**3 + 2/17*z**2 + 0*z + 2/17*z**4.
2*z**2*(z + 1)**2/17
Suppose 15*n - n - 12 - 5*n**2 - 4*n**2 + 7*n**2 = 0. Calculate n.
1, 6
Suppose 14/13*b**2 - 46/13*b + 12/13 = 0. What is b?
2/7, 3
Let w = 9 + -6. Let s = w + -3. What is k in 0 - 1 + 0 + k**2 + s*k**2 = 0?
-1, 1
Let y be (18 - 19)/(-2*14/8). Let -2/7*j**4 - y*j**3 + 2/7*j**2 + 2/7*j + 0 = 0. What is j?
-1, 0, 1
Factor 0 - 1/5*o**4 + 0*o**2 + 0*o + 1/5*o**3.
-o**3*(o - 1)/5
Find v, given that -3/2*v**4 + 0 + 3/2*v**2 - 3/2*v**3 + 0*v + 3/2*v**5 = 0.
-1, 0, 1
Let j(g) be the third derivative of -g**6/40 - 3*g**5/4 - 75*g**4/8 - 125*g**3/2 + g**2. Factor j(d).
-3*(d + 5)**3
Let x(u) = 4*u**5 + u**4 - u**3 - 4*u**2 - 6*u + 5. Let p = 15 + -10. Let w(v) = 3*v**5 - 2*v**3 - 4*v**2 - 5*v + 4. Let f(s) = p*w(s) - 4*x(s). Factor f(z).
-z*(z + 1)**4
Let s be (-6 - -6) + (2 - -1). Let y be 4*1*(-1 - -2). Factor -2*q**s + 5 + 2*q + 0*q - q**4 - y.
-(q - 1)*(q + 1)**3
Find x, given that 5/4*x**3 + 5/4*x**5 + 0 + 0*x**2 + 0*x - 5/2*x**4 = 0.
0, 1
Let s(g) be the first derivative of -3*g**5/5 + g**3 + 16. Suppose s(z) = 0. Calculate z.
-1, 0, 1
Let o be (1 - 4/(-42)) + (-27)/63. Let p(v) be the second derivative of 7/6*v**4 + 4*v + 2/5*v**5 + o*v**3 + 0 - v**2. Determine a so that p(a) = 0.
-1, 1/4
Find n, given that n**5 - 6*n**2 + 9*n**3 - 24*n**4 + 8*n**5 + 12*n**2 = 0.
-1/3, 0, 1, 2
Let y = 9 - 1. Let p = -5 + y. Factor 1/3*q**p + 0 - 1/3*q + 0*q**2.
q*(q - 1)*(q + 1)/3
Factor -9/8*k + 1/8*k**3 + 3/8*k**2 + 5/8.
(k - 1)**2*(k + 5)/8
Let z(a) = -a**3 - 5*a**2 + 5. Let w be z(-5). Factor 5*t**4 + w*t**2 - 5*t**3 + 5*t**2 - 4*t**4 - 4*t - 2*t**2.
t*(t - 2)**2*(t - 1)
Let t(j) be the first derivative of -3/8*j**4 - 3/4*j**2 + 1 - j**3 + 0*j. Find f, given that t(f) = 0.
-1, 0
Let l(z) be the second derivative of -1/9*z**2 - 1/27*z**3 + 0 + 1/54*z**4 + 1/90*z**5 - 2*z. Factor l(c).
2*(c - 1)*(c + 1)**2/9
Find k, given that -16*k**4 + 8/3 + 44/3*k - 44/3*k**3 + 40/3*k**2 = 0.
-1, -2/3, -1/4, 1
Solve -14/13*t**2 + 0 - 6/13*t - 10/13*t**3 - 2/13*t**4 = 0 for t.
-3, -1, 0
Let r(u) be the third derivative of u**9/241920 - u**8/80640 + u**5/20 - 2*u**2. Let v(f) be the third derivative of r(f). What is j in v(j) = 0?
0, 1
Let i(w) be the third derivative of w**7/525 - w**6/600 - 2*w**5/75 + w**4/30 - 20*w**2. Find a, given that i(a) = 0.
-2, 0, 1/2, 2
Determine g so that -4 - 6*g**3 - 22/3*g - 14/3*g**4 + 22*g**2 = 0.
-3, -2/7, 1
Let o(k) be the first derivative of 2*k**4/3 + 14*k**3/9 - 2*k**2/3 - 8. Factor o(n).
