5 + 1/120*u**4 - 5*u**2 + 0*u**3. Factor v(b).
-b*(b - 1)*(b + 1)**2/5
Let a(n) be the first derivative of n**5/30 - n**4/12 + n**2/2 + 3. Let f(y) be the second derivative of a(y). Find b, given that f(b) = 0.
0, 1
Let v(h) = 2*h**4 - 4*h**3 - 4*h**2 + 4*h + 2. Let g(o) = o**3 + o**2 - o - 1. Let c(d) = 2*g(d) + v(d). Suppose c(q) = 0. What is q?
-1, 0, 1
Let r = 23 - 20. Suppose -4/3*v - 5/3*v**r + 0 + 4*v**2 = 0. Calculate v.
0, 2/5, 2
Suppose 0*a = -4*a + 20. Suppose -3*n + 3 = r - 11, 4*r + a*n = 28. Solve 1/2 + 21/4*v**r + 5/4*v**4 + 17/4*v**3 + 11/4*v = 0.
-1, -2/5
Suppose -5 + 9 = g, -3*i + 5*g = 8. Factor 0 + 5/4*k**i - 3/4*k**5 + 0*k - 1/2*k**3 + 0*k**2.
-k**3*(k - 1)*(3*k - 2)/4
Let f(b) = -b**3 + b + 1. Let c(s) = -s**3 - s**2. Let l(r) = 14*r**3 + 10*r**2 - 4*r - 4. Let k(y) = -8*c(y) - l(y). Let a(p) = -4*f(p) + k(p). Factor a(v).
-2*v**2*(v + 1)
Let v(p) = p**3 + 5*p**2 - 2*p - 5. Let s be v(-5). Suppose 2*b - s = -3*h - 11, -2 = -4*b + h. Find q such that b*q - 2/5*q**3 + 0 - 2/5*q**4 + 0*q**2 = 0.
-1, 0
Let b(o) be the first derivative of o**3/12 - o**2/8 - 3*o/2 + 2. Suppose b(i) = 0. What is i?
-2, 3
Let b be (10/(-125))/((-1)/40). Determine z, given that -2/5*z**3 - 24/5*z - b - 12/5*z**2 = 0.
-2
Suppose -8 = 5*w - 7*w. Factor 5*x**3 - x - 3*x**w + 2*x**3 - x**3 + 3 - 5*x.
-3*(x - 1)**3*(x + 1)
Suppose 0 = -131*p + 130*p + 2. Let x(j) be the first derivative of -2 - j**p + 0*j**3 + 1/5*j**5 - j + 1/2*j**4. Factor x(u).
(u - 1)*(u + 1)**3
Let r(a) be the second derivative of a**7/4620 - a**5/660 - a**3/6 - 6*a. Let y(t) be the second derivative of r(t). What is b in y(b) = 0?
-1, 0, 1
Let v(k) be the second derivative of -k**8/13440 + k**7/5040 - k**4/4 + 3*k. Let n(w) be the third derivative of v(w). Let n(g) = 0. What is g?
0, 1
What is q in 0*q + 6/5*q**2 - 8/5 + 2/5*q**3 = 0?
-2, 1
Let q(r) be the first derivative of 5*r**2 - 1/2*r**4 - 6*r + 5 - 2/3*r**3. Factor q(z).
-2*(z - 1)**2*(z + 3)
Let t = 9 + -7. Solve f**t + f - 9 + 9 = 0.
-1, 0
Let k(u) be the third derivative of u**5/20 + 5*u**2. Determine l, given that k(l) = 0.
0
Factor 235*r**2 - 2*r**3 + 8*r - 2 - 231*r**2 - 14.
-2*(r - 2)**2*(r + 2)
Let c(q) be the third derivative of -q**8/336 - q**7/42 - 7*q**6/120 + q**5/60 + q**4/3 + 2*q**3/3 - 5*q**2. Factor c(k).
-(k - 1)*(k + 1)**2*(k + 2)**2
Factor -8*u - 3*u**2 - 8 - 4*u**2 + 5*u**2.
-2*(u + 2)**2
Let k = 143/2004 + 2/167. Let u(h) be the first derivative of -1/8*h**2 + 0*h + k*h**3 + 3. Factor u(j).
j*(j - 1)/4
Let y(q) be the second derivative of q**6/180 - q**4/24 + q**3/18 + 4*q. Suppose y(r) = 0. What is r?
-2, 0, 1
Let k(t) be the first derivative of -t - t**3 + 2 - 1/4*t**4 - 3/2*t**2. Factor k(h).
-(h + 1)**3
Let g(a) be the second derivative of a**7/168 + a**6/60 + a**5/80 + 3*a. Factor g(h).
h**3*(h + 1)**2/4
Let r(z) be the first derivative of 4 - 1/6*z**3 - 1/12*z**6 + 1/8*z**4 + 1/10*z**5 + 0*z**2 + 0*z. Find x, given that r(x) = 0.
