e 5*o - 3*b = 6*o - 21, -4*o + n*b - 1 = 0. Factor 6*p**3 - 3*p**5 - 3*p**2 - o*p**4 + 5*p**5 + p**2.
2*p**2*(p - 1)**3
Suppose -2*j = -7*j. Factor -4*c**2 + c**2 + j*c**2.
-3*c**2
Let n = -91 - -95. Factor 0 + 3/2*p**3 + 3/2*p**2 + 1/2*p**n + 1/2*p.
p*(p + 1)**3/2
Let t = 3833/14 - 543/2. Let y(l) be the first derivative of -10/21*l**3 + t*l**2 - 25/14*l**4 - 8/7*l - 2. Let y(v) = 0. Calculate v.
-1, 2/5
Let m(y) be the third derivative of -y**9/5040 + y**8/1400 - y**7/1400 - y**3 + y**2. Let p(l) be the first derivative of m(l). What is u in p(u) = 0?
0, 1
Let q(w) be the third derivative of w**8/23520 - w**7/4410 - w**4/12 + w**2. Let v(a) be the second derivative of q(a). Suppose v(c) = 0. Calculate c.
0, 2
Determine t so that 0 + 32/3*t - 8/3*t**3 + 4/3*t**4 - 16/3*t**2 = 0.
-2, 0, 2
Let s be 7/(-3) - (-1)/3. Let r be 0/(s + 1 + 2). Solve 6*j**2 + j - 5*j**2 + r*j**2 = 0.
-1, 0
Let t be -3*(42/45 + -1). Factor -t*v**2 - 4/5 + 4/5*v.
-(v - 2)**2/5
Suppose 0 = -4*k + 16, 5*k - 20 = 12*u - 7*u. Find r, given that -4/5*r + u - 2/5*r**2 = 0.
-2, 0
Let g(j) be the first derivative of 8*j**5/15 + j**4/2 - 2*j**3/9 - 14. Suppose g(x) = 0. Calculate x.
-1, 0, 1/4
Let s(c) = 6*c**4 + 6*c**3 + 3*c. Let j = 0 - 15. Let v(z) = z**4 - z**3 + z**2. Let n(t) = j*v(t) + s(t). Factor n(q).
-3*q*(q - 1)**2*(3*q - 1)
Let v = -6 - -8. Factor -5*z**5 - z**3 - 6*z**4 + 151*z - v*z**4 + 2*z**2 - 151*z.
-z**2*(z + 1)**2*(5*z - 2)
Let i = 40 - 37. Let z(h) be the first derivative of -1/8*h**2 + 1/16*h**4 - 1 + 1/12*h**i - 1/4*h. Factor z(n).
(n - 1)*(n + 1)**2/4
Suppose g - 4 = 0, 0 = 5*o - g - g - 2. Let y(f) be the first derivative of 1 - 2*f**2 + 2/3*f**3 + o*f. Find l such that y(l) = 0.
1
Let m = -19354/5 - -3701. Let z = -169 - m. Solve 22/5*f + 48/5*f**2 + z + 52/5*f**3 + 6/5*f**5 + 28/5*f**4 = 0.
-1, -2/3
Factor f**2 + 1/3*f**4 - 4/3 - 4/3*f + 4/3*f**3.
(f - 1)*(f + 1)*(f + 2)**2/3
Let w(s) be the third derivative of s**5/480 + s**4/192 + s**2. What is n in w(n) = 0?
-1, 0
Let r(t) = 21*t**4 + 15*t**3 - 3*t**2 - 15*t + 18. Let i(s) = s**4 + s**3 - s + 1. Let z(c) = -18*i(c) + r(c). Factor z(q).
3*q*(q - 1)**2*(q + 1)
Let v(q) = q**2 - 5*q + 10. Let u be v(5). Suppose -5*o = -u*o + 10. Determine h, given that -1/4*h - 3/4*h**3 + 1/4*h**4 + 3/4*h**o + 0 = 0.
0, 1
Let f(y) = -2*y**3 + 6*y**2 + 2*y + 2. Let d be (-2)/(-8) + 102/(-24). Let k(q) = -4*q**3 + 11*q**2 + 4*q + 3. Let x(i) = d*k(i) + 7*f(i). Factor x(v).
2*(v - 1)**2*(v + 1)
What is w in -32*w**2 - 36*w**5 + 21*w**3 - 120*w**4 - 65*w**3 - 68*w**3 = 0?
-2, -2/3, 0
Suppose 49 = 5*h - p, -2*h + 7*h - 46 = 4*p. Suppose 3*w = h - 1. Factor -3/2*y**w - 9/2*y - 9/2*y**2 - 3/2.
-3*(y + 1)**3/2
Let m be 2/(-3) - ((-7)/(-3) + -3). Factor -3*c**4 - 3/4*c**5 - 9/2*c**3 - 3/4*c - 3*c**2 + m.
