e the second derivative of -k**7/350 - k**6/100 + k**2 + 3*k. Let n(u) be the first derivative of b(u). Factor n(f).
-3*f**3*(f + 2)/5
Let x be 2/1 + (-4 - -6). Let y be x/2*3/2. Determine h, given that 4*h - 8*h**4 - 5*h**5 - 2*h - 2 + 4*h**y + 10*h**2 - h = 0.
-1, 2/5, 1
Suppose -v - 8*v = 0. Let j be ((-2)/4)/(2/(-12)). Solve 4/3*b**2 + v*b + 0*b**j - 2/3 - 2/3*b**4 = 0.
-1, 1
Suppose -2*z + 583 = 2*z + 5*h, z + h = 145. Let t = -992/7 + z. Factor -t*u + 0 + 2/7*u**4 + 2/7*u**3 - 2/7*u**2.
2*u*(u - 1)*(u + 1)**2/7
Suppose -3*w - 2*w + 20 = -4*c, -2*w - 4*c = 20. Determine v so that v - 1/2*v**3 + 1/2*v**2 + w = 0.
-1, 0, 2
Let n(x) be the third derivative of x**10/50400 + x**9/10080 - x**7/840 - x**6/240 + x**5/12 + x**2. Let r(m) be the third derivative of n(m). Factor r(a).
3*(a - 1)*(a + 1)**3
Let z be (0 - 1)*(-3 + (-5)/(-2)). Let 1/2 + 0*i - z*i**2 = 0. What is i?
-1, 1
Let f = -19 + 22. Let h be 5/f - (-11)/(-33). Factor -h*n + 4/3 + 1/3*n**2.
(n - 2)**2/3
Let c(g) be the first derivative of -g**6/15 - 2*g**5/5 - 9*g**4/10 - 14*g**3/15 - 2*g**2/5 + 49. Factor c(x).
-2*x*(x + 1)**3*(x + 2)/5
Let b(v) be the third derivative of v**5/75 - 2*v**4/15 + 8*v**3/15 - 2*v**2. Factor b(i).
4*(i - 2)**2/5
Let x(g) be the third derivative of 4*g**2 - 1/168*g**8 - 1/60*g**6 + 0 - 1/35*g**7 + 1/6*g**4 + 1/10*g**5 + 0*g**3 + 0*g. Let x(a) = 0. Calculate a.
-2, -1, 0, 1
Let n(h) be the first derivative of h**3/3 - 2*h**2 + 3*h - 18. Determine f, given that n(f) = 0.
1, 3
Let h(u) be the first derivative of -4*u**5/5 + 4*u**3/3 + 16. Factor h(t).
-4*t**2*(t - 1)*(t + 1)
Suppose -5*n = 4*r - 10, -1 + 7 = 2*n + 2*r. Let a be 0/4*n/(-4). Determine f, given that a - 1/2*f + 3/4*f**2 + 2*f**3 + 3/4*f**4 = 0.
-2, -1, 0, 1/3
Let k = 12 - 15. Let x be 11/k + 1 + 3. Factor -1/3*n**3 + x - n + n**2.
-(n - 1)**3/3
Determine z so that -12 - 7*z**2 + 3*z**2 + 7*z**2 = 0.
-2, 2
Suppose q = 22*q - 3*q. Factor 3/5 - 6/5*v**2 + 0*v + 3/5*v**4 + q*v**3.
3*(v - 1)**2*(v + 1)**2/5
Let m(h) be the first derivative of 2/9*h**3 + 5 + 0*h + 0*h**2. Solve m(l) = 0 for l.
0
Let b(s) = s - 4. Suppose 3*o + 5*v - 19 = 4*o, 0 = 2*o + 2*v - 22. Let m be b(o). Factor -6*x**4 - 2*x**5 + 3 + 6*x - 4*x**3 - 1 + 0*x**5 + 4*x**m.
-2*(x - 1)*(x + 1)**4
Factor 31*v**3 - 10*v**3 - 7*v**3 - 5*v - 9*v**3.
5*v*(v - 1)*(v + 1)
Let m(y) be the first derivative of y**3/3 + y**2 + y - 3. Determine n so that m(n) = 0.
-1
Let g(x) = -x**4 - x**3 - x - 1. Suppose -3*v = v + 4. Let s(p) = 2*p**4 - 21*p**3 + 12*p**2 + 5*p - 3. Let f(o) = v*s(o) + 3*g(o). Factor f(w).
-w*(w - 2)**2*(5*w + 2)
Suppose -49 = -11*f - 16. Let a(s) be the second derivative of -5/18*s**3 - 1/6*s**2 - 1/18*s**6 + 0 - 1/126*s**7 + f*s - 1/6*s**5 - 5/18*s**4. Solve a(b) = 0.
-1
Let o(f) be the third derivative of f**7/2205 - f**6/210 + 2*f**5/105 - 2*f**4/63 + 8*f**2. Factor o(m).
