 + 3*s. Factor 2*n**2 + 0*n**3 + s*n - 1/2*n**5 + 0 - 3/2*n**4.
-n**2*(n - 1)*(n + 2)**2/2
Let p(t) be the second derivative of -t**6/10 - 9*t**5/10 - 5*t**4/4 - 2*t + 7. Solve p(f) = 0 for f.
-5, -1, 0
Let s be (1/(-3))/((-3)/27). Suppose 4*i = -0*u + 5*u - 2, s*u = 4*i - 2. Suppose 1/5*t**i + 1/5 - 2/5*t = 0. Calculate t.
1
Let q(k) = 11*k**2 + 17*k + 6. Let z(d) = -4*d**2 - 6*d - 2. Let i(w) = -3*q(w) - 8*z(w). Factor i(m).
-(m + 1)*(m + 2)
Let v(i) be the second derivative of 1/2*i**2 + 2*i + 0*i**3 + 0 - 1/180*i**5 + 0*i**4. Let l(f) be the first derivative of v(f). Factor l(y).
-y**2/3
Let q = 1 + -5. Let k = 4 + q. Solve 1/3*y**2 + k*y + 1/3*y**3 + 0 = 0.
-1, 0
Factor -16/9 - 2/9*z**2 + 2/9*z**3 - 20/9*z.
2*(z - 4)*(z + 1)*(z + 2)/9
Let y be 111/39 + 2/13. Let q be 2/(y - 2)*2. Factor 0*r + 3/4*r**q + 3/4*r**2 + 0 - 3/2*r**3.
3*r**2*(r - 1)**2/4
Suppose 5*s - v + 7 = 4*s, -2*v + 2 = 4*s. Let n be ((-9)/6)/(1/s). Factor 0*c - 2/5*c**2 - 4/5*c**n + 0 - 2/5*c**4.
-2*c**2*(c + 1)**2/5
Factor 1/8*y**3 - 1/8 + 1/8*y**2 - 1/8*y.
(y - 1)*(y + 1)**2/8
Let s = -109 - -112. Factor -8/7 - 1/7*z**s - 12/7*z - 6/7*z**2.
-(z + 2)**3/7
Let r(i) be the second derivative of -i**7/105 + i**5/50 + 2*i + 12. Suppose r(u) = 0. Calculate u.
-1, 0, 1
Let n be (8/(-10))/((-12)/24). Suppose -4*b + 4 = -4. Factor -n*o - 2/5*o**b - 8/5.
-2*(o + 2)**2/5
Let l = 11 + -7. Suppose -b + 3*b - 4 = 0. Factor 10*s**2 - l*s - 3*s - s - 4*s**3 + b.
-2*(s - 1)**2*(2*s - 1)
Let z = 573 - 1714/3. Determine u, given that -8/3*u - z*u**2 - 1/3*u**3 - 4/3 = 0.
-2, -1
Factor 10*o**2 + 10*o**2 - 16*o**2 - 2*o - 2*o**3.
-2*o*(o - 1)**2
Let m = 245/3 - 81. What is r in 2/3*r**2 + 0 - 2/3*r**4 + 2/3*r - m*r**3 = 0?
-1, 0, 1
Suppose 14/5*n + 2/5*n**3 + 6/5 + 2*n**2 = 0. What is n?
-3, -1
Let k be 66/99*(-1 - (-5)/4). Let -1/3*c**2 + 1/6*c + 0 + k*c**3 = 0. What is c?
0, 1
Let g(p) be the first derivative of -p**6/200 + p**5/25 - p**4/8 + p**3/5 + 4*p**2 - 8. Let z(t) be the second derivative of g(t). Solve z(q) = 0 for q.
1, 2
Suppose -3*i - y = 3, -2*i + y + 3 = -0*i. Suppose 0 = 5*r - i*r - 15. Suppose 3*z**3 + z**3 - 6 + 9*z**2 - z**r - 3*z**4 - 3*z = 0. What is z?
-1, 1, 2
Factor -2/9*w**2 + 0 - 2/9*w**3 + 0*w.
-2*w**2*(w + 1)/9
Determine d, given that 0 + 15/2*d**5 + 3*d + 9/2*d**2 - 9/2*d**4 - 21/2*d**3 = 0.
-1, -2/5, 0, 1
Let m(l) be the second derivative of -1/2*l**4 + 1/3*l**3 + 0*l**2 + 8*l + 3/10*l**5 + 0 - 1/15*l**6. Factor m(g).
-2*g*(g - 1)**3
Let b(n) = 2*n**2 + 12*n - 8. Let l(m) = 3*m**2 + 13*m - 8. Let y(r) = -5*b(r) + 4*l(r). Determine i, given that y(i) = 0.
2
Factor 5/3*m - 10/3 + 10/3*m**2 - 5/3*m**3.
-5*(m - 2)*(m - 1)*(m + 1)/3
Suppose 0 = 24*g - 32*g. Find p, given that 0*p + 2/3*p**3 + 0 + g*p**2 = 0.
