e second derivative of -t - 1/2*t**5 - 3*t**3 - 2*t**2 + 0 - 2*t**h. Suppose q(n) = 0. What is n?
-1, -2/5
Determine q, given that -8/9*q**5 + 0 + 2/3*q**3 + 32/9*q**2 - 22/9*q**4 - 8/9*q = 0.
-2, 0, 1/4, 1
Let f(q) be the second derivative of 0*q**2 - 1/12*q**3 + 0 - 5/48*q**4 - q. Determine d so that f(d) = 0.
-2/5, 0
Let t(y) = 15*y**3 - 12*y**2 - 3*y. Let j(c) = -c**3 + c. Let d(u) = -12*j(u) - t(u). Factor d(k).
-3*k*(k - 3)*(k - 1)
Factor 2*n + 2*n + 2 - 6*n - 42*n**2 + 40*n**2 + 2*n**3.
2*(n - 1)**2*(n + 1)
Let d(j) be the first derivative of 12/25*j**5 + 3/4*j**4 + 2/5*j**3 + 0*j + 3 + 0*j**2 + 1/10*j**6. Factor d(x).
3*x**2*(x + 1)**2*(x + 2)/5
Let n(u) be the first derivative of 0*u**2 + 2 - 1/12*u**3 - u + 1/20*u**5 + 1/24*u**4. Let s(w) be the first derivative of n(w). Factor s(z).
z*(z + 1)*(2*z - 1)/2
Let h(r) be the second derivative of r**7/14 - 3*r**5/20 - 3*r. Factor h(u).
3*u**3*(u - 1)*(u + 1)
Let f(i) be the third derivative of -1/330*i**5 + 1/66*i**4 + 0*i + i**2 + 0 - 1/33*i**3. Factor f(z).
-2*(z - 1)**2/11
Let d(u) = -u**3 - 5*u**2 + 4*u - 7. Let k be d(-6). Factor 9*v**2 + v**k - 2*v**4 + 2*v - 7*v**2 - 3*v.
v*(v - 1)**3*(v + 1)
Suppose 12 = d - 5*k, 2*k - 7 = -5*d - 1. Let a(z) be the third derivative of 1/105*z**7 - 1/30*z**5 + 0*z**6 + 0*z + 2*z**d + 0*z**3 + 0*z**4 + 0. Factor a(h).
2*h**2*(h - 1)*(h + 1)
Suppose -1/2*q + 3/4 - 1/4*q**2 = 0. Calculate q.
-3, 1
Let x be 100/26 - (-72)/468. Factor 1/3 - 1/3*q + 1/3*q**x - 2/3*q**2 - 1/3*q**5 + 2/3*q**3.
-(q - 1)**3*(q + 1)**2/3
Suppose -5*w = -10 - 5. What is h in -14/5*h**5 + 8/5*h - 32/5*h**2 + 0 + 6/5*h**w + 32/5*h**4 = 0?
-1, 0, 2/7, 1, 2
Let q(l) be the third derivative of -l**7/210 + l**5/60 + 8*l**2. Factor q(o).
-o**2*(o - 1)*(o + 1)
Let g(l) be the first derivative of -2*l**5/65 + 2*l**3/39 - 3. Suppose g(b) = 0. Calculate b.
-1, 0, 1
Let c = -328 - -4272/13. Determine p, given that c*p + 2/13*p**2 + 6/13 = 0.
-3, -1
Let s = 7 - 3. Factor -2*v**3 + 2*v**5 - 6*v**2 - v**s + 8*v**2 - v**4.
2*v**2*(v - 1)**2*(v + 1)
Factor 1/5*q**2 + 2/5*q + 0.
q*(q + 2)/5
Suppose -2/9*p + 0 - 4/9*p**2 - 2/9*p**3 = 0. Calculate p.
-1, 0
Let p(l) be the second derivative of l**7/630 + l**6/45 + l**5/10 - l**4/4 + 10*l. Let d(o) be the third derivative of p(o). Factor d(n).
4*(n + 1)*(n + 3)
Let i(a) be the second derivative of -3*a**4/16 + 13*a**3/8 - 3*a**2/2 + 3*a - 4. What is z in i(z) = 0?
1/3, 4
Suppose -3*l - 2*l + 346 = 2*p, -66 = -l - 2*p. Suppose -b**4 + 3*b**3 - b**2 + l - b**3 - 70 = 0. Calculate b.
0, 1
Suppose 4*l - 7*l + 9 = 0. Let w(p) be the second derivative of 2*p**2 - 1/2*p**4 + 0 - 1/3*p**3 + 1/10*p**5 - l*p + 1/15*p**6. Factor w(m).
2*(m - 1)**2*(m + 1)*(m + 2)
Suppose -5*w = -3*w - 4. Factor -2*q + 0*q**2 + q**4 + 2 + q**4 + 4*q**3 - 6*q**w - 2*q**5 + 2*q**2.
