q - 6*h = -4*h, -4*q - 2*h = 10. Let j be (-2)/(-6) - (2 + q). Factor -1/3*r**2 + 0 - j*r.
-r*(r + 1)/3
Let t(f) be the third derivative of f**8/3024 - f**6/1080 + 50*f**2. Factor t(i).
i**3*(i - 1)*(i + 1)/9
Let l be (196/20)/((-4)/10). Let v = -24 - l. Solve v*d - 1/4*d**2 - 1/4 = 0.
1
Let s be 0/(-3*1) + 3. Suppose 8*b = s*b + 35. What is o in 0*o + 23*o - b*o + 7*o**2 + 4 = 0?
-2, -2/7
Let o = -304 - -307. Suppose 2/5*k + 0 + 2/5*k**5 + 12/5*k**o - 8/5*k**2 - 8/5*k**4 = 0. What is k?
0, 1
Let b(o) = -o**2 + 3. Let j = -31 - -13. Let g(t) = 5*t**2 - t - 13. Let l(h) = j*b(h) - 4*g(h). Determine n so that l(n) = 0.
1
Let r = -18 - -20. Suppose -b + r = -1. What is p in 0*p + 0 + 1/3*p**2 - 1/3*p**4 + 0*p**b = 0?
-1, 0, 1
Let m(v) = -9*v**4 + 3*v**3 - 5*v**2 - 8*v - 1. Let k(z) = -4*z**4 + 2*z**3 - 2*z**2 - 4*z. Let n(w) = 5*k(w) - 2*m(w). Solve n(t) = 0 for t.
-1, 1
Let w(v) = 3*v**4 - 21*v**3 + 47*v**2 - 67*v + 17. Let l(c) = -2*c**4 + 14*c**3 - 31*c**2 + 45*c - 11. Let x(f) = 7*l(f) + 5*w(f). Determine u so that x(u) = 0.
1, 2
Factor -23*z**2 + 15*z + 5*z + 20 - 21*z**3 + 8*z**2 + z**3 - 5*z**4.
-5*(z - 1)*(z + 1)*(z + 2)**2
Factor 0*j**2 + 0 - 3/4*j + 3/4*j**3.
3*j*(j - 1)*(j + 1)/4
Let o(r) = r**2 + 15*r + 8. Let j be o(-14). Let x be j/21 + (-48)/(-21). Factor 0*i + 2/5 - 2/5*i**x.
-2*(i - 1)*(i + 1)/5
Let i(v) be the first derivative of v**3/4 + 3*v**2/8 - 13. What is s in i(s) = 0?
-1, 0
Let m(c) be the third derivative of c**7/1470 - c**6/420 - c**5/420 + c**4/84 + 23*c**2. Factor m(r).
r*(r - 2)*(r - 1)*(r + 1)/7
Let a(d) be the first derivative of 6*d**3 - 11/2*d**4 + 1 + d + 13/5*d**5 - 1/2*d**6 - 7/2*d**2. Factor a(c).
-(c - 1)**4*(3*c - 1)
Let k(i) be the second derivative of -i**5/40 + 5*i**4/24 - 7*i**3/12 + 3*i**2/4 - 7*i. Factor k(w).
-(w - 3)*(w - 1)**2/2
Let a(f) be the first derivative of 14*f**3/9 + 23*f**2/3 + 4*f - 31. Factor a(r).
2*(r + 3)*(7*r + 2)/3
Let y(a) be the third derivative of -7*a**6/360 + a**5/20 - a**4/36 + 27*a**2. Let y(n) = 0. Calculate n.
0, 2/7, 1
Let c(q) be the second derivative of -15*q**4/4 - 55*q**3/6 - 5*q**2 + 9*q - 1. Factor c(a).
-5*(a + 1)*(9*a + 2)
Factor -2/3*y + 4/3 + 2/3*y**3 + 2/3*y**4 - 2*y**2.
2*(y - 1)**2*(y + 1)*(y + 2)/3
Let o(l) be the first derivative of l**4/12 - l**2/2 - 2*l/3 + 5. Suppose o(z) = 0. What is z?
-1, 2
Determine u so that 14*u**3 - 4*u**4 + 10*u**2 - 6*u**3 + 3*u**2 - u**2 = 0.
-1, 0, 3
Let w(t) = 60*t**3 - 120*t**2 + 35*t - 35. Let u(y) = -5*y**3 + 10*y**2 - 3*y + 3. Let f(q) = -35*u(q) - 3*w(q). Factor f(c).
-5*c**2*(c - 2)
Let c(t) be the second derivative of 4*t**7/105 - t**6/20 - t**5/30 - 3*t**2/2 - t. Let q(h) be the first derivative of c(h). Determine x so that q(x) = 0.