2*n*(n + 2)*(4*n - 1)/3
Let m(p) = p**3 + 2*p**2 - 4*p - 2. Let z be m(-3). Let a = 3 - z. Factor 1/3*o**3 + 1/3*o**a - 2/3*o + 0.
o*(o - 1)*(o + 2)/3
Let d be (-12)/(-15) - 387/15. Let r = d + 27. Factor 0 + w**3 - w + 3/2*w**r.
w*(w + 2)*(2*w - 1)/2
Let p(s) be the second derivative of 1/42*s**7 + 1/12*s**4 - s + 3/20*s**5 + 1/10*s**6 + 0*s**3 + 0 + 0*s**2. Factor p(r).
r**2*(r + 1)**3
Suppose 2*r - 81 = -r. Factor -r*z - 1 + 13*z**2 + 6*z**2 + 2*z**2 + 7.
3*(z - 1)*(7*z - 2)
Let v(o) be the third derivative of 1/60*o**4 + 0 + 0*o + 2/45*o**3 + 2*o**2 + 1/450*o**5. Factor v(r).
2*(r + 1)*(r + 2)/15
Let h(k) = -3*k**3 + 101*k**2 - 384*k + 517. Let w(q) = 20*q**3 - 656*q**2 + 2496*q - 3360. Let m(f) = 32*h(f) + 5*w(f). Let m(j) = 0. What is j?
4
Suppose 7*g - 2*s - 35 = 2*g, 20 = 5*g + s. Let v be 7/((-98)/(-4)) + 0. Factor 0 + 2/7*p**4 + 2/7*p**g - v*p**3 + 0*p - 2/7*p**2.
2*p**2*(p - 1)*(p + 1)**2/7
Suppose -12 = -2*q - 2*q. Suppose 6 - q = k. Let -8/3*h - 6*h**k + 0 + 8*h**2 = 0. What is h?
0, 2/3
Factor u**2 + 10*u - 34 + 88 - 45.
(u + 1)*(u + 9)
Factor -3/4 + 3/4*w**3 - 3/4*w + 3/4*w**2.
3*(w - 1)*(w + 1)**2/4
Let u(a) be the first derivative of 3 - a**2 + 5/4*a**4 + 0*a - a**3. Let u(l) = 0. What is l?
-2/5, 0, 1
Let j(a) be the first derivative of -a + 3 + 1/2*a**2 + 1/3*a**3 - 1/4*a**4. Factor j(w).
-(w - 1)**2*(w + 1)
Let l(d) be the second derivative of d**7/168 + 13*d**6/1440 + d**5/240 + d**3/2 - 2*d. Let z(n) be the second derivative of l(n). Factor z(r).
r*(4*r + 1)*(5*r + 2)/4
Let g(b) be the third derivative of 0*b - 1/360*b**5 - 2*b**2 + 1/1080*b**6 + 0 - 1/36*b**4 - 1/2*b**3. Let q(p) be the first derivative of g(p). Factor q(d).
(d - 2)*(d + 1)/3
Let t(d) be the first derivative of d**5/180 + d**4/72 - d**3/9 + d**2 + 3. Let i(p) be the second derivative of t(p). Factor i(j).
(j - 1)*(j + 2)/3
Suppose -5*k - 3*h + 15 = 0, 2*h = 7*h - 25. Solve -g**4 + 0*g**2 + 0*g + k + 1/4*g**3 = 0 for g.
0, 1/4
Factor 0*z + 8/7 - 2/7*z**2.
-2*(z - 2)*(z + 2)/7
Let x(z) be the third derivative of z**6/24 + z**5/3 + 5*z**4/8 + 18*z**2. What is c in x(c) = 0?
-3, -1, 0
Let i(c) be the second derivative of -2*c**6/3 + 3*c**5/4 + 15*c**4/4 + 5*c**3/3 + 3*c. Suppose i(l) = 0. What is l?
-1, -1/4, 0, 2
Let t be 90/24 + (-2)/(-8). Let n(b) be the first derivative of 5/3*b**3 + 19/12*b**t + 7/15*b**5 + 1/6*b**2 - 2/3*b - 1. Factor n(u).
(u + 1)**3*(7*u - 2)/3
Let y(g) = g**4 - g**3 + g - 1. Let s(f) = -10*f**4 + 20*f**3 - 12*f**2 - 8*f + 10. Let d(l) = -2*s(l) - 12*y(l). Find b such that d(b) = 0.
-1/2, 1, 2
Let u(f) be the first derivative of f**4/22 - 4*f**3/33 - 4*f**2/11 + 16*f/11 + 12. Factor u(w).
2*(w - 2)**2*(w + 2)/11
Determine m, given that 24*m**2 + 91 - 3*m**4 - 71 - 68 = 0.
-2, 2
Let j(y) be the first derivative of -2 + 1/12*y**4 - 3*y + 0*y**2 + 1/6*y**3. Let s(z) be the first derivative of j(z). Solve s(a) = 0 for a.
-1, 0
Let y(n) = n**3 + 6. Suppose 7*s = 4*s. Let j be y(s). Factor j*b**3 - 2*b**3 - b**2 - 2*b**3 - b**4.
