4.
-2*(y - 1)**2*(y + 1)**2
Suppose 2*l + 10 = 4*m, -l - 11 = -3*m - m. Let s be 0/(-4) - (1 - m). Factor 4*p**5 - p**2 + 7*p**3 - 6*p**4 - p + s*p**3 - 5*p**4.
p*(p - 1)**3*(4*p + 1)
Let f(a) be the second derivative of 1/75*a**6 - 3/50*a**5 - 1/15*a**3 + 4*a + 0 + 0*a**2 + 1/10*a**4. Solve f(h) = 0 for h.
0, 1
Determine i, given that -8/3 - 14/3*i**5 - 146/3*i**3 - 74/3*i**4 - 134/3*i**2 - 56/3*i = 0.
-2, -1, -2/7
Let h(f) be the first derivative of -1/6*f**4 - 1/3*f**3 + 0*f**2 + 2*f - 3 + 1/15*f**6 + 1/10*f**5. Let j(i) be the first derivative of h(i). Factor j(s).
2*s*(s - 1)*(s + 1)**2
Let w(d) be the second derivative of -d**4/6 - 8*d**3/3 - 16*d**2 - d. Factor w(u).
-2*(u + 4)**2
Let t(g) be the third derivative of -g**7/1260 + g**6/360 - g**5/360 - 18*g**2. Find l, given that t(l) = 0.
0, 1
Let z(u) be the first derivative of u**6/30 - u**5/25 - u**4/10 + 2*u**3/15 + u**2/10 - u/5 + 2. Factor z(h).
(h - 1)**3*(h + 1)**2/5
Let j(s) be the third derivative of -s**6/1080 + s**5/360 + s**4/36 - s**3/2 - 2*s**2. Let f(g) be the first derivative of j(g). Factor f(p).
-(p - 2)*(p + 1)/3
Let w(c) = 3*c - 1. Let j be w(-1). Let g be (-12)/j - 50/18. Suppose g - 4/9*y**2 - 2/9*y = 0. Calculate y.
-1, 1/2
Let j(d) be the third derivative of d**7/840 + d**6/240 - d**5/20 + d**4/8 + d**2. Let q(a) be the second derivative of j(a). Solve q(o) = 0 for o.
-2, 1
Factor -6*p**3 + 4*p**3 - 2*p**2 - p**2 - p**3.
-3*p**2*(p + 1)
Let l(m) be the third derivative of m**7/280 - m**6/120 - m**5/240 + m**4/48 - m**2. Factor l(s).
s*(s - 1)**2*(3*s + 2)/4
Suppose 3*q - 4 - 2 = 0. Suppose 0 = -3*h - 3*y + 27, 3*h - q*y = 2*y - 8. Find f such that -2*f + 5*f**3 - h*f**3 + f**3 = 0.
-1, 0, 1
Suppose 0*g = 6*g - g. Determine c so that 4/7*c**4 + 0*c + g*c**2 + 0 - 2/7*c**5 - 2/7*c**3 = 0.
0, 1
Let w(r) be the second derivative of -r**6/30 - 13*r**5/80 - 11*r**4/48 - r**3/12 - 2*r. Factor w(f).
-f*(f + 1)*(f + 2)*(4*f + 1)/4
Let w be ((-32)/12)/(-4)*9. Factor -12*q**4 - 3 + w + 3*q - 3 - 3*q**3 + 12*q**2.
-3*q*(q - 1)*(q + 1)*(4*q + 1)
Suppose -r**2 + 0*r**2 - 2*r + 8 - r**2 - 2*r + r**3 = 0. Calculate r.
-2, 2
Let h(z) be the first derivative of 6*z**2 + 2/3*z**3 + 10 + 18*z. Determine n, given that h(n) = 0.
-3
Let r be 2 + 6/(-9)*-9. Suppose r + 4 = 2*o. Factor -o*n**2 - 2*n**3 + n**3 + 2*n**2 + 3*n**2.
-n**2*(n + 1)
Let u(w) = 0*w + 3*w**2 - 3*w**2 + w + 2*w**2. Let a(t) = -2*t**2. Let k(c) = -3*a(c) - 2*u(c). Factor k(d).
2*d*(d - 1)
Let i = -54 + 54. Let q(t) be the second derivative of -1/15*t**3 - t - 1/30*t**4 + 0*t**2 + i. Factor q(o).
-2*o*(o + 1)/5
Let f(i) be the third derivative of -i**6/200 - i**5/150 + i**4/120 - 10*i**2. Factor f(x).
-x*(x + 1)*(3*x - 1)/5
Suppose -z - 4*z + 7 = f, -4*f - 5*z + 13 = 0. Factor -4*p**2 + p**f + 4*p**3 + 2*p**4 + 5*p**2.