-2*(q - 1)**3*(q + 1)**2
Let w = 99 - 691/7. Factor 0*o - 2/7*o**5 + w*o**4 + 2/7*o**3 + 0 - 2/7*o**2.
-2*o**2*(o - 1)**2*(o + 1)/7
Suppose -4*u + 12 = -2*u. Factor -2*r - 5*r - u*r**2 + 2*r + 3*r.
-2*r*(3*r + 1)
Suppose 4*s = 2*s. Determine w so that 2/5*w**4 + s*w**2 + 0*w + 0 + 2/5*w**3 = 0.
-1, 0
Let k = -24/19 - -91/57. Factor 0*b**2 - 1/3*b**3 + 0 + k*b.
-b*(b - 1)*(b + 1)/3
Factor -15*n**2 - 18*n**2 + 16*n**3 + 17*n**2 - 12*n**2 - 8*n.
4*n*(n - 2)*(4*n + 1)
Let h be (1 + -3)/(6/15). Let d be (12/10 - 2)*h. Find p, given that 5*p + 2*p**5 - 5*p + 2*p**d - 4*p**4 = 0.
0, 1
Let s(l) be the third derivative of 0*l**3 + 1/330*l**5 + l**2 - 1/660*l**6 + 0*l**4 - 2/1155*l**7 + 0*l + 0. Solve s(t) = 0 for t.
-1, 0, 1/2
Let c be (3/(-24))/(3/(-8)). Let h be (-2)/2 + 15/9. Factor -2/3*n**2 + c*n**3 + h - 1/3*n.
(n - 2)*(n - 1)*(n + 1)/3
Let t = -8549/6 + 1425. Suppose 5*h - w = 10, 9 - 1 = 4*h - w. Suppose -1/3*k + t*k**h + 1/6 = 0. Calculate k.
1
Factor 5*v**2 - 3*v**3 - 2*v**2 + 24*v - 48 + 12.
-3*(v - 2)**2*(v + 3)
Factor -38 - 3*n**2 - 7*n + 46 + 2*n**2.
-(n - 1)*(n + 8)
Let c = 1121 - 1121. Factor 0*h**2 - 1/3*h**4 + 0 + c*h + h**3.
-h**3*(h - 3)/3
Suppose -7 = -t - 3. Suppose 0 = t*u - 9 - 3. Solve 0 - 14/3*g**u - 4/3*g - 6*g**2 = 0.
-1, -2/7, 0
Let n(y) be the second derivative of 2*y**7/21 + 3*y**6/10 + y**5/10 - 2*y**4/3 - y**3 - y**2/2 - 3*y. Determine g so that n(g) = 0.
-1, -1/4, 1
Let c(p) be the third derivative of p**11/498960 - p**9/90720 - p**5/60 + 3*p**2. Let s(u) be the third derivative of c(u). Factor s(g).
2*g**3*(g - 1)*(g + 1)/3
Determine t so that 12*t**5 - 15*t**2 - 3*t**3 - 7*t**3 + 15*t**4 + 0*t + t**3 - 3*t = 0.
-1, -1/4, 0, 1
Let a(x) = -4*x + 2*x + x. Let n(i) = -7*i**2 - 3*i. Suppose 0*k + 3*k - 12 = 3*z, -4*z - 4*k - 24 = 0. Let p(y) = z*a(y) + n(y). Factor p(u).
-u*(7*u - 2)
Suppose -4*t = -0*t. Suppose 2*z + 2*z = t. Suppose z - 1/4*a**2 - 1/4*a**3 + 1/4*a + 1/4*a**4 = 0. Calculate a.
-1, 0, 1
Let u(a) be the first derivative of 2*a + 1 + 0*a**2 + 1/18*a**4 + 1/9*a**3. Let c(q) be the first derivative of u(q). Find m, given that c(m) = 0.
-1, 0
Let u = 6 + -2. Suppose -u*a + 15 = -25. Factor -7*z**2 - 5*z**4 + 2*z + 2 - 5*z + 3*z**3 + a*z**4.
(z - 1)*(z + 1)**2*(5*z - 2)
Let x(w) = 12*w**2 - 12*w - 40. Let c(k) = 4*k**2 - 4*k - 13. Let z(h) = -16*c(h) + 5*x(h). Factor z(f).
-4*(f - 2)*(f + 1)
What is u in -11*u**3 - 4*u**4 + 13*u**3 + 3*u**4 + 0*u**4 - u**2 = 0?
0, 1
Let m be (1 + 5 - 0)/2. Factor -l**3 - m - 1 - 6*l - 6*l**2 + 2 - l**3.
-2*(l + 1)**3
Suppose 0 = 5*q - 12 + 2. What is r in -3*r**3 + 2*r**3 - 2*r**2 - q*r**4 + 3*r**3 + 2*r**3 = 0?
0, 1
Suppose 9 = 5*m - 6. Factor w - 12*w**2 - 7*w**3 - 25*w - 16 + 5*w**m.