2*m*(m - 2)**3/21
Let y(m) be the first derivative of 1/11*m**2 + 7 + 0*m - 1/22*m**4 + 2/33*m**3 - 2/55*m**5. What is p in y(p) = 0?
-1, 0, 1
Let i(s) = s. Let x be i(3). Suppose -v = v + 4*y + 2, 0 = v + 3*y + x. Suppose -4*l + v*l + 2 - 5*l + 6*l**2 - 2*l**3 = 0. Calculate l.
1
Let r = -7/12 + 5/6. Factor 0*n**3 + 1/2*n**2 + 0*n - 1/4*n**4 - r.
-(n - 1)**2*(n + 1)**2/4
Factor -3/5*x**2 - 2/5*x**3 + 2/5*x + 0.
-x*(x + 2)*(2*x - 1)/5
Let k(x) be the second derivative of x**5/60 - x**4/9 + 10*x. Factor k(r).
r**2*(r - 4)/3
Suppose -16 = 4*t, 11 = -2*l + 7*l + t. Suppose -2*r - 4 = -3*p, 3*r = -l*p - 2*r + 11. What is m in -2/3*m + 1/3*m**p + 1/3 = 0?
1
Let b(n) = n**3 - 6*n**2 - n + 10. Let s = -8 + 14. Let a be b(s). Factor 0*w + 0 + 0*w**3 - 2/7*w**2 + 2/7*w**a.
2*w**2*(w - 1)*(w + 1)/7
Suppose 8*i - 152 = 4*i. Factor -5 + 84*t**3 + 38*t - i*t**4 + 0 - 1 - 84*t**2 + 6*t**5.
2*(t - 3)*(t - 1)**3*(3*t - 1)
Factor -5*w**3 + 4*w**3 - 11*w**2 + 12*w**2.
-w**2*(w - 1)
Let m = 13482/7403 + -2/673. Factor 20/11*f**2 + 2/11 - m*f**3 - 10/11*f - 2/11*f**5 + 10/11*f**4.
-2*(f - 1)**5/11
Let w(c) = c**3 + 6*c**2 + 5*c + 2. Let h = -8 + 3. Let u be w(h). Factor -2*m**2 - 2*m**u + 5*m**2 + m**3.
m**2*(m + 1)
Suppose -2*i + 23 = -5. Suppose 4*g + 16 = 2*g - 5*s, 0 = -g - 4*s - i. Suppose 0 + 1/5*x**g - 1/5*x + 1/5*x**3 - 1/5*x**4 = 0. What is x?
-1, 0, 1
Let i(f) = -3*f**3 - 2*f**2 + 3*f + 2. Let v(a) = -16*a**3 - 10*a**2 + 16*a + 10. Let p(z) = 11*i(z) - 2*v(z). Let p(k) = 0. What is k?
-2, -1, 1
Let k be (-2)/2*(-2 - 0). Suppose 4*u + 4 = a + k*a, 3*a - u = 10. Factor f**5 - 2*f**3 + 4*f**a - f**5 - 2*f**5.
-2*f**3*(f - 1)**2
Let p(u) be the first derivative of 14*u**5/15 + u**4/3 - 14*u**3/9 - 2*u**2/3 - 18. Let p(q) = 0. What is q?
-1, -2/7, 0, 1
Let l(y) = 3*y**3 + 3*y**2 - 3*y - 7. Let h(w) = -4*w**3 - 2*w**2 + 4*w + 7. Let t(b) = -4*h(b) - 5*l(b). Factor t(k).
(k - 7)*(k - 1)*(k + 1)
Let j(s) be the first derivative of s**7/840 + s**6/160 + s**5/120 + 5*s**2/2 + 5. Let v(c) be the second derivative of j(c). Factor v(b).
b**2*(b + 1)*(b + 2)/4
Find r such that 2*r**2 + r**5 - 3*r**4 + r - 2 + 1 - 2*r**3 + 2*r**4 = 0.
-1, 1
Let p(m) = -m**2 - 12*m + 137. Let x be p(7). Factor b**2 + 0 + 1/3*b**5 - 2/3*b - b**x + 1/3*b**3.
b*(b - 2)*(b - 1)**2*(b + 1)/3
Let w(o) be the third derivative of 0*o**3 + 4*o**2 + 0*o**4 + 0 - 1/120*o**5 + 0*o. Determine p so that w(p) = 0.
0
Let x = 113/218 + -2/109. Factor -3/2*a**2 - 1/2 - 3/2*a - x*a**3.
-(a + 1)**3/2
Let f(x) be the first derivative of 3 + 2*x**2 - x**4 + 0*x + 14/5*x**5 - 14/3*x**3. Factor f(z).