-b**2*(b - 1)**2
Let u(g) = -15*g**2 - 5*g. Let z(q) = 16*q**2 + 4*q. Let a(v) = 4*u(v) + 3*z(v). Factor a(f).
-4*f*(3*f + 2)
Let l(t) be the first derivative of t**3/9 - 7*t**2/3 + 49*t/3 - 58. Solve l(p) = 0 for p.
7
Find v such that -2/7*v - 5/7*v**2 + v**3 + 0 = 0.
-2/7, 0, 1
Suppose 0*w + 2/5*w**3 + 0 - 8/5*w**2 = 0. Calculate w.
0, 4
Let o(w) = 2*w**2 - 24*w - 24. Let n(t) = -8*t**2 + 97*t + 96. Let x(a) = -2*n(a) - 9*o(a). Determine p, given that x(p) = 0.
-1, 12
Let o(y) be the third derivative of -y**6/60 - y**5/30 + y**4/2 - 28*y**2. Factor o(h).
-2*h*(h - 2)*(h + 3)
Let m(v) = v - 3. Let a = -13 + 18. Let k be m(a). Suppose -c**3 + 0*c + 1/4*c**k + 0 = 0. What is c?
0, 1/4
Let n(r) be the third derivative of r**7/126 + r**6/20 - 7*r**5/20 + 13*r**4/18 - 2*r**3/3 + 12*r**2. Factor n(y).
(y - 1)**2*(y + 6)*(5*y - 2)/3
Let n = -33/62 + 1024/31. Let o = n + -32. Let -1 - o*r + 1/2*r**2 = 0. What is r?
-1, 2
Let f(v) be the first derivative of 2*v**3/15 + 3*v**2/5 - 8*v/5 + 13. Find z such that f(z) = 0.
-4, 1
Factor -2 + 0*i**2 - i - 2*i + 3*i**2 - 4.
3*(i - 2)*(i + 1)
Let j(k) be the first derivative of -k**5/80 - k**4/48 + k**3/6 + k**2/2 + 4*k - 9. Let w(v) be the first derivative of j(v). Factor w(g).
-(g - 2)*(g + 1)*(g + 2)/4
Let f(t) be the first derivative of -5*t**4/12 + 2*t**3/9 + 5*t**2/6 - 2*t/3 + 1. Factor f(v).
-(v - 1)*(v + 1)*(5*v - 2)/3
Let y(h) be the first derivative of 4*h**3/3 + 8*h**2 + 12*h - 19. Factor y(c).
4*(c + 1)*(c + 3)
Let u(s) be the third derivative of 3*s**6/40 - s**5/20 - s**4/4 - 7*s**2. Factor u(g).
3*g*(g - 1)*(3*g + 2)
Let m(o) be the second derivative of -4*o - 3/80*o**5 + 0*o**3 + 0 - 3/16*o**4 + 3/2*o**2. Factor m(p).
-3*(p - 1)*(p + 2)**2/4
Let q = 151/2 + -75. Factor -1/2*j**3 + 1/2 - q*j**2 + 1/2*j.
-(j - 1)*(j + 1)**2/2
Suppose -2*j - j = -2*i - 11, -3*i - 3 = 0. Find h such that 8*h**2 + 7 - 3 - 2*h**3 - 4*h**j + 4*h**3 - 10*h = 0.
1, 2
Factor -6*v**2 + 2*v**4 + v**3 - 1/2*v**5 - 9/2*v + 0.
-v*(v - 3)**2*(v + 1)**2/2
Let o be 4/(-3)*(-3)/12*6. Let i(y) be the third derivative of 2*y**o + 0 - 5/36*y**5 - 1/18*y**3 - 5/36*y**4 + 0*y. Factor i(a).
-(5*a + 1)**2/3
Let w = -10 - -12. Factor 0*d**4 + w*d**2 + 2*d**4 - 4*d**4.
-2*d**2*(d - 1)*(d + 1)
Let l(a) = a + 2. Let d be l(-5). Let u be 1/(-5)*d*5. Suppose -w + 5*w**2 + u*w**2 - 9*w**2 = 0. What is w?
-1, 0
Let h(o) be the third derivative of o**5/300 - o**4/40 - 5*o**2. Factor h(m).
m*(m - 3)/5
Let r be ((-24)/10)/(10/(-25)). Factor 13*x**2 + 3 - 4*x**2 + 15*x**2 + 21*x - r*x**2.
3*(x + 1)*(6*x + 1)
Let r(s) = s**3 + 2*s**2 - 4*s - 1. Let w be r(-3). Factor 6*i**4 - 6*i**5 - i**3 - w*i**3 + 3*i**5.
-3*i**3*(i - 1)**2
Let i(b) be the third derivative of -b**7/126