-2*(w + 2)**3
Let z(v) = -v**2 - v - 1. Let k(w) = 3*w**2 + 5*w. Let q(i) = k(i) + 2*z(i). Let x be q(-4). Factor -2/5*b**4 - 6/5*b**3 - 6/5*b**x + 0 - 2/5*b.
-2*b*(b + 1)**3/5
Let p be (-5)/15 + 20/6. Let w(s) be the third derivative of -1/360*s**6 + 0 + 0*s - 1/90*s**5 - 1/72*s**4 + 0*s**p + s**2. Factor w(i).
-i*(i + 1)**2/3
Suppose 0 = -4*q + 2*j + 4 + 8, 5*j = 5*q - 20. Let l(h) be the first derivative of -1/3*h**q + 3 - 2/9*h**3 + 0*h. Factor l(x).
-2*x*(x + 1)/3
Let p(g) be the first derivative of -g**3/15 - g**2/10 + 2*g/5 - 6. Factor p(x).
-(x - 1)*(x + 2)/5
Let r = 295 - 293. Solve 1/3*y**3 - 1/6*y - 3/2*y**5 + 0 - 2/3*y**2 + r*y**4 = 0 for y.
-1/3, 0, 1
Let p(q) be the first derivative of -q**4 + 36*q**3 - 486*q**2 + 2916*q - 1. Factor p(i).
-4*(i - 9)**3
Let q = -455/3 + 153. Find h, given that -1/3 - h**2 + q*h**4 - 5/3*h + 5/3*h**3 = 0.
-1, -1/4, 1
Let j(b) be the first derivative of -b**6/45 - b**5/15 - b**4/18 - 4*b - 2. Let w(n) be the first derivative of j(n). Factor w(m).
-2*m**2*(m + 1)**2/3
Let t(h) be the first derivative of 2744*h**6/15 - 588*h**5/25 - 889*h**4/5 + 2056*h**3/15 - 216*h**2/5 + 32*h/5 - 13. Solve t(o) = 0.
-1, 1/4, 2/7
Determine l, given that -4/13*l**3 + 0 + 6/13*l**4 - 2/13*l**5 + 0*l + 0*l**2 = 0.
0, 1, 2
Let w(o) = o + 1. Let j be w(3). Let q(z) be the second derivative of 7/15*z**6 + 5/3*z**3 + 0 + 2*z**2 - 3/2*z**j - 1/2*z**5 + 2*z. Factor q(r).
2*(r - 1)**2*(r + 1)*(7*r + 2)
Let q be 1 + -2*((-76)/24 - -3). Factor -q*b**2 + 0 + 2/3*b**3 + 2/3*b.
2*b*(b - 1)**2/3
Let m be (2/(-4))/((-1)/12). Suppose 5*n = -0*n - 2*o, 4*n = -3*o - 7. Factor m - 4*v + 2/3*v**n.
2*(v - 3)**2/3
Let u = 28 + -16. Let n be u/16 + (-18)/(-8). Factor a - a - 3*a**2 - 3*a + 3 + 3*a**n.
3*(a - 1)**2*(a + 1)
Suppose 10 = 5*d - 3*r + r, 2*d + r - 13 = 0. Let h(o) = 3 - 6 + 3*o**2 + 5*o**2 + d*o. Let c(v) = 7*v**2 + 4*v - 2. Let f(w) = -7*c(w) + 6*h(w). Factor f(m).
-(m + 2)**2
Suppose -m = -f - 7, 5*f + 8 = -12. Factor 6*q + 2 + q**3 + 3*q**3 - 2*q**m + 6*q**2.
2*(q + 1)**3
Let z be -12*-4*(-4)/(-168). Factor -8/7*u - z - 2/7*u**2.
-2*(u + 2)**2/7
Let r be 280/72*12/2. Determine x so that 16*x - r*x**4 + 62/3*x**2 - 16*x**3 + 8/3 = 0.
-1, -2/5, -2/7, 1
Suppose -4*b + 3*j + 2 = -2, -3*b = j - 16. Suppose 0 = 5*m + 4*a - 16, -5*m + b*a - 16 = -m. Factor 2/9*s**3 + 2/9*s**2 + m - 2/9*s**4 - 2/9*s.
-2*s*(s - 1)**2*(s + 1)/9
Let v(z) = -8*z**3 - 32*z**2 - 30*z - 16. Suppose -2*h = -4*q + 19 + 31, 2*q - 5*h = 45. Let t(c) = c**2 + c + 1. Let l(r) = q*t(r) + v(r). Solve l(n) = 0.
-1, -3/4
Factor 0 - 1/6*j + 0*j**3 + 1/6*j**5 + 1/3*j**2 - 1/3*j**4.
j*(j - 1)**3*(j + 1)/6
Let i(h) be the first derivative of -h**8/840 + 2*h**7/525 - h**6/300 -