et o(k) = s*n(k) - i(k). Factor o(l).
2*(l + 1)*(l + 2)
Let x(d) be the second derivative of 6*d - 2/35*d**5 - 2/7*d**2 + 0 + 11/21*d**3 + 16/105*d**6 - 1/3*d**4 - 1/21*d**7. Suppose x(s) = 0. Calculate s.
-1, 2/7, 1
Let g = -95 - -98. Let o(z) be the second derivative of -g*z + 0*z**2 + 0 + 3/22*z**4 + 2/33*z**3. Factor o(x).
2*x*(9*x + 2)/11
Let a(s) be the first derivative of -5*s**6/6 - 12*s**5 - 165*s**4/4 + 170*s**3/3 + 210*s**2 - 360*s - 261. Solve a(u) = 0.
-6, -2, 1
Suppose -5*a + 3*a - 4*c + 18 = 0, 0 = 2*a + 3*c - 16. Let o(p) = p**3 - 5*p**2 - 6*p + 3. Let q be o(6). Factor r + 4*r**q - 2*r**a + 3*r**5 - r**3 - 5*r**3.
r*(r - 1)**2*(r + 1)**2
Let n(k) be the first derivative of k**5/4 - 5*k**4/6 + 5*k**3/6 + 8*k - 3. Let x(l) be the first derivative of n(l). Factor x(c).
5*c*(c - 1)**2
Suppose -22*j + 2*d + 2 = -20*j, 4*d + 7 = 5*j. Let z(p) be the third derivative of 0 + j*p**2 + 0*p**3 + 1/12*p**5 + 5/24*p**4 + 0*p. Solve z(l) = 0 for l.
-1, 0
Let f(w) be the second derivative of -1/28*w**7 + 0*w**2 + 0*w**3 + 3/40*w**5 + 29 + 1/10*w**6 + 2*w - 1/4*w**4. Find a, given that f(a) = 0.
-1, 0, 1, 2
Suppose -5*v - 273 = -273. Factor -1/9*w**2 - 1/9*w**4 + 2/9*w**3 + v*w + 0.
-w**2*(w - 1)**2/9
Factor 300/7 - 87/7*o + 3/7*o**2.
3*(o - 25)*(o - 4)/7
Let x(u) be the second derivative of -u**6/2520 + u**5/168 - u**4/28 - 11*u**3/6 - 13*u. Let z(k) be the second derivative of x(k). Let z(h) = 0. Calculate h.
2, 3
Let y(s) be the first derivative of 2/9*s**3 + 0*s - 1/15*s**5 + 0*s**2 - 4 + 1/12*s**4. Factor y(n).
-n**2*(n - 2)*(n + 1)/3
Solve 2/9*i**3 + 32/3*i + 8 + 26/9*i**2 = 0 for i.
-6, -1
Let w(a) = -2*a**2 + 4*a - 8. Let y(i) = -8*i**2 + 15*i - 34. Let c(h) = 9*w(h) - 2*y(h). Factor c(d).
-2*(d - 2)*(d - 1)
Suppose -2/15*w**2 + 8/15 + 2/5*w = 0. Calculate w.
-1, 4
Let h(x) be the second derivative of 2/3*x**3 + 3/2*x**2 + 0 + 19*x - 1/4*x**4 - 1/5*x**5. Determine m so that h(m) = 0.
-1, -3/4, 1
Let q be (2/4)/((-3)/(-24)). Factor -285*u + 10*u**5 + 285*u + 4*u**5 - 10*u**q - 4*u**3.
2*u**3*(u - 1)*(7*u + 2)
Suppose -209*b + 102 = -158*b. Factor -8/7*c**4 - 10/7*c + 4/7*c**b + 4/7 + 2/7*c**5 + 8/7*c**3.
2*(c - 2)*(c - 1)**3*(c + 1)/7
Let k(i) be the first derivative of -i**4 - 12*i**3 - 12*i**2 + 64*i - 195. Factor k(d).
-4*(d - 1)*(d + 2)*(d + 8)
Suppose -3*m = 24 - 18, -2*n = -m - 6. Let w(i) be the second derivative of -3*i + 1/160*i**5 + 0*i**n + 0 + 0*i**3 + 0*i**4 - 1/240*i**6. Factor w(b).
-b**3*(b - 1)/8
Let v(u) be the third derivative of -u**6/100 - u**5/10 - 5*u**4/12 + 19*u**3/6 + 12*u**2. Let j(w) be the first derivative of v(w). Solve j(m) = 0 for m.
-5/3
Let d(c) = -c**3 + 11*c**2 - 22*c + 39. Let p be d(9). Let r(z) be the first derivative of -2/33*z**p + 2/11*z**2 - 13 + 6/11*z. Factor r(f).