0
Let a(i) = -2*i**3 + 9*i**2 + 7*i - 10. Let k be a(5). Factor 2/3*n**2 + 0 + 2/3*n**4 - 4/3*n**3 + k*n.
2*n**2*(n - 1)**2/3
Suppose 3*b - 2*b = 4. Solve -3*q**5 + 2*q**b + 0*q**5 + q**5 = 0.
0, 1
Let c(s) = s**2. Let n(y) = -2*y**2 + 10*y. Let p(q) = 4*c(q) + n(q). Determine z, given that p(z) = 0.
-5, 0
Suppose 5*s = 2*s + 21. Suppose -2*w + 6 = 2*u, u + s = 2*w + 4*u. Factor l**3 + 2*l + l**3 + 0*l**2 - 7*l**2 + 3*l**w.
2*l*(l - 1)**2
Let h(v) = v + 10. Let x be h(-6). Factor 2*r**x + 50*r**3 - 4 - 4*r**4 - 52*r**3 + 2*r + 6*r**2.
-2*(r - 1)**2*(r + 1)*(r + 2)
Let u(c) be the first derivative of c**6/6 + 2*c**5/5 + c**4/4 - 7. Factor u(v).
v**3*(v + 1)**2
Let w = 3 + 2. Suppose 17 = -i - 4*z, 7*i = 2*i + w*z + 40. Suppose 2/7*q + 6/7*q**2 - 2/7*q**4 - 4/7 - 2/7*q**i = 0. Calculate q.
-2, -1, 1
Factor 0 - 1/3*p**3 - 4/3*p + 4/3*p**2.
-p*(p - 2)**2/3
What is z in 0 - 6*z**3 - 12*z**4 + 8/9*z**2 - 6*z**5 + 8/9*z = 0?
-1, -2/3, 0, 1/3
Suppose -9*g + 13*g = 8. Factor -2/9*m**g + 0*m - 2/9*m**4 - 4/9*m**3 + 0.
-2*m**2*(m + 1)**2/9
Let g be ((-2)/(-28))/((-6)/(-21)). Factor -1/2*r + g*r**4 + 1/2*r**3 - 1/4 + 0*r**2.
(r - 1)*(r + 1)**3/4
Let q = -12 - -21. Suppose 0 = -3*w - q, -4*t + 3*w = 2*w - 11. Suppose -5*m**t + 5*m**4 - 4*m**5 + 0*m**2 + 11*m**5 - 9*m**3 + 2*m = 0. Calculate m.
-1, 0, 2/7, 1
Suppose -m + 4*t = 8 + 7, -t = -m - 9. Let q(j) = 2*j**3 + 16*j**2 - 7. Let u(l) = l**3 + 5*l**2 - 2. Let k(w) = m*u(w) + 2*q(w). Factor k(v).
-3*v**2*(v + 1)
Let y(m) = 8 - m**3 - 4 - 8*m**2 - 4*m**2. Let n be y(-12). Solve 0*v**3 - 1/2*v - v**n + 1/2*v**5 + 0 + v**2 = 0.
-1, 0, 1
Suppose 0*z - u = 3*z - 11, u = -z + 3. Factor 4*y**3 + 17*y**4 + 0*y**3 - 21*y**z - 4*y + 4*y**2.
-4*y*(y - 1)**2*(y + 1)
Suppose 30 = v - 33. Let y be 102/v + 6/(-21). Determine r so that -14/3*r**2 - 10/3*r + y = 0.
-1, 2/7
Let j(u) be the third derivative of u**8/224 - u**7/20 + u**6/8 + 9*u**5/20 - 27*u**4/16 - 27*u**3/4 - 15*u**2. Factor j(c).
3*(c - 3)**3*(c + 1)**2/2
Suppose -2*j - 7*j + 18 = 0. Factor -2/3*o - 1/3*o**3 + o**j + 0.
-o*(o - 2)*(o - 1)/3
Let w(t) = -t**3 + t. Let b(o) = -4*o**3 + 15*o**2 - 11*o. Let f(y) = b(y) - w(y). Find n such that f(n) = 0.
0, 1, 4
Let h be 1/3 + (-478)/(-24). Let c = -20 + h. Find t, given that 1/4*t**2 - c + 0*t = 0.
-1, 1
Suppose 0 = -3*x - p + 5, 6 = x + 3*p - 9. Let h be 2 + 0/(-3) + x. Solve -1 + g**3 + 0*g - g - 8*g**2 + 9*g**h = 0.
-1, 1
Suppose -5*p + 2*a - 4 = 0, 0*a - 2 = -4*p - a. Find v such that -15/2*v**3 - 7/2*v**2 - 9/2*v**4 + p - 1/2*v = 0.
-1, -1/3, 0
Let z(u) = 5*u**2. Let x be z(1). Factor f + f**2 + x*f - 4*f.
f*(f + 2)
Let j(v) = -3*v**3 + 5*v**2 - v - 4. Let p(z) = -z**3 + z**2 + z. Let u(a) = j(a) - 5*p(a). Determine l, given that u(l) = 0.