2*z*(z - 1)*(z + 1)*(7*z - 2)
Let f(l) be the third derivative of l**7/70 - 3*l**6/40 + l**4/2 - 5*l**2. Factor f(t).
3*t*(t - 2)**2*(t + 1)
Let r(m) = -2*m**2 - m - 3. Suppose 4 = -4*z + 2*z, -l + 3*z = -12. Let x(h) = 2*h**2 + 2. Let c(j) = l*x(j) + 4*r(j). Factor c(v).
4*v*(v - 1)
Let r = 158 + -158. Factor r + 1/4*p**3 + 1/2*p**4 + 0*p**2 + 0*p - 3/4*p**5.
-p**3*(p - 1)*(3*p + 1)/4
Let q(i) be the third derivative of 1/60*i**4 + 0*i**3 + 3*i**2 + 1/150*i**5 + 0*i + 0. Factor q(o).
2*o*(o + 1)/5
Let j be ((-115)/25 - -4)*(-50)/105. Factor 6/7*q**2 - 6/7*q - 2/7*q**3 + j.
-2*(q - 1)**3/7
Let c(y) be the first derivative of -3/4*y**4 + 0*y + 0*y**2 - 4 + y**3. Factor c(s).
-3*s**2*(s - 1)
Let b(o) be the first derivative of 2*o**3/3 + 4*o**2 - 11. What is c in b(c) = 0?
-4, 0
Let s = -32 + 32. Factor 0 - 2/3*v + s*v**2 + 2/3*v**3.
2*v*(v - 1)*(v + 1)/3
Let b(l) = 3*l + 25. Let r be b(-7). Determine s so that 1/2*s**3 + 2 - 7/2*s**2 - 1/2*s**5 + 3/2*s**r + 0*s = 0.
-1, 1, 2
Suppose 4*k = -0*k - 5*f - 13, 18 = k - 3*f. Let b(p) be the first derivative of 4 + 2*p**2 + 4*p + 1/3*p**k. Factor b(z).
(z + 2)**2
Let f be (0 + -2)*(-12)/8. Let s(m) be the third derivative of -1/160*m**6 + 1/840*m**7 + 0 + 0*m**f - 1/96*m**4 + 0*m - 2*m**2 + 1/80*m**5. Factor s(u).
u*(u - 1)**3/4
Let f = -2 + 6. Let s = 229 - 227. Determine q so that -2/9*q**3 + 0*q + 2/9*q**5 - 2/9*q**s + 0 + 2/9*q**f = 0.
-1, 0, 1
Let o(i) = -i - 3. Let d be o(-6). Solve f**3 + 2*f - d*f + 2*f**2 - 2*f**2 = 0.
-1, 0, 1
Let x(l) be the first derivative of -l**9/12096 - l**8/3360 + l**6/720 + l**5/480 + 4*l**3/3 + 1. Let t(j) be the third derivative of x(j). Factor t(k).
-k*(k - 1)*(k + 1)**3/4
Let s(t) be the first derivative of t**3/9 + t**2/3 - t + 5. Factor s(j).
(j - 1)*(j + 3)/3
Let d = 3/20 + -1/20. Let u(s) be the second derivative of 3/2*s**2 - d*s**6 + 3*s + 0 - 3/10*s**5 + 0*s**4 + s**3. Factor u(q).
-3*(q - 1)*(q + 1)**3
Let l(d) = d**3 + 2*d**2 + 3*d + 6. Let q be l(-2). Factor 9/5*c**4 + q + 7/5*c**5 + 0*c + 0*c**2 + 2/5*c**3.
c**3*(c + 1)*(7*c + 2)/5
Factor 4/3*h**2 - 20/3*h + 8.
4*(h - 3)*(h - 2)/3
Let s be ((-4)/(-2) - 1) + (-50)/(-125). Factor -8/5*m**2 - s*m - 1/5 + 16/5*m**3.
(m - 1)*(4*m + 1)**2/5
Let j(b) = 3*b**2 - 282*b + 1215. Let w(r) = -r**2 + 113*r - 486. Let v(u) = 5*j(u) + 12*w(u). Factor v(z).
3*(z - 9)**2
Factor -39*w**3 - 3*w**5 - 47*w**2 + 1188*w**4 - 1194*w**4 + 69*w - 18 + 93*w**3 - 49*w**2.
-3*(w - 1)**4*(w + 6)
Let t be 6/(140/104 + 2/13). Factor 2/3 + 0*h**2 - 4/3*h**3 + 4/3*h - 2/3*h**t.
-2*(h - 1)*(h + 1)**3/3
Let u(r) = r**2 + 1. Let v(t) be the third derivative of -47*t**5/20 - 7*t**4/2 - t**3 + t**2. Let n(h) = 6*u(h) - v(h). Factor n(y).
3*(7*y + 2)**2
Let 3*b - 46*b - 45*b + 2*b**2 + 0*b**2 + 968 = 0. What is b?
2