1 - -5. Factor 6*x**3 - 3 + 0 + 3*x**w - 8*x + 2*x.
3*(x - 1)*(x + 1)**3
Let l(r) be the first derivative of -2*r**3/3 + 2*r - 6. Let y(n) = -4*n - 2. Let u be y(-4). Let t(m) = -6*m**2 + 6. Let d(z) = u*l(z) - 5*t(z). Factor d(o).
2*(o - 1)*(o + 1)
Let f(s) be the third derivative of s**9/241920 - s**8/40320 + s**7/20160 - s**5/30 - 2*s**2. Let i(j) be the third derivative of f(j). Factor i(b).
b*(b - 1)**2/4
Let l(p) be the first derivative of 4*p**3/15 + 2*p**2/5 + 20. Factor l(u).
4*u*(u + 1)/5
Let x(k) be the third derivative of -7*k**2 + 1/40*k**6 + 0 + 0*k**4 + 0*k + 0*k**3 - 1/20*k**5. Factor x(g).
3*g**2*(g - 1)
Let a(g) be the first derivative of -g**3/6 - g**2 - 2*g + 18. Factor a(h).
-(h + 2)**2/2
Suppose -5*r**4 - 5*r**2 + 459 - 459 + 10*r**3 = 0. What is r?
0, 1
Let x(u) be the first derivative of 1/14*u**4 + 4/35*u**5 + 0*u**3 - 2 + 0*u + 0*u**2 + 1/21*u**6. Factor x(p).
2*p**3*(p + 1)**2/7
Let a = -194/3 - -66. Let w be 6/9 + 1/(-3). Factor w*x**2 - 4/3*x + a.
(x - 2)**2/3
Let 1/4*x**5 - 7/12*x**3 - 1/3*x**2 + 0 + 1/3*x + 1/3*x**4 = 0. Calculate x.
-2, -1, 0, 2/3, 1
Suppose -2*i + 1 + 1 = -4*w, 3*w - 4*i + 14 = 0. Let l be w/(-3) + (-28)/(-6). Suppose 3/5*y**5 - 8/5 + 17/5*y**3 - 6/5*y**2 - 4*y + 14/5*y**l = 0. Calculate y.
-2, -1, -2/3, 1
Let g(l) = l**3 + 6*l**2 + 6*l + 7. Let c be g(-5). Let f(k) be the first derivative of c - k**2 - 1/3*k**3 - k. Factor f(u).
-(u + 1)**2
Let t(i) be the second derivative of -i**6/40 + i**5/20 + i**4/8 - i**3/2 - 5*i**2/2 - 2*i. Let k(l) be the first derivative of t(l). Factor k(r).
-3*(r - 1)**2*(r + 1)
Let i be ((-354)/(-48) + -7)/((-2)/(-24)). Factor -3/2*n**3 + 9/2*n**2 - i*n + 3/2.
-3*(n - 1)**3/2
Let z = -10 + 12. Let o(g) be the third derivative of 0*g**3 + 0 + 0*g**6 + 3*g**z + 0*g**4 + 1/210*g**5 - 1/735*g**7 + 0*g. Let o(b) = 0. What is b?
-1, 0, 1
Let r(b) be the first derivative of b**4/4 - 3*b**3 + 7*b**2/2 + 11*b - 2. Let a be r(8). Factor a*y**2 - y + 4*y**2 - y**2 - 5*y**2.
y*(y - 1)
Let w be (-1 - 0) + -3 - -4. Factor 1/4*x**2 + 1/4*x + w.
x*(x + 1)/4
Suppose 9 = 3*h - 6*h. Let p be (-2)/(-10) + (h - -3). Let -p*v**3 + 1/5*v + 1/5*v**2 - 1/5*v**4 + 0 = 0. What is v?
-1, 0, 1
Find v such that 0*v + 0*v**3 + 0 + 2/7*v**4 - 2/7*v**2 = 0.
-1, 0, 1
Find l, given that 16*l + 28*l**2 - 9*l**5 - 120*l**3 - 6*l**5 - l**5 + 92*l**4 = 0.
-1/4, 0, 1, 4
Let h(n) be the first derivative of -1 + 1/2*n**2 + 0*n + 2/3*n**3. Factor h(u).
u*(2*u + 1)
Let n(r) = -r + 9. Let b be n(7). Suppose 0 = 2*x + b - 14. Suppose -3 + 2 + x*z - 3 + 40*z**2 = 0. What is z?
-2/5, 1/4
Let s(h) be the second derivative of h**4/4 - 17*h**3/10 + 9*h**2/5 - 13*h. Determine u, given that s(u) = 0.
2/5, 3
Let n be (-494)/(-12) + 10/(-30). Let w = n + -49/6. Find h, given that 0*h + w*h**2 - 8/3 = 0.
