 + 76*s**3 + 268*s**2 + 258*s + 36. Let m(p) = p**4 + p**3. Let z(o) = 2*f(o) + 44*m(o). Factor z(i).
4*(i + 2)*(i + 3)**2*(6*i + 1)
Let s(o) be the second derivative of 2/15*o**6 + 6*o - 4/5*o**5 + 0 + 0*o**2 - 4/3*o**3 + 5/3*o**4. Find h such that s(h) = 0.
0, 1, 2
Suppose 4*v - r = 4*r + 2, 2*v = r + 4. Factor 18*j - v*j - 9 - 3*j**2 - 3*j.
-3*(j - 3)*(j - 1)
Let u(x) be the second derivative of -x**8/2240 + x**7/840 + x**6/120 + x**4/2 + x. Let b(n) be the third derivative of u(n). Let b(h) = 0. What is h?
-1, 0, 2
Suppose 0 = -15*d + 3 + 72. Let h(l) be the second derivative of -1/70*l**d + 0*l**2 + 3*l + 0 + 1/21*l**3 + 1/28*l**4. Factor h(w).
-w*(w - 2)*(2*w + 1)/7
Let v(h) be the first derivative of 242*h**6/3 + 1628*h**5/5 + 499*h**4 + 1060*h**3/3 + 112*h**2 + 16*h + 43. Find s, given that v(s) = 0.
-1, -2/11
Let b(h) be the second derivative of h**4/24 + h**3/12 - 3*h**2 + 368*h. Factor b(g).
(g - 3)*(g + 4)/2
Let h(y) = y**2 - 23*y - 21. Let a be h(24). Suppose -2*w + 2*j = -0*j + 2, a*j = 4*w + 1. Suppose -6*i + 4 + 3*i**w - 1/2*i**3 = 0. Calculate i.
2
Let y(z) be the third derivative of 1/96*z**4 + 1/12*z**3 - 1/240*z**6 - 1/60*z**5 + 10*z**2 + 1/420*z**7 + 0 + 0*z + 1/1344*z**8. Suppose y(v) = 0. What is v?
-2, -1, 1
Suppose 5*x - 2*i - 31 = 0, -x + 3*i = 2*i - 8. Suppose 5 = -x*j, 8 = 3*f - 3*j + j. Factor -20/3*w**3 - 16/3*w + 32/3*w**f + 4/3*w**4 + 0.
4*w*(w - 2)**2*(w - 1)/3
Let f(x) be the third derivative of -1/40*x**5 - x**2 + 0*x + 0 - 1/4*x**4 + 0*x**3. Find n, given that f(n) = 0.
-4, 0
Suppose -6*q - 4*x + 44 = -2*q, -5*q + x + 25 = 0. Let d(s) = -2*s**3 + s**2 - 3*s - 6. Let u(p) = 3*p**3 + 3*p + 6. Let b(l) = q*d(l) + 5*u(l). Factor b(n).
3*(n - 1)*(n + 1)*(n + 2)
Let m(y) be the third derivative of 0*y - 1/12*y**5 - 5/24*y**4 + 0*y**3 + 1/24*y**6 + 1/42*y**7 - 12*y**2 + 0. Factor m(d).
5*d*(d - 1)*(d + 1)**2
Let k(o) = 4*o + 7. Let g be k(-7). Let t = -18 - g. Factor -3*n**3 + t*n - 4*n**4 + 7*n**4 + 5 - 3*n**2 - 5.
3*n*(n - 1)**2*(n + 1)
Let l(w) = -16*w**4 - 17*w**3 + 21*w**2 - 11*w. Let m(a) = -3*a**4 - 3*a**3 + 4*a**2 - 2*a. Let c(k) = 4*l(k) - 22*m(k). Factor c(v).
2*v**2*(v - 2)*(v + 1)
Let n(p) = -2*p**2 + 15*p + 8. Let k(g) = -3*g**2 + 15*g + 7. Let z(x) = 3*k(x) - 4*n(x). Let b be z(-14). Factor 15*h + 4*h**2 - h**2 + h**b - 13*h.
h*(h + 1)*(h + 2)
Let k(h) be the second derivative of -119*h**4/24 + 59*h**3/3 + h**2 + 169*h. Determine b, given that k(b) = 0.
-2/119, 2
Factor 8*k**5 - 145*k - 16*k**3 - 20*k**4 + 4*k**2 + 44*k**2 + 145*k.
4*k**2*(k - 2)**2*(2*k + 3)
Let w(d) be the second derivative of 58/3*d**3 + 4/3*d**4 + 14*d**2 + 0 - 27*d. Solve w(o) = 0 for o.
-7, -1/4
Suppose 2*q - 6*q + p + 11 = 0, -2*q - p + 13 = 0. Factor -f**4 + 3*f**3 - 2*f**q - 6*f**2 - 12*f**3.