2*p**2*(p + 1)**2
Let h = 99/206 + 2/103. Let g(s) be the first derivative of s - h*s**4 - 2 + 1/5*s**5 - 2/3*s**3 + 1/2*s**2 + 1/6*s**6. Solve g(r) = 0 for r.
-1, 1
Let d(r) = 13*r + 11. Let x be d(8). Let u = x + -457/4. Factor -1/4*s**3 - 3/4*s + u*s**2 + 1/4.
-(s - 1)**3/4
Let h(b) be the first derivative of -2*b**3/33 - 2*b**2/11 + 6*b/11 + 6. Solve h(z) = 0 for z.
-3, 1
Suppose -3*d = 4*w - 31, -5*w = 4*d + 7 - 47. Suppose 0 = x - 3*x + w. Factor -5*k**2 + 4*k**2 + k**4 - k + k**3 + 0*k**x.
k*(k - 1)*(k + 1)**2
Let x(b) be the second derivative of b**5/10 - b**3 + 2*b**2 + 7*b. Factor x(n).
2*(n - 1)**2*(n + 2)
Let y = -609/5 - -122. Factor 4/5*x**3 + y + 6/5*x**2 + 4/5*x + 1/5*x**4.
(x + 1)**4/5
Determine y, given that -y**5 - 11/5*y**3 + 17/5*y**4 - 4/5 + 16/5*y - 13/5*y**2 = 0.
-1, 2/5, 1, 2
Let o(z) be the third derivative of -z**8/112 + 2*z**7/35 - 3*z**6/20 + z**5/5 - z**4/8 + 5*z**2. Factor o(n).
-3*n*(n - 1)**4
Let v(d) be the third derivative of -5*d**2 + 1/2*d**3 + 1/4*d**4 + 1/20*d**5 + 0*d + 0. Factor v(k).
3*(k + 1)**2
Let f(d) be the third derivative of -3*d**8/112 + d**7/70 + 3*d**6/40 - d**5/20 - 6*d**2. Determine q so that f(q) = 0.
-1, 0, 1/3, 1
Let w(j) be the second derivative of 4*j - 1/42*j**4 - 1/7*j**3 + 0 + 0*j**2. Factor w(t).
-2*t*(t + 3)/7
Let x(w) be the second derivative of w**7/63 + 7*w**6/45 + 3*w**5/5 + 10*w**4/9 + 8*w**3/9 - 46*w. Solve x(k) = 0.
-2, -1, 0
Let n(t) be the first derivative of 4*t**3/3 - 36*t**2 + 324*t + 37. Factor n(f).
4*(f - 9)**2
Let t(u) be the second derivative of 5*u**7/14 + 7*u**6/10 - 9*u**5/20 - 7*u**4/4 - u**3 - 13*u. What is o in t(o) = 0?
-1, -2/5, 0, 1
Let w(t) be the first derivative of -2/27*t**3 + 2 - 1/18*t**4 + 0*t + 2/9*t**2. Find i, given that w(i) = 0.
-2, 0, 1
Suppose 0 = -2*j + q + 4, -3*j - q + 6 - 10 = 0. Find s, given that j - 4/9*s**3 + 0*s - 2/9*s**4 - 2/9*s**2 = 0.
-1, 0
Let r(a) be the second derivative of 1/18*a**3 - 1/18*a**4 + 1/45*a**6 + 0*a**2 + 0 - 3*a - 1/126*a**7 + 0*a**5. Factor r(x).
-x*(x - 1)**3*(x + 1)/3
Suppose -89 - 24 = 4*o - b, -5*b = o + 44. Let l = -86/3 - o. Let l*s**3 - 1/3*s + 1/3*s**2 - 1/3 = 0. What is s?
-1, 1
Let z(v) be the second derivative of -v**5/10 - 7*v**4/16 - 3*v**3/4 + v**2 + 3*v. Let d(w) be the first derivative of z(w). Find a such that d(a) = 0.
-1, -3/4
Let c(q) = 5*q**4 + 13*q**3 + 13*q. Let s(k) be the third derivative of -k**7/210 - k**6/40 - k**4/8 + 2*k**2. Let b(n) = 6*c(n) + 26*s(n). Factor b(o).
4*o**4
Let s(m) be the second derivative of -1/60*m**4 + 1/30*m**3 + 0 + 0*m**2 + 6*m. Let s(f) = 0. Calculate f.
0, 1
Suppose -2*o + o = 0. Suppose -m = -o*m. Factor m*v - 1/4*v**2 + 3/4*v**3 + 0 + v**4.
v**2*(v + 1)*(4*v - 1)/4
Let a be 50/(-20)*((-71)/(-25) + -3). Determine w, given that 3/5*w**2 - a*w + 0 = 0.