-2/7, 2/7
Let l = 8 - 8. Suppose -3*g = -5*o + 31, 5*g = -o - 5 - l. Let k(f) = f**2 + 2*f + 1. Let r(q) = q**3 + q**2 - q - 1. Let c(s) = g*r(s) - 2*k(s). Factor c(y).
-2*y*(y + 1)**2
Let k(x) = x**3 - x**2 - 1. Let j(u) = 2*u**3 - 10*u**2 - 3. Let c(v) = j(v) - 3*k(v). Factor c(y).
-y**2*(y + 7)
Let i(k) = 3*k**5 + 21*k**4 - 11*k**2 - 8*k + 5. Let h(l) = -l**5 - 11*l**4 + 5*l**2 + 4*l - 3. Let w(f) = 5*h(f) + 3*i(f). Factor w(j).
4*j*(j - 1)*(j + 1)**3
Let m = 478 + -470. Suppose 1/2*o**5 + m*o**2 + 3*o**4 + 1 + 7*o**3 + 9/2*o = 0. Calculate o.
-2, -1
Factor 2/5 + 2/5*h**2 - 4/5*h.
2*(h - 1)**2/5
Let f(y) be the first derivative of -y**8/840 - y**7/420 - 2*y**3/3 + 3. Let o(q) be the third derivative of f(q). Determine t, given that o(t) = 0.
-1, 0
Suppose 0 = -18*s + 43*s. Factor 3/4*v**3 - 3/4*v**4 + 0*v + 0*v**2 + s.
-3*v**3*(v - 1)/4
Let t be 6/21*(-1)/(-4). Let n(v) be the second derivative of 0*v**2 + 0*v**5 + 0*v**3 + 3*v + t*v**7 + 0*v**4 + 1/30*v**6 + 0. Factor n(d).
d**4*(3*d + 1)
Let i(m) be the third derivative of m**8/1344 - m**7/140 + 11*m**6/480 - m**5/120 - m**4/8 + m**3/3 - 6*m**2. Determine u, given that i(u) = 0.
-1, 1, 2
Solve -63*y**3 - 2*y**2 - 21*y**4 - 32*y**5 + 41*y**5 - y**2 + 24 + 54*y = 0 for y.
-1, -2/3, 1, 4
Let 10*n**2 - 18*n**2 + 15*n**3 + 0*n - 13*n**2 + 6*n = 0. Calculate n.
0, 2/5, 1
Suppose 5*z = -5*v, 5*v + 12 = 2*v. Let n be (z/(-25))/(14/(-35)). Factor -n*g**2 + 0*g + 0.
-2*g**2/5
Let k(w) be the first derivative of w**5/20 - w**4/4 + 5*w**3/12 - w**2/4 + 12. Let k(d) = 0. Calculate d.
0, 1, 2
Let t(k) be the first derivative of 3 - 4/3*k**3 - k + 5/2*k**2. Factor t(r).
-(r - 1)*(4*r - 1)
Let q = -481 + 481. Let -1/4*p**4 + q*p + 0*p**2 - 1/4*p**5 + 0*p**3 + 0 = 0. What is p?
-1, 0
Factor 0 - 33/7*i**3 - 3*i**5 + 0*i + 6/7*i**2 + 48/7*i**4.
-3*i**2*(i - 1)**2*(7*i - 2)/7
Let b(n) be the first derivative of n**5/30 - n**4/24 - n**3/9 - 10. Factor b(f).
f**2*(f - 2)*(f + 1)/6
Let h(a) be the second derivative of a**7/2520 + a**6/720 + a**4/6 + a. Let o(i) be the third derivative of h(i). Factor o(d).
d*(d + 1)
Let h be (-2 + (0 - 8))*(-4)/20. Solve 2/11*u**5 + 0*u + 4/11*u**h + 0 - 2/11*u**3 - 4/11*u**4 = 0 for u.
-1, 0, 1, 2
Let t(a) be the third derivative of -a**6/120 + a**5/30 - 2*a**2. Factor t(p).
-p**2*(p - 2)
Let h(u) = u**4 + u**3 - u**2 + u. Let z(y) = 9*y**4 + 3*y**3 - y**2 + 5*y. Let t(i) = -24*h(i) + 3*z(i). Factor t(j).
3*j*(j - 3)*(j - 1)**2
Suppose 8*d = -d + 18. Let r(l) be the first derivative of -2*l - 3 - 14/3*l**3 + 5*l**d + 3/2*l**4. Factor r(z).
2*(z - 1)**2*(3*z - 1)
Let z be (1 + 5 + -6)/(-2 - -3). Let m(k) be the second derivative of 0*k**2 - 5/6*k**4 - 2*k - 2/5*k**5 + 2/3*k**3 + 1/5*k**6 + z. Factor m(x).