-1, 2
Let t be 3/(-12) + (-77)/(-84). Suppose 0 = -6*i + 4*i. Factor i + t*b**3 + 4/3*b**2 + 0*b.
2*b**2*(b + 2)/3
Let o(q) = -76*q**2 - 88*q + 32. Let k(w) = -7*w**2 - 8*w + 3. Let z(t) = 32*k(t) - 3*o(t). Factor z(g).
4*g*(g + 2)
Suppose 5*c = 8 + 2. Let x be 2 - -4 - 28/6. Factor -14/3*f + x - 4/3*f**c + 14/3*f**3.
2*(f - 1)*(f + 1)*(7*f - 2)/3
Let t(x) = 125*x**3 + 1065*x**2 + 1190*x + 335. Let f(o) = 9*o**3 + 76*o**2 + 85*o + 24. Let n(s) = 85*f(s) - 6*t(s). Solve n(v) = 0 for v.
-3, -1, -2/3
Suppose 3*h = 5*a - 25, 3*h + 17 = 4*a - 0. Let d be 27/72 + 33/a. Let 15/2*j**4 + 6*j**5 - d*j**3 - 15/2*j**2 - 3/2*j + 0 = 0. What is j?
-1, -1/4, 0, 1
Let t = 14 - 11. Determine v, given that 0*v**3 + 2*v**3 + 9*v**2 - 6*v - 2*v**t - 9*v**4 + 3*v**5 + 3*v**3 = 0.
-1, 0, 1, 2
Find k, given that 6/13*k**2 + 0 + 14/13*k**3 + 10/13*k**4 + 0*k + 2/13*k**5 = 0.
-3, -1, 0
Let x = -21997/150 + 440/3. Let r(h) be the second derivative of 2/5*h**2 + 0 - 1/3*h**3 + 1/10*h**4 - h + x*h**5 - 1/75*h**6. Factor r(p).
-2*(p - 1)**3*(p + 2)/5
Let x(i) be the third derivative of 1/600*i**6 - 1/60*i**4 + 0*i - 3*i**2 + 0 + 0*i**3 + 1/300*i**5. Determine f so that x(f) = 0.
-2, 0, 1
Suppose 3*r - 10 = 2*p, -4 - 17 = -5*r - p. Let b be (-24)/(-40) + (-51)/(-15). Factor 3*i**r - 2*i + 8*i**4 - 2*i**2 - 9*i**b + 2*i**3.
2*i*(i - 1)*(i + 1)**2
Suppose 9*y**3 - 7*y**2 + 57*y - 6*y**3 + 32*y**2 + 8*y**2 + 27 = 0. What is y?
-9, -1
Solve 6*m**3 - 8/3*m**2 - 8*m + 0*m**4 + 0 - 2/3*m**5 = 0.
-3, -1, 0, 2
What is j in -18*j**2 + 0*j**3 + 0*j**3 - 5*j**3 + 63*j**2 = 0?
0, 9
Factor -160*c + 16 + 100*c**2 + 15 + 0 + 33.
4*(5*c - 4)**2
Let r be (-1 + (0 - 3))/(-2). Let m(s) be the second derivative of 2*s - 1/48*s**4 + 1/80*s**5 - 1/24*s**3 + 1/8*s**r + 0. Find n such that m(n) = 0.
-1, 1
Let s(c) be the second derivative of -c**4/3 - 2*c**3/3 - 41*c. Factor s(x).
-4*x*(x + 1)
Let w(v) = v**2 + 7*v - 6. Let b be (27/(9/3))/(-1). Let c be w(b). Solve 4 + c*i - 2*i - 3*i**2 - 3*i**2 = 0 for i.
-1/3, 2
Let f = 7 + -5. Suppose -s = -2*s + f. Factor s - i**3 - 2*i**3 - 2.
-3*i**3
Suppose 3*p + 4*z + 10 + 4 = 0, p + 13 = -3*z. Factor -x + 0*x + x - 1 - x**p + 2*x.
-(x - 1)**2
Let c(u) be the second derivative of 3*u + 0 - 2/9*u**3 - 1/3*u**2 - 1/18*u**4. Solve c(p) = 0 for p.
-1
Let y be (-60)/(-27) + 6/(-27). Let i = 4 - y. Factor -1/4*q**5 + 0*q - 1/2*q**4 - 1/4*q**3 + 0*q**i + 0.
-q**3*(q + 1)**2/4
Let t = -37/3 + 326/15. Let d = -9 + t. Factor 0 - d*c**2 + 4/5*c.
-2*c*(c - 2)/5
Let 1/4*t**3 + 0*t - 1/4*t**5 + 1/4*t**2 - 1/4*t**4 + 0 = 0. What is t?
-1, 0, 1
Factor -20/23*a**2 + 0 + 2/23*a**3 + 50/23*a.
2*a*(a - 5)**2/23
Let v be (18/(-16))/(1/4). Let u = v - -29/6. Let -1/3*y - u*y**2 + 1/3*y**3 + 1/3*y**4 + 0 = 0. What is y