-1, 0, 1
Let h be 165/396 + 3/12. Factor -4/3*z**2 + 0*z**3 + 2/3*z**4 + 0*z + h.
2*(z - 1)**2*(z + 1)**2/3
Let p(w) = 15*w. Let r be p(1). Let t be (44/6)/(5/r). Let -4 + 30*n**2 + 7 + 1 + t*n = 0. Calculate n.
-2/5, -1/3
Let s(q) = 2*q**2 + q - 2. Let r be s(-2). Let -4*p**2 - 4*p + 4*p**3 - 6 + 6 + 4*p**r = 0. Calculate p.
-1, 0, 1
Let w(g) = g**2 - 5*g + 6. Let u be w(4). Suppose -2 - 3*x - u*x - 2*x**2 + x = 0. What is x?
-1
Suppose 0 = -8*j + 13 + 3. Suppose -2*b - 2*m - m = -21, -4*m = 4*b - 36. Factor -2/5*p - 4/5 + b*p**j.
2*(3*p + 1)*(5*p - 2)/5
Let k = -726/7 + 104. Factor 4/7*c + 0 - k*c**2.
-2*c*(c - 2)/7
Let k(h) = 4*h**4 - 5*h**2 + 3*h + 1. Let l(z) = 2*z**4 + z**2 - z + z - z - 3*z**4. Let u(g) = -2*k(g) - 6*l(g). Factor u(n).
-2*(n - 1)**2*(n + 1)**2
Let p(n) = -2*n**2 + 1 + 3*n**3 + 14*n - 14*n. Let q be p(1). Factor -2*y**2 - q + 7*y**3 + 2.
y**2*(7*y - 2)
Factor 2*w**5 + 108*w**2 + 20*w**4 + 36*w - 8*w + 26*w + 72*w**3.
2*w*(w + 1)*(w + 3)**3
Let b(u) be the second derivative of u**5/210 - u**4/28 + 2*u**3/21 - u**2/2 - 3*u. Let p(d) be the first derivative of b(d). Determine c so that p(c) = 0.
1, 2
Let a(h) be the third derivative of 0*h - 1/40*h**4 + 0*h**3 + 1/100*h**5 + 0 - 5*h**2. Factor a(g).
3*g*(g - 1)/5
Suppose 3*s = o - 11, 3*s = -0*o + 4*o - 26. Let a be o/2 + 0/(-2). Factor -9/2*k**2 - 1/2*k**4 + 7/2*k + a*k**3 - 1.
-(k - 2)*(k - 1)**3/2
Let u = 380 + -8745/23. Let y = 91/207 + u. Find d, given that 4/9*d + y*d**2 + 2/9 = 0.
-1
Let o(f) be the third derivative of -f**8/840 + f**6/300 - 2*f**2. Factor o(y).
-2*y**3*(y - 1)*(y + 1)/5
Let r(a) be the first derivative of -2/9*a**3 + 1 - 1/3*a**2 + 0*a. Factor r(y).
-2*y*(y + 1)/3
Suppose -3*n = 7 - 13. Let q(o) be the third derivative of -3*o**n - 1/150*o**5 - 1/20*o**4 - 2/15*o**3 + 0*o + 0. Factor q(g).
-2*(g + 1)*(g + 2)/5
Let l be (-1)/2*(1 + 3). Let w(h) = -h**3 + h. Let y(z) = 4*z**3 + z**2 - 5*z. Let q(f) = l*y(f) - 14*w(f). Factor q(n).
2*n*(n - 1)*(3*n + 2)
Let w be (-8)/4 + 5 + -1. Factor 4*v - 2 + 6*v**w - 14*v**2 + 6*v**2.
-2*(v - 1)**2
Let i(l) = -6*l**2 + 2*l + 3. Let s(x) = 5*x**2 - 2*x - 4. Let z(q) = -4*i(q) - 5*s(q). Solve z(t) = 0.
-2, 4
Let l(p) be the first derivative of 2*p**3/45 + 7*p**2/15 + 4*p/5 - 9. Factor l(q).
2*(q + 1)*(q + 6)/15
Let x be (0/(-1))/(3 + 0). Let f(u) be the third derivative of u**2 + 1/105*u**7 + 0*u - 1/30*u**5 + x - 1/60*u**6 + 0*u**3 + 1/12*u**4. Factor f(n).
2*n*(n - 1)**2*(n + 1)
Factor -1/3*c**4 + 2/3*c + 0*c**2 - 2/3*c**3 + 1/3.
-(c - 1)*(c + 1)**3/3
Let r be (-3)/(-3 + 0) - -8. Suppose -4*w - 30 = -2*n - 3*n, -5*n = 5*w + 15. Factor 3 - 4 + r + 2*c**n + 8*c.