2*x*(x - 2)*(x + 1)*(3*x - 1)
Find d, given that -1/4*d**2 - 5/4*d - 1 = 0.
-4, -1
Let h(r) = r**2 + r - 3. Let b be h(-3). Factor -b*c**3 + 0*c**3 + 5*c**3 - c**4 - c**2.
-c**2*(c - 1)**2
Suppose 6*d**3 + 0 - 9*d**5 + 1/3*d + 0*d**4 + 8/3*d**2 = 0. Calculate d.
-1/3, 0, 1
Let a(m) be the third derivative of m**8/504 - m**7/105 + m**6/90 + m**5/45 - m**4/12 + m**3/9 + 4*m**2. Determine k so that a(k) = 0.
-1, 1
Let l(k) be the second derivative of k**9/10080 - k**8/2240 - k**7/1680 + k**6/240 - k**4/4 - 4*k. Let h(d) be the third derivative of l(d). Factor h(q).
3*q*(q - 2)*(q - 1)*(q + 1)/2
Let a(c) = -7*c**4 + 27*c**3 - 23*c**2 + 8*c - 5. Let d(z) = -z**4 + z**2 - z + 1. Let r(y) = -a(y) - 5*d(y). Solve r(q) = 0 for q.
0, 1/4, 1
Suppose -5*x = a - 2*x - 2, -a = -4*x - 2. Factor 1/3*o + 0*o**a - 1/3*o**3 + 0.
-o*(o - 1)*(o + 1)/3
Factor -1/3 - 3*n**2 + 4/3*n**3 + 2*n.
(n - 1)**2*(4*n - 1)/3
Suppose 0 = 4*k - 12 - 0. Let q be 18/k + 1/(-1). Let 6*p**5 - p**4 - 5*p**5 - 1 - p**3 + q*p + 2*p**2 - p**3 - 4*p = 0. Calculate p.
-1, 1
Let b(n) be the second derivative of -n**6/10 - 3*n**5/20 + n**4 + 2*n**3 - 2*n. Suppose b(h) = 0. Calculate h.
-2, -1, 0, 2
Let f(x) be the third derivative of -2*x**7/105 - x**6/5 - 3*x**5/5 - 2*x**4/3 + 3*x**2 - x. Factor f(a).
-4*a*(a + 1)**2*(a + 4)
Factor -53*h**5 - 3*h**4 - 18*h**2 + 13*h**4 + 3*h**5 + 42*h**3.
-2*h**2*(h + 1)*(5*h - 3)**2
Let l(u) be the second derivative of -u**6/720 - u**5/120 - u**4/72 - 5*u**2/2 - 4*u. Let j(z) be the first derivative of l(z). Factor j(h).
-h*(h + 1)*(h + 2)/6
Suppose -l - 1 = 0, -5*f = -2*f - 3*l - 9. Factor g + g**2 + f*g - g - 4*g.
g*(g - 2)
Let n be ((-2)/3)/(4/(-6)). Suppose 10 = c - 1. Factor m**2 + c*m - n - 11*m.
(m - 1)*(m + 1)
Let i(y) be the third derivative of y**6/60 + 2*y**5/15 + y**4/4 - 11*y**2. Factor i(z).
2*z*(z + 1)*(z + 3)
Let l(x) be the third derivative of 49*x**5/20 + 21*x**4/4 + 9*x**3/2 - 7*x**2. Factor l(h).
3*(7*h + 3)**2
Let t(s) = s**2 + 7*s. Let o be t(-7). Let w(x) be the first derivative of -2 + 2/15*x**3 + o*x - 1/5*x**2. Factor w(r).
2*r*(r - 1)/5
Let a(g) be the second derivative of 25*g**7/42 - g**6/9 - 103*g**5/60 + g**4/2 + 14*g**3/9 - 4*g**2/3 + 7*g. Suppose a(z) = 0. What is z?
-1, -2/3, 2/5, 1
Solve 0 + 0*p**3 + 1/4*p**2 - 1/8*p**5 - 1/4*p**4 + 1/8*p = 0.
-1, 0, 1
Let z(s) be the second derivative of -s**7/7 + 7*s**6/10 - 21*s**5/20 + s**4/2 - 6*s. Suppose z(q) = 0. What is q?
0, 1/2, 1, 2
Let o(x) = x + x + 2 - 5. Let w be o(3). Factor -3*s**3 - s + 4*s**4 - s**4 - 4*s**4 - w*s**2.
-s*(s + 1)**3
Factor -5*o + 2*o**2 - 4*o**2 + o**2 - 5*o**3 + 11*o**2.
-5*o*(o - 1)**2
Let z(v) be the third derivative of 0 + 1/240*v**5 - 5*v**2 + 0*v + 1/