-2*(f - 3)*(f + 1)/11
Suppose 5*r - 14 = 5*q + 1, 0 = 4*q. Factor -2/5*p**5 + 0 + 0*p + 0*p**2 + 0*p**4 + 2/5*p**r.
-2*p**3*(p - 1)*(p + 1)/5
Let l(x) be the first derivative of 8/3*x**3 + 8/5*x**5 + 0*x + 6 + 5*x**4 + 0*x**2. Factor l(h).
4*h**2*(h + 2)*(2*h + 1)
Suppose 0 + 36/11*d**3 + 112/11*d - 120/11*d**2 - 2/11*d**4 = 0. What is d?
0, 2, 14
Let k(m) be the first derivative of -3*m**4 + 424*m**3/3 - 1800*m**2 - 2592*m - 46. Factor k(q).
-4*(q - 18)**2*(3*q + 2)
Let i(f) be the third derivative of 5*f**8/1008 + f**7/126 - f**6/24 - 5*f**5/36 - 5*f**4/36 - 18*f**2. Factor i(x).
5*x*(x - 2)*(x + 1)**3/3
Find j, given that 32 + 32*j**4 - 2/3*j**5 - 2/3*j - 64*j**2 + 4/3*j**3 = 0.
-1, 1, 48
Let d(u) be the second derivative of -u**6/6 - 11*u**5/2 - 605*u**4/12 + 140*u. Let d(r) = 0. Calculate r.
-11, 0
Let n(o) be the second derivative of o**5/80 + o**4/24 + o**3/24 - 2*o + 24. Factor n(g).
g*(g + 1)**2/4
Let g(o) be the third derivative of o**8/4032 + 5*o**7/252 + 25*o**6/36 + 3*o**5/10 - 17*o**2. Let f(q) be the third derivative of g(q). Factor f(x).
5*(x + 10)**2
Let t(o) be the first derivative of o**8/1680 + o**7/420 + o**6/360 + 10*o**3/3 - 2. Let l(f) be the third derivative of t(f). Factor l(y).
y**2*(y + 1)**2
Let r = -103/20 + 111/20. Factor r*n**2 + 0 + 8/5*n.
2*n*(n + 4)/5
Factor -i**4 - 916 - 2*i**3 + 916 + 5*i**3 - 3*i + i**2.
-i*(i - 3)*(i - 1)*(i + 1)
Let f(u) = 3*u + 2*u**3 - 5*u + 5*u + 11*u - 16*u**2. Let x be f(7). Factor 3/2*l**5 - 3/2*l**3 + 0*l**2 + x*l**4 + 0 + 0*l.
3*l**3*(l - 1)*(l + 1)/2
Suppose 3*a = 3*a - 9*a + 18. Determine k, given that -5 + 7/2*k - 1/2*k**a = 0.
2, 5
Factor -2/3*l + 2/3*l**3 + 20/3*l**2 - 20/3.
2*(l - 1)*(l + 1)*(l + 10)/3
Let u(s) = -s**3 + 7*s**2 - 16. Let n be u(5). Suppose -2*d = -z - 5*d + 18, -3*z + n = 5*d. Factor -9*t**2 + 3*t**z + 4*t**3 + 1 + 5*t - 2 - 2*t**4.
-(t - 1)**3*(2*t - 1)
Let y be 1 - (-1)/3*0/2. Let g be (1 - y)/(-2) + 26/52. Factor g*c + 0 + 0*c**2 + 1/2*c**5 - c**3 + 0*c**4.
c*(c - 1)**2*(c + 1)**2/2
Let 3/4*s**3 + 9*s - 9/2*s**2 - 6 = 0. Calculate s.
2
Determine o, given that 2 + 56*o**5 + 10 - 8*o**4 - 53*o**5 + 21*o**3 + 3*o**2 - 7*o**4 - 24*o = 0.
-1, 1, 2
Let w = 1/2064 - -24761/14448. Factor -4/7*r**2 + w - 10/7*r + 2/7*r**3.
2*(r - 3)*(r - 1)*(r + 2)/7
Let q(u) be the third derivative of u**6/90 - u**5/15 - u**4/2 + u**3/2 - 17*u**2. Let j(b) be the first derivative of q(b). Let j(h) = 0. What is h?
-1, 3
Let w(p) = -p**3 - 5*p**2 - 3*p + 12. Let h be w(-5). Let q be ((-6)/h)/((-3)/27). Factor 4/5*i + 0 + 2/5*i**q.
2*i*(i + 2)/5
Let j = 24905 + -123349/5. Factor 4/5*l**4 + 9604/5 + 112/5*l**3 + j*l**2 + 5488/5*l.