0, 2/3
Let r = -138 - -140. Find c, given that 4/3*c**3 + 0 + 2/3*c + 2*c**r = 0.
-1, -1/2, 0
Let s(v) = -2*v - 7. Let b be s(-5). Factor 8*a**4 + 20*a**2 - 20*a**b + 2*a + 2 - 10*a - 2*a**5 + 2*a**4 - 2*a.
-2*(a - 1)**5
Let o(g) be the first derivative of 3*g**4/5 + 4*g**3/15 - 3. Factor o(u).
4*u**2*(3*u + 1)/5
Let n(y) be the first derivative of -3/5*y**5 - 11/4*y**4 - 9/2*y**2 - 5*y**3 - 2*y + 4. Solve n(a) = 0.
-1, -2/3
Let h(a) be the second derivative of -a**9/11340 - a**8/6720 + a**7/7560 - a**4/6 - 2*a. Let j(z) be the third derivative of h(z). Factor j(w).
-w**2*(w + 1)*(4*w - 1)/3
Find m such that 0*m**2 + 2/3*m**4 + 8/3*m + 0 - 2*m**3 = 0.
-1, 0, 2
Let i(z) be the third derivative of z**6/12 + 2*z**5/5 + z**4/3 - z**2. Solve i(n) = 0.
-2, -2/5, 0
Solve 8/7 - 6/7*a**2 - 8/7*a - 2/7*a**4 + 8/7*a**3 = 0 for a.
-1, 1, 2
Factor 3*x**3 - 12*x**4 - 10*x - 15*x + 22*x + 2*x**2 + 10*x**2.
-3*x*(x - 1)*(x + 1)*(4*x - 1)
Let k(j) be the first derivative of -5*j**7/42 + j**6/10 + j**5/10 + 4*j + 4. Let c(x) be the first derivative of k(x). Factor c(b).
-b**3*(b - 1)*(5*b + 2)
Let a = 21 - 19. Determine u, given that a*u + 2*u**2 + 0*u - 3*u**2 - 3*u = 0.
-1, 0
Let f = -2/2125 + -36929/48875. Let b = 1/23 - f. Factor -2/5*l**3 - b*l**4 + 0*l + 0*l**2 - 2/5*l**5 + 0.
-2*l**3*(l + 1)**2/5
Let c(b) = -5*b**2 + 14*b - 6. Let t(j) be the first derivative of 3 - 19*j + 41/2*j**2 - 14/3*j**3. Let v(z) = 7*c(z) - 2*t(z). Let v(s) = 0. Calculate s.
2/7, 2
Let b(n) = -n**3 + 4*n + 3. Let o be b(-2). Suppose 4*i = -4*w - 14 + 6, -o*i + 19 = -2*w. Determine y so that 2 - 2*y**i + y**3 - y + 2*y**2 - 2 = 0.
0, 1
Let o(k) = -k + 1. Let w be o(-3). Let r be (-48)/(-21) + w/(-2). Find s such that -2/7*s**2 + r*s + 0 = 0.
0, 1
Determine o so that -2/3*o - 2/15 - 2/15*o**5 - 4/3*o**2 - 2/3*o**4 - 4/3*o**3 = 0.
-1
Let v = 26426/2695 - 3/539. Let s = -167/35 - -39/7. Determine y so that s + 4*y + v*y**4 - 3/5*y**2 - 14*y**3 = 0.
-2/7, 1
Let g(z) = -2*z**2 - 9*z + 10. Let f be g(-5). Let v be (-1034)/(-385) - 2/f. Suppose 2/7*h**5 + v*h**3 + 8/7*h**2 + 0 + 10/7*h**4 + 0*h = 0. What is h?
-2, -1, 0
Factor 0*n**3 + 0 - 1/9*n**4 - 2/9*n + 1/3*n**2.
-n*(n - 1)**2*(n + 2)/9
Let m(a) be the third derivative of -a**10/100800 + a**9/40320 - a**5/20 + a**2. Let j(v) be the third derivative of m(v). Factor j(r).
-3*r**3*(r - 1)/2
Suppose -3*y = 2*m - y - 16, -4*y + 26 = 2*m. Let i(g) be the first derivative of 3 - 1/3*g**m - g + g**2. Factor i(w).
-(w - 1)**2
Let u(m) = -26*m**3 + 34*m + 19. Let q(x) = 5*x**3 - 7*x - 4. Let v(r) = -11*q(r) - 2*u(r). Solve v(o) = 0.
-1, 2
Factor -43*r**3 + 36*r**