-3*f**2*(f + 1)*(f + 2)
Let u(m) be the second derivative of -m**4/18 - 2*m**3/9 + m**2 + 17*m. Suppose u(c) = 0. Calculate c.
-3, 1
Factor -2*f + 2*f**3 + 64 + 166*f**2 - 92*f**2 - 138*f**2.
2*(f - 32)*(f - 1)*(f + 1)
Suppose -7 = -2*p - 3. Suppose 7 = p*u + 3. Find b, given that b**u + 2*b**2 - 3*b**3 + 7*b - 3*b + 2*b = 0.
-1, 0, 2
Let o be 20/(-6)*(-2 - (-2)/4). Factor 6*g**4 + 6*g**3 + 3*g**5 + g**o - 18*g**4 + 2*g**3.
4*g**3*(g - 2)*(g - 1)
Factor 44 + 460*r - 324*r - 4*r**2 + 16*r**2.
4*(r + 11)*(3*r + 1)
Let z = 33401/40 - 835. Let y(n) be the third derivative of -6*n**4 + 3/5*n**5 - z*n**6 - 8*n**2 + 0 + 0*n + 32*n**3. Factor y(c).
-3*(c - 4)**3
Let o(f) be the first derivative of -9*f**5/20 + 57*f**4/16 - 67*f**3/12 - 65*f**2/8 - 3*f - 182. Determine x, given that o(x) = 0.
-1/3, 3, 4
Factor -1/3*n**5 - 16*n**3 + 13/3*n**4 + 0 + 12*n**2 + 0*n.
-n**2*(n - 6)**2*(n - 1)/3
Let m(y) be the third derivative of -y**5/80 - y**4/2 - 15*y**3/2 + 242*y**2. Factor m(i).
-3*(i + 6)*(i + 10)/4
Let g(w) be the first derivative of 1/6*w**3 + 3/4*w**2 + 20 + w. Suppose g(j) = 0. What is j?
-2, -1
Let g = -342 + 345. Let w(j) be the second derivative of -5/42*j**4 + g*j + 0 + 0*j**2 - 1/105*j**6 - 2/35*j**5 - 2/21*j**3. Find y such that w(y) = 0.
-2, -1, 0
Let a(l) be the third derivative of -l**8/462 + l**7/231 + l**6/220 - l**5/66 + l**4/132 - 44*l**2. Solve a(u) = 0 for u.
-1, 0, 1/4, 1
Let i(h) be the second derivative of -h**7/84 - 7*h**6/60 - h**5/8 + 7*h**4/24 + h**3/2 + 27*h + 3. Suppose i(t) = 0. Calculate t.
-6, -1, 0, 1
Suppose 0*q + 4 = 2*q. Factor 12*x**3 + x**2 + 11*x**3 - 22*x**3 - q*x.
x*(x - 1)*(x + 2)
Suppose -2*v - v + 4*d = -91, 0 = 3*v + 4*d - 59. Suppose v = 3*s + 5*k, -25 = s + 4*s - 5*k. Factor -14/11*h**2 + s + 32/11*h**4 - 2/11*h - 16/11*h**3.
2*h*(h - 1)*(4*h + 1)**2/11
Suppose 4*g + 10 = 2*c, -3*c = 2*g - 0*c + 25. Let v be (-2)/12*(g + 2). Suppose 0*s - 1/2*s**2 + 0 + v*s**3 = 0. Calculate s.
0, 1
Let f be (-2)/8 - (-7)/28. Factor f*t + 3/4*t**2 - 3/4.
3*(t - 1)*(t + 1)/4
Let v(f) be the second derivative of 0*f**2 - 4*f + 1/5*f**3 - 1/20*f**4 + 0. Factor v(u).
-3*u*(u - 2)/5
Let m(t) = t - 6. Let u be m(-6). Let j = u - -17. Factor 3*w + 4*w - 3*w**5 + 4*w**4 - j*w + w**5 - 4*w**2.
-2*w*(w - 1)**3*(w + 1)
Factor -2 - 3*c**2 + 17*c**2 - 6*c**2 - 9*c**2 + 11.
-(c - 3)*(c + 3)
Suppose 3/8*f - 3/4 + 3/8*f**2 = 0. What is f?
-2, 1
Suppose 0 = 78*f + 7 - 48 - 115. Factor 0*n - 2/11*n**f + 2/11.
-2*(n - 1)*(n + 1)/11
Let j(x) be the third derivative of 0*x + 0 + 0*x**5 - 16*x**2 + 1/504*x**8 + 1/360*x**6 - 1/210*x**7 + 0*x**3 + 0*x**4. Factor j(n).
n**3*(n - 1)*(2*n - 1)/3
Let l be 129/(-770) - 4/(-22). Let q(m) be the third derivative of 3*m**4 + 11/10*m**5 + 0*m + 0 + 9/2*m**3 - 6*m**2 + 1/5*m**6 + l*m**7. Factor q(u).
