 1
Let i = -41/2 - -21. Determine w, given that 0 - i*w**5 - 1/4*w**4 + 3/4*w**3 - 1/4*w + 1/4*w**2 = 0.
-1, 0, 1/2, 1
Let j be (1/(-1))/(2/(-16)). Let l = j - 4. Factor 0*h**5 + l*h**4 - 2*h**5 - 2*h**3 + 0*h**3.
-2*h**3*(h - 1)**2
Suppose -3*o**5 - 9/4*o**2 + 0 + 15/4*o**3 + 9/4*o**4 - 3/4*o = 0. What is o?
-1, -1/4, 0, 1
Let a(q) be the second derivative of -q**10/7560 + q**9/3780 - q**4/12 - 2*q. Let z(u) be the third derivative of a(u). Suppose z(p) = 0. Calculate p.
0, 1
Let c(a) be the third derivative of a**6/60 - a**5/30 - a**4/2 - 52*a**2. Factor c(u).
2*u*(u - 3)*(u + 2)
Let a(o) = o**3 - 11*o**2 - 11*o - 7. Let v be a(12). Suppose 2*n - 24 = -4*r, -v*n + 4*r + r - 15 = 0. Factor -4 - 1 - 7*d + 3 + 0 - 5*d**n.
-(d + 1)*(5*d + 2)
Let s(d) be the first derivative of -d**3/3 - 3*d**2 - 6*d + 1. Let w be s(-4). Factor 0*k - 2 - 45*k**3 + w*k + 43*k**3 + 2*k**2.
-2*(k - 1)**2*(k + 1)
Determine y so that 0*y - 2*y**2 + 0 + 0*y**3 + 1/2*y*