2*(c + 2)**2
Let m = -20 + 38. Let f be (-6)/12 + 21/m. Factor -2/3*j**4 + 0*j**2 - f*j**3 + 0 + 0*j.
-2*j**3*(j + 1)/3
Let c(t) be the third derivative of t**5/240 - t**4/16 + 3*t**3/8 + 3*t**2. Solve c(u) = 0 for u.
3
Suppose -j = 3*j - 3*x - 35, j = -4*x - 15. Suppose -6 = -j*k + 2*k. Find g such that -g - 2*g**3 - 2 + 3*g + 0 + 2*g**k = 0.
-1, 1
Let r be (9/6)/(2 + 15/(-12)). Let -10/7*x**r - 2*x**3 + 0 + 4/7*x = 0. What is x?
-1, 0, 2/7
Let x(c) = -c**2 + 3*c + 3. Let v(t) = -1. Let j(w) = 5*v(w) + x(w). Factor j(g).
-(g - 2)*(g - 1)
Determine o so that -2/11*o - 12/11 + 2/11*o**2 = 0.
-2, 3
Let v = 161/3 - 53. Suppose v*i + 0 - 1/3*i**2 - 1/3*i**3 = 0. What is i?
-2, 0, 1
Let o(a) be the second derivative of -a**8/3360 + a**7/630 - a**6/360 - a**4/6 - 2*a. Let f(w) be the third derivative of o(w). Factor f(q).
-2*q*(q - 1)**2
What is z in 2/3*z**2 - 8/3*z + 8/3 = 0?
2
Let x be 1/(-3)*22/(-18). Let q(t) be the second derivative of 11/90*t**5 - 7/54*t**4 - 2*t + 1/15*t**6 - x*t**3 - 2/9*t**2 + 0. Solve q(y) = 0 for y.
-1, -2/9, 1
Let w be 9*1*2/6. Let s = -1 + w. Factor -s*k**5 + 8*k**4 - 1 - 6*k**4 + 1.
-2*k**4*(k - 1)
Let r(c) be the third derivative of -c**10/75600 - c**9/10080 - c**8/3360 - c**7/2520 + c**5/20 + 6*c**2. Let n(y) be the third derivative of r(y). Factor n(l).
-2*l*(l + 1)**3
Let w(x) = x**4 + 10*x**3 - 4*x**2 - 2*x - 1. Let q(n) = -2*n**4 - 29*n**3 + 11*n**2 + 7*n + 2. Let j(v) = 4*q(v) + 11*w(v). Factor j(l).
3*(l - 1)**3*(l + 1)
Let r be (-8)/(-12) - (200/6)/(-10). Find f, given that -2/3*f**5 + 0*f + 0 + 0*f**2 + 2/3*f**r + 4/3*f**3 = 0.
-1, 0, 2
Suppose -35 - 1 = -12*f. Factor 0 - o - 2*o**2 - 1/4*o**4 - 5/4*o**f.
-o*(o + 1)*(o + 2)**2/4
Let k be 0 - -1*(-3 - -4). Let l be 15/10*k/3. Factor 1/2*v**2 + 1/2*v**5 - l*v**3 - 1/2*v**4 + 0 + 0*v.
v**2*(v - 1)**2*(v + 1)/2
Suppose 0 = -5*i + 3*i + 6. Let w = i + -1. Factor 2*k**2 + 2*k**w - k**2 - 2*k**4 - k**4.
-3*k**2*(k - 1)*(k + 1)
Let k(g) = g**2 + 10*g - 5. Let b be k(-11). Let h(m) be the first derivative of -4 + 8/5*m**5 + 0*m**3 - 1/2*m**4 + 0*m**2 + 0*m - m**b. Factor h(y).
-2*y**3*(y - 1)*(3*y - 1)
Suppose g - 6 = -2*g. Suppose 0*o - 4*o = -4*h + 24, o = g*h - 8. Find r, given that 1/2*r - h*r**2 + 0 + 2*r**4 - 1/2*r**3 = 0.
-1, 0, 1/4, 1
Let z(d) be the first derivative of -25*d**4/18 + 10*d**3/27 + 16*d**2/9 + 8*d/9 + 5. Determine x so that z(x) = 0.
-2/5, 1
Let l(j) = 7*j**3 + j**2 - 6. Let h(u) = -6*u**3 - u**2 + 5. Let g(s) = -6*h(s) - 5*l(s). What is k in g(k) = 0?
-1, 0
Let y(t) = 4*t**3 - 22*t**2 + 34*t - 14. Let u(d) = 8*d**3 - 45*d**2 + 69*d - 27. Let s(l) = -2*u(l) + 5*y(l). Factor s(a).
4