-1/4, 0, 1
Let m(z) be the third derivative of -1/30*z**5 + 7/60*z**6 - 2/21*z**8 + 0 - 3*z**2 + 0*z**3 - 8/105*z**7 + 0*z + 0*z**4. Factor m(d).
-2*d**2*(d + 1)*(4*d - 1)**2
Suppose -6 = -2*c - 2. Let y(d) be the first derivative of -d**3 + 1/5*d**5 - c*d - 5/2*d**2 + 3 + 1/4*d**4. Factor y(l).
(l - 2)*(l + 1)**3
Let a(j) be the first derivative of 1/15*j**5 + 0*j + 1/12*j**4 + 0*j**2 + 0*j**3 - 1/9*j**6 + 2. Determine h, given that a(h) = 0.
-1/2, 0, 1
Factor 1/4 - 3/8*j**2 - 1/8*j + 1/8*j**4 + 1/8*j**3.
(j - 1)**2*(j + 1)*(j + 2)/8
Let l(d) be the second derivative of 3*d**7/14 - 11*d**6/10 + 21*d**5/10 - 3*d**4/2 - d**3/2 + 3*d**2/2 + 5*d. Find s, given that l(s) = 0.
-1/3, 1
Let k(f) = 3*f**4 - 33*f**3 + 33*f**2 + 24*f - 3. Let z(q) = q**4 + q**2 + q + 1. Let i(x) = -k(x) - 3*z(x). Factor i(h).
-3*h*(h - 3)**2*(2*h + 1)
Let i(s) be the second derivative of s**6/15 + 3*s**5/5 + 2*s**4 + 10*s**3/3 + 3*s**2 - 13*s. Suppose i(h) = 0. What is h?
-3, -1
Let g(c) be the first derivative of -1/10*c**5 - 3/4*c**4 + 0*c - 2*c**2 - 4 - 2*c**3. Factor g(x).
-x*(x + 2)**3/2
Let -4*v**3 + 0*v**3 - v**3 + 0*v**3 - 5 + 5*v**2 + 5*v = 0. What is v?
-1, 1
Let i be (-4)/12 - 20/3. Let p(u) = -u**3 - 6*u**2 + 6*u - 5. Let y be p(i). Factor 0*c + 0 - 1/4*c**y - 1/4*c**3.
-c**2*(c + 1)/4
Let j be (-3)/1 + 7 - 1. Let n = 2 + j. Factor 4/3*m**4 + 0*m**3 + 0 - 2/3*m + 2/3*m**n - 4/3*m**2.
2*m*(m - 1)*(m + 1)**3/3
Suppose 0 = -t + 1 + 1. Let i(c) be the second derivative of c**t + 0 + 1/10*c**5 - 1/3*c**3 - 1/6*c**4 + 2*c. Determine y so that i(y) = 0.
-1, 1
Let f = 182 - 110. Let h = -141/2 + f. Determine a, given that 0 - 7/2*a**2 + h*a**3 - 5/2*a**5 + a + 7/2*a**4 = 0.
-1, 0, 2/5, 1
Let p(c) = -12*c**3 + 40*c**2 - 15*c - 13. Let b(s) = -11*s**3 + 40*s**2 - 15*s - 14. Let q(w) = 3*b(w) - 4*p(w). Determine l, given that q(l) = 0.
-1/3, 1, 2
Factor 1/3*c**3 - 2/3*c + 1/3*c**2 + 0.
c*(c - 1)*(c + 2)/3
Let u = 249 - 247. Determine r so that 0*r + 2/11*r**u - 2/11 = 0.
-1, 1
Let f(i) be the third derivative of i**7/70 + i**6/20 + i**5/20 - 5*i**2. Factor f(u).
3*u**2*(u + 1)**2
Let g(m) be the first derivative of -m**5/120 - m**2 + 3. Let u(i) be the second derivative of g(i). What is y in u(y) = 0?
0
Let i = -11 + 19. Suppose w = -3*f - 13, w + 3*f + i = f. Solve 2*s**2 - 2*s - 6*s**w + 2*s**2 = 0.
-1, 0
Suppose 4 = k - 0*k, 3*w - k = -34. Let l(d) = 1 - 1 - 1. Let c(i) = -2*i**2 + 4*i + 8. Let j(q) = w*l(q) - c(q). Factor j(v).
2*(v - 1)**2
Let v(f) = 3*f**3 - 12*f**4 + 122*f**2 + f - 116*f**2 - f. Let q(b) = -12*b**2 - 6*b**3 + 4*b**4 + b**4 + 18*b**4. Let l(u) = 3*q(u) + 5*v(u). Factor l(n).
3*n**2*(n - 1)*(3*n + 2)
Let n(p) be the second derivative of p**6/30 - p**5/5 + p**4/2 - 2*p**3/3 + p**2/2 - 5*p. Let n(o) = 0. What is o?