3*(u + 1)**2*(u + 3)**2
Let c be (-1 + -2 - 0)/(-1). Suppose -9*q**3 - 7*q**4 + 0*q**c - 14*q + 10*q**4 + 26*q = 0. Calculate q.
-1, 0, 2
Suppose 0 = -3*q + r + 10, 4*q - 3 = -r + 1. Factor 14*c**2 - 8*c**3 - 7*c**q + 3*c**2 - 2*c.
-2*c*(c - 1)*(4*c - 1)
Let w(s) be the third derivative of -s**6/540 - 13*s**5/270 - 5*s**4/18 - 197*s**2. Let w(a) = 0. Calculate a.
-10, -3, 0
Let y(s) = 55*s + 220. Let c be y(-4). Let q(b) be the first derivative of 1/24*b**3 + 1/48*b**6 + 0*b + 3 + c*b**2 - 1/32*b**4 - 1/40*b**5. Factor q(u).
u**2*(u - 1)**2*(u + 1)/8
Let u(c) be the second derivative of -1/15*c**6 + 12*c + 0*c**3 + 0*c**5 + 0 - c**2 + 1/3*c**4. Factor u(w).
-2*(w - 1)**2*(w + 1)**2
Let b(k) = -3*k - 6. Let c(d) = 4*d + 7. Let l(v) = 5*b(v) + 4*c(v). Let y be l(5). Factor -5*u**2 + 4*u**3 - 11*u - 2*u**2 + 7*u + 4 + y*u**2.
4*(u - 1)**2*(u + 1)
Suppose -5066*c + 5077*c = 22. Let 1/4*l - 1/2 + 1/4*l**c = 0. Calculate l.
-2, 1
Let v(k) be the second derivative of -1/9*k**4 + 2/3*k**2 - 1/30*k**5 + 0 + 1/9*k**3 + 23*k. Factor v(y).
-2*(y - 1)*(y + 1)*(y + 2)/3
Let s be -5 - 1/(-2)*(-4824)/(-252). What is t in -s - 2/7*t**2 - 16/7*t = 0?
-4
Let z = -25 + 1. Let p be z/40*(-10)/7. Factor 3/7*v**2 + p*v + 3/7.
3*(v + 1)**2/7
Let n = -2489 - -2492. Solve -2/3*q**n + 0 + 2*q + 4/3*q**2 = 0.
-1, 0, 3
Let o = -870/7 + 727/21. Let u = 90 + o. Let 8/3*m - 3*m**4 - u - 22/3*m**2 + 8*m**3 = 0. Calculate m.
1/3, 1
Let w be -4 + 24*((-120)/810)/((-2)/3). Factor 8/3*n**2 - 14/3*n - w.
2*(n - 2)*(4*n + 1)/3
Let c(o) be the second derivative of -52*o**5/25 - 34*o**4/15 - 29*o**3/30 - o**2/5 - 3*o + 23. Let c(d) = 0. Calculate d.
-1/4, -2/13
Let m = 107 + -21. Let u = m - 80. Factor -6*i - 2*i**3 + 0 + 2/9*i**4 + u*i**2.
2*i*(i - 3)**3/9
Suppose 0 = 39*o - 91*o - 40*o. Factor -1/6*j**5 + 1/6*j**3 + 0*j**4 + o*j**2 + 0*j + 0.
-j**3*(j - 1)*(j + 1)/6
Let n = 2482 - 2479. Factor -10/3*b**2 - 64/9*b + 2*b**n - 8/3.
2*(b - 3)*(3*b + 2)**2/9
Let f(p) be the first derivative of -7 + 0*p + 8*p**2 + 4/5*p**5 - 4*p**4 - 4/3*p**3. Suppose f(n) = 0. What is n?
-1, 0, 1, 4
Suppose 99*b**2 - 51*b**2 - 45*b**2 + 18 - 15*b = 0. What is b?
2, 3
Let g(s) be the first derivative of 1/7*s**4 - 2/7*s**2 - 8 + 4/21*s**3 - 4/7*s. Factor g(l).
4*(l - 1)*(l + 1)**2/7
Factor -1/11*u**2 + 24/11 - 10/11*u.
-(u - 2)*(u + 12)/11
Let r be (-2220)/(-3256) + 6/(-33). Suppose -r*f**3 + 0 + 1/2*f**2 + 1/6*f**4 - 1/6*f = 0. What is f?
0, 1
Factor -30/13*j + 2/13*j**2 + 0.
2*j*(j - 15)/13
Let c(p) be the second derivative of p**5/160 + 19*p**4/96 - 41*p**3/48 + 21*p**2/16 + p + 94. Factor c(o).
(o - 1)**2*(o + 21)/8
Factor -3/4*r**3 + 0 + 18*r - 69/4*r**2.