4*(l + 7)**4/5
Let r(q) be the third derivative of q**6/600 - 7*q**4/120 - q**3/5 - 31*q**2. Suppose r(k) = 0. What is k?
-2, -1, 3
Let l(g) be the second derivative of g**6/150 + 9*g**5/100 + 9*g**4/20 + 9*g**3/10 + g + 19. Find r, given that l(r) = 0.
-3, 0
Let y = -76 + 80. Factor 4*f + 2*f**y + 2 - 4*f**3 - 5 + 4 - 3.
2*(f - 1)**3*(f + 1)
Factor -3/5*q**4 + 0*q + 0 + 6/5*q**2 - 3/5*q**3.
-3*q**2*(q - 1)*(q + 2)/5
Let m(d) be the third derivative of d**6/2880 + d**5/80 + 3*d**4/16 + 8*d**3 + 21*d**2. Let w(z) be the first derivative of m(z). Find y such that w(y) = 0.
-6
Let v = -7/15 - -41/75. Let n(g) be the first derivative of -1/20*g**4 - v*g**5 + 0*g**3 - 1/30*g**6 - 12 + 0*g + 0*g**2. What is w in n(w) = 0?
-1, 0
Let p(s) be the third derivative of 0 + 7/6*s**4 + 0*s + 1/3*s**5 + 42*s**2 + 4/3*s**3. Factor p(i).
4*(i + 1)*(5*i + 2)
Let f(w) = 2*w**3 + w + 1. Let g(h) = -11*h**3 - 4*h**2 + 6*h - 11. Let z(s) = 5*f(s) + g(s). Find c such that z(c) = 0.
-6, 1
Factor -12/5*i**3 - 147/5*i - 156/5*i**2 - 36/5.
-3*(i + 12)*(2*i + 1)**2/5
Find d such that -12*d + 191*d**2 + 89*d**3 + 8 - 64*d**4 - 315*d**2 + 103*d**3 = 0.
-1/4, 1/4, 1, 2
Factor -13/2*n**2 - 5*n + 0 + 1/2*n**4 - n**3.
n*(n - 5)*(n + 1)*(n + 2)/2
Let r(q) = -3*q**3 - 13*q**2 + 55*q - 83. Let o(c) = -5*c**3 - 26*c**2 + 110*c - 164. Let g(j) = 4*o(j) - 7*r(j). Factor g(z).
(z - 5)**2*(z - 3)
Suppose -2*v = v - 42. Let i be 7/v + (-3)/(-2). Determine r, given that 2 + 18*r**3 + 9*r**4 + r**3 - 6*r + i*r**3 - 3*r + r**2 = 0.
-2, -1, 1/3
Let y(i) be the first derivative of 10*i - 9 - 55/2*i**2 - 5*i**4 + 65/3*i**3. Determine x, given that y(x) = 0.
1/4, 1, 2
Factor -256 - 1/4*w**2 + 16*w.
-(w - 32)**2/4
Let n(a) be the first derivative of -a**3 + 33*a**2/2 - 72*a + 149. Suppose n(t) = 0. What is t?
3, 8
Suppose 4*q + 3*r - 16 = -r, 5*q = -4*r + 23. Let u(x) = x**3 - 7*x**2 + 2*x - 9. Let p be u(q). Let 5*o - o**2 + 19*o + p*o**2 + 30 + 6 = 0. Calculate o.
-3
Find c such that -43732/7*c - 172/7*c**3 - 2/7*c**4 - 696*c**2 + 48778/7 = 0.
-29, 1
Let y(x) be the third derivative of -x**6/40 + x**5/10 - x**4/8 - 117*x**2. Factor y(i).
-3*i*(i - 1)**2
Find h, given that h**2 + 0*h - 1/2*h**4 + 0*h**3 - 1/2 = 0.
-1, 1
Let o(j) be the third derivative of 5*j**8/336 + 3*j**7/14 + 31*j**6/24 + 17*j**5/4 + 25*j**4/3 + 10*j**3 - 318*j**2. Suppose o(b) = 0. What is b?
-3, -2, -1
Suppose -35 = -5*z - 10. Suppose -z*u + 15 = -5. Let 4*m + 48*m**u + 50*m**4 - 9*m**3 + 2*m**3 - 20*m**2 = 0. Calculate m.
-1/2, 0, 2/7
Let i(l) be the third derivative of l**5/20 + 49*l**4/4 - l**2 + 9*l. Let i(u) = 0. Calculate u.
-98, 0
Let j(y) be the second derivative of 0*y**2 + 5*y + 1/357*y**7 - 1/255*y**6 + 0 + 0*y**4 - 1/85*y**5 + 0*y**3. Factor j(b).
2*b**3*(b - 2)*(b + 1)/17
Let m(l) = -7*l**5 + 21*l**4 +