-3*c*(c + 1)**4/4
Let a(w) = -4*w**5 + 28*w**4 - 12*w**3 - 28*w**2 + 16*w - 24. Let v(r) = -r**4 + r**3 + r**2 - r + 1. Let o(y) = -a(y) - 24*v(y). Determine n so that o(n) = 0.
-1, 0, 1, 2
Suppose -2/3*f**3 + 0*f**2 + 0 + 2/3*f = 0. Calculate f.
-1, 0, 1
Let 5*t**5 + 478*t**3 - 485*t**3 - 2*t**4 + 12*t + 8*t**2 - 4*t**5 = 0. Calculate t.
-2, -1, 0, 2, 3
Let i(b) be the second derivative of 1/15*b**6 + 3*b + 0*b**3 + 1/84*b**7 + 0*b**2 + 1/8*b**5 + 1/12*b**4 + 0. Factor i(n).
n**2*(n + 1)**2*(n + 2)/2
Factor -72*f + 3*f**4 + 66*f**2 + 48 - 127*f**2 + 18*f**3 + 64*f**2.
3*(f - 1)**2*(f + 4)**2
What is y in 0 + 0*y - 1/3*y**2 = 0?
0
Let w(y) be the third derivative of 0 + 1/8*y**4 + 1/20*y**5 + 1/120*y**6 - 4*y**2 + 1/6*y**3 + 0*y. Suppose w(q) = 0. Calculate q.
-1
Let a = 1 - -3. Determine r so that 4*r**3 - 2*r**a - r**2 + 4*r**2 - r**2 - 2*r**5 - 2*r**3 = 0.
-1, 0, 1
Suppose 4*c = -4*f + 4, 3*c = 6*c - f + 1. Let y(w) be the first derivative of c*w + 1/3*w**3 - 1/2*w**2 - 1. Factor y(b).
b*(b - 1)
Solve 0*r**3 + 2*r**5 - 128*r + 128*r - 2*r**3 = 0 for r.
-1, 0, 1
Suppose -2*b = -9 + 3. Suppose 3*t = -n + 1, -5*t + 0 - b = 4*n. Factor -t - 1/4*y**2 - y.
-(y + 2)**2/4
Suppose 0*j = 6*j - 12. Factor h**j - 3*h - 2*h**2 + 4 + 0*h**2 - 6.
-(h + 1)*(h + 2)
Determine y, given that 1/2*y**4 + 0*y**3 - 1/2*y**2 - 1/4*y**5 + 1/4*y + 0 = 0.
-1, 0, 1
Factor -192 - 400*y + 111 - 85*y**2 - 239 - 5*y**3.
-5*(y + 1)*(y + 8)**2
Let r be (-2 - 0)*(-45)/2. Let y be (-2)/9 + 235/r. Factor 1/2*o**2 + 0*o - 7/2*o**4 + 0 - 2*o**y - o**3.
-o**2*(o + 1)**2*(4*o - 1)/2
Let k(y) be the first derivative of 2*y + 0*y**2 - 1/135*y**6 + 0*y**3 + 0*y**4 - 1 + 0*y**5. Let o(v) be the first derivative of k(v). Factor o(c).
-2*c**4/9
Let v(s) be the first derivative of -3*s + 4*s**2 + 5*s**2 + 1 - 3*s**2 - 3*s**3. Factor v(i).
-3*(i - 1)*(3*i - 1)
Let s(u) be the first derivative of -7*u**6/51 - 32*u**5/85 - 11*u**4/34 - 4*u**3/51 - 12. Find m, given that s(m) = 0.
-1, -2/7, 0
Let c = 2 + -3. Let y(a) = -a - 1. Let f be y(c). Find p, given that 1/2*p**2 + 1/2*p + f = 0.
-1, 0
Let m(x) = -5*x**3 + 5*x + 6. Let a(w) = w**3 - w - 1. Let z(c) = -6*a(c) - m(c). Suppose z(h) = 0. Calculate h.
-1, 0, 1
Suppose 12*r - 2*r - 32 + 4*r**2 - 6*r**2 + 6*r = 0. Calculate r.
4
Let 7*k**2 - 5*k**2 - 8 + 4*k + 3*k**3 - 4*k**3 = 0. Calculate k.
-2, 2
Factor 0*u + 2/7*u**2 - 2/7.
2*(u - 1)*(u + 1)/7
Let q be 3/(-2) + (-147)/(-42). Suppose -1 = l - 5. Find n, given that 2*n**l + 0*n**2 + q*n**2 - 3*n**2 - n**2 = 0.
-1, 0, 1
Let a be 7/(-21)*6/(-2). Find v, given that -3/2*v**2 + 1/2*v**4 + 1/2*v + a - 1/2*v**3 = 0.