1
Let r(l) = -4*l**2 + 111*l + 30. Let a be r(28). Factor -2/3*s**a + 4*s - 6.
-2*(s - 3)**2/3
Determine d, given that 3/2*d**4 + 11/2*d + 13/2*d**3 + 19/2*d**2 + 1 = 0.
-2, -1, -1/3
Let f(v) = 7*v**4 + 3*v**3 - 3*v**2 + 5*v + 6. Let g = 1 + -7. Let j(l) = l**4 + l**3 - l**2 + l + 1. Let i(t) = g*j(t) + f(t). Solve i(w) = 0.
0, 1
Let m(h) be the second derivative of h**6/60 - 2*h**5/15 + 5*h**4/12 - 2*h**3/3 - h**2 + 4*h. Let q(z) be the first derivative of m(z). Factor q(k).
2*(k - 2)*(k - 1)**2
Find d, given that 8/3 - 8/3*d - 2/3*d**2 + 2/3*d**3 = 0.
-2, 1, 2
Suppose -6 = -2*v + 4. Suppose 0 = v*w - 6 - 29. Factor 4*s**2 + 2*s**5 + 2*s**2 - 2*s**2 + 3*s**4 - 2*s - w*s**4.
2*s*(s - 1)**3*(s + 1)
Let v(p) be the first derivative of 0*p - 2/3*p**3 + 1 - 1/2*p**4 + 0*p**2. Factor v(a).
-2*a**2*(a + 1)
Let u(i) be the first derivative of -i**6/6 + 3*i**5/5 - i**4/2 + 8. Solve u(z) = 0 for z.
0, 1, 2
Let m(b) be the third derivative of b**8/13440 - b**7/1680 + b**6/480 - b**5/240 + b**4/12 + 4*b**2. Let w(x) be the second derivative of m(x). Factor w(s).
(s - 1)**3/2
Let z(w) be the second derivative of -3/4*w**2 - 1/4*w**4 - 11*w + 0 + 3/4*w**3. Factor z(k).
-3*(k - 1)*(2*k - 1)/2
Let i(o) be the second derivative of 7*o**5/10 - 5*o**4/6 - 2*o**3/3 + 12*o. Factor i(x).
2*x*(x - 1)*(7*x + 2)
Let q(m) = -m - 4. Let u be q(-4). Let b(s) = s**2 + s - 2. Let y be b(2). Factor 2*d + u - 4 - 2*d**y + 0*d**4 - 2*d**3 + 6*d**2.
-2*(d - 1)**2*(d + 1)*(d + 2)
Let p(x) be the second derivative of 1/20*x**5 + 0*x**4 + 0 + 1/15*x**6 + 1/42*x**7 - 6*x + 0*x**3 + 0*x**2. Factor p(z).
z**3*(z + 1)**2
Let u(f) be the second derivative of -1/8*f**2 + 0 + f + 0*f**3 + 1/48*f**4. Factor u(n).
(n - 1)*(n + 1)/4
Let t be ((-2)/4)/(4/(-16)). Let d(k) be the first derivative of 1/15*k**3 + 2 + 1/5*k + 1/5*k**t. Let d(s) = 0. What is s?
-1
Let w be -1*(-2 + -2 + 1). Let t be ((-24)/30)/((-4)/10). Factor 2*x**3 + x**4 - 2*x**w - x + x**3 - x**t.
x*(x - 1)*(x + 1)**2
Let i = -5 + 6. Let g be (i - -8)*(4 - 3). Factor 2*f**4 - 3*f**2 + 7*f + f**2 - g*f + 2*f**3.
2*f*(f - 1)*(f + 1)**2
Let f be ((-2)/4)/(4/(-8)). Let r(l) be the first derivative of 0*l + f - 1/3*l**3 + l**4 + 3/5*l**5 - l**2. Factor r(q).
q*(q + 1)**2*(3*q - 2)
Let a(m) be the first derivative of 1/6*m**4 + 1 - 2*m**2 + 1/3*m**3 - 3*m. Let r(x) be the first derivative of a(x). Solve r(j) = 0.
-2, 1
Let z = 368/2145 - -2/195. Find x such that 0 + 4/11*x**3 - z*x**2 - 2/11*x = 0.
-1/2, 0, 1
Let x(i) be the third derivative of 0*i**5 - 1/480*i**6 - 1/140*i**7 + 0*i + 0*i**3 + 0 - i**2 + 0*i**4 - 3/448*i**8. Factor x(d).
-d**3*(3*d + 1)**2/4
Let m(h) be the first derivative of h + 7/12*h**6 - 8 - 8/5*h**5 + 1/2*h**4 + 7/3*h**3 - 11/4*h**2. Factor 