-1, 1, 2
Let t = 2/41 + 68/287. Let r(d) be the first derivative of 2/3*d**3 + t*d**2 + 3/14*d**4 + 2 - 2/5*d**5 - 5/21*d**6 + 0*d. Find v such that r(v) = 0.
-1, -2/5, 0, 1
Let k(r) be the third derivative of -r**5/20 - 5*r**4/8 - 3*r**3 - 55*r**2. Factor k(o).
-3*(o + 2)*(o + 3)
Factor 4/7*u**2 - 2/7*u - 12/7.
2*(u - 2)*(2*u + 3)/7
Let p be (20/(-12))/(-2*(-30)/(-48)). Let -20*g - p*g**3 - 12 - 28/3*g**2 = 0. Calculate g.
-3, -1
Let l(b) = -2*b - 4. Let j be l(-7). Let c be (-4)/(-3) - j/(-15). Factor -2*y + 4*y**2 - 3*y**2 + 0*y**c.
y*(y - 2)
Let s be ((-18)/10)/(24/(-80)). Let b(f) be the third derivative of 0*f**3 - 1/8*f**4 + 0*f + 1/40*f**s + 0*f**5 + 0 - 4*f**2. Suppose b(l) = 0. Calculate l.
-1, 0, 1
Let l(p) be the third derivative of -p**6/40 - p**5/20 + p**4/4 - 5*p**2. Factor l(q).
-3*q*(q - 1)*(q + 2)
Let r(u) = -5*u**3 - 1. Let c be r(-1). Let a be ((-14)/c + 2)/(-3). Factor -1/4*z**2 + 0*z + a*z**3 + 0 - 1/4*z**4.
-z**2*(z - 1)**2/4
Let p(v) be the first derivative of 7*v**6/60 + 3*v**5/10 + v**4/6 + 2*v**2 - 2. Let f(s) be the second derivative of p(s). Factor f(q).
2*q*(q + 1)*(7*q + 2)
Suppose -5*h = -a + 20, 0 = -2*a - 0*a + 3*h + 12. Suppose a*r + 8 = 4*q + 3*r, 4*q - 2*r - 8 = 0. Let -2*k - q - 1/2*k**2 = 0. Calculate k.
-2
Factor 0*n + n**3 - 2/3*n**2 + 0.
n**2*(3*n - 2)/3
Let v be 6/(360/(-125))*-16. Factor 80*o**2 - v*o**3 - 112/3*o + 16/3 - 125/3*o**4.
-(o + 2)*(5*o - 2)**3/3
Let n = -7759/9 + 863. Let w(i) be the first derivative of -2/27*i**3 + 2 - n*i + 4/9*i**2. Factor w(v).
-2*(v - 2)**2/9
Suppose 2*a - 2 = -6. Let r be 2 + (a - (1 + -3)). Factor t**r - t**4 + t**3 - t**2.
-t**3*(t - 1)
Let y(i) be the first derivative of -i**2 + 1 + 2/3*i**3 + 0*i. Factor y(w).
2*w*(w - 1)
Solve -6*a + 45*a**3 - 123*a**2 - 12 + 86*a - 8*a = 0 for a.
1/3, 2/5, 2
Let t(s) = s**2 + 7*s + 9. Let r be t(-6). Let m be 28/21 + (-2)/r. Factor -2/3*a**3 + 1/3*a + 1/3*a**5 + 1/3*a**4 + 1/3 - m*a**2.
(a - 1)**2*(a + 1)**3/3
Let s(u) be the first derivative of u**5/25 + u**4/20 - 2*u**3/15 - 56. Let s(w) = 0. Calculate w.
-2, 0, 1
Let i(l) be the second derivative of 6*l**7/7 - l**6/5 - 2*l**5/5 + l**4/6 - l. Factor i(b).
2*b**2*(2*b + 1)*(3*b - 1)**2
Let v(o) be the first derivative of 0*o**2 + 0*o - 98/3*o**6 + 52*o**4 - 32/3*o**3 - 3 - 56*o**5. Solve v(b) = 0.
-2, 0, 2/7
Let z = -6/13 - -44/39. Let r(g) be the first derivative of 0*g - 1/4*g**4 - z*g**3 + 3 - 1/2*g**2. Let r(w) = 0. What is w?
-1, 0
Let h(s) be the first derivative of s**6/24 + s**5/5 + 3*s**4/16 - s**3/3 - s**2/2 - 53. Solve h(t) = 0.
-2, -1, 0, 1
Let x(w) be the second derivative of 0*w**3 - 3*w - w**2 - 1/6*w**4 + 0 + 1/6*w**5. Let g(f) be the first derivative of x(f). What is b in g(b) = 0?
0, 2/5
Let i(f) = f - 3. Let y be i(5). What is l in -4/3 + 2/3*l**y - 2/3*l = 0?
-1, 2
Let i(j) 