e o, given that n(o) = 0.
-3/2
Let x(s) be the third derivative of -s**9/10080 - s**8/1680 - s**7/720 - s**6/720 - s**4/8 - s**2. Let a(h) be the second derivative of x(h). Factor a(i).
-i*(i + 1)**2*(3*i + 2)/2
Let u(x) be the first derivative of 8*x**3/3 - 2*x**2/3 - 358. Factor u(y).
4*y*(6*y - 1)/3
Let x(t) be the second derivative of t**5/50 - t**4/2 - t**3/15 + 3*t**2 + 735*t. Factor x(l).
2*(l - 15)*(l - 1)*(l + 1)/5
Let r(s) be the third derivative of -7*s**5/330 + 257*s**4/132 + 74*s**3/33 + 7*s**2 - 3. Factor r(a).
-2*(a - 37)*(7*a + 2)/11
Let s(r) be the third derivative of 0*r - r**2 + 0 + 0*r**6 + 1/140*r**5 - 1/1470*r**7 + 1/84*r**4 + 0*r**3. Let s(p) = 0. What is p?
-1, 0, 2
Let w(g) = g**3 - 15*g**2 + 18*g + 106. Let z be w(13). Factor -9/4*b + 9/4*b**3 + 3/2 - 3/2*b**z.
3*(b - 1)*(b + 1)*(3*b - 2)/4
Let a be 11/(77/(-70)) + 12. Factor -x**a + 1/2*x**5 + 3/2*x**4 + x**3 - 1/2 - 3/2*x.
(x - 1)*(x + 1)**4/2
Factor 2*x**3 + 17*x**2 + 2*x**3 - 8*x**3 + 39*x**2.
-4*x**2*(x - 14)
Let k(u) = 3*u**2 - 6*u - 6. Let m = -112 - -115. Let d(p) = -3*p**2 + 5*p + 4. Let h(t) = m*d(t) + 4*k(t). Solve h(b) = 0.
-1, 4
Let b(k) be the first derivative of -k**7/6720 - k**6/2880 - 13*k**3/3 + 19. Let n(o) be the third derivative of b(o). Factor n(c).
-c**2*(c + 1)/8
Suppose 13*z - 56 = 9. Suppose g - v = -1, -z*g - 4*v + 2 = -2. Factor -5/2*u**3 - 5*u**2 + 15/2*u + g.
-5*u*(u - 1)*(u + 3)/2
Let i = 983 + -977. Let b(s) be the second derivative of 1/3*s**2 + 5/72*s**4 + 0 + 1/120*s**5 + i*s + 2/9*s**3. Suppose b(m) = 0. What is m?
-2, -1
Find w such that 0 + 12/7*w - 24/7*w**2 + 15/7*w**3 - 3/7*w**4 = 0.
0, 1, 2
Factor 19*l + 96/5 - 1/5*l**2.
-(l - 96)*(l + 1)/5
Let s(g) be the third derivative of -g**5/30 + 35*g**4/12 - 34*g**3/3 - 130*g**2. Factor s(v).
-2*(v - 34)*(v - 1)
Let b(p) be the second derivative of -p**6/105 - 12*p**5/35 - 33*p**4/7 - 216*p**3/7 - 729*p**2/7 - 8*p + 2. Determine y so that b(y) = 0.
-9, -3
Let f(j) = -22*j + 114. Let y be f(5). Let t(g) be the second derivative of 1/3*g**y - 2*g**2 + 2/3*g**3 + 13*g - 1/5*g**5 + 0. Factor t(m).
-4*(m - 1)**2*(m + 1)
Let d(k) be the first derivative of -k**6/6 + 6*k**5/5 - 9*k**4/4 + 4*k**3/3 - 199. Factor d(b).
-b**2*(b - 4)*(b - 1)**2
Suppose 0 = 5*o - 11*o. Suppose -11*l + 7*l + 12 = o. Factor 2*z**l - 6*z**3 + 0*z**3.
-4*z**3
Let u(a) = -a**4 + a**3 - a**2 + a + 1. Let j(f) = 1 + 41*f**3 + f - f**4 - 42*f**3 - f**4 - 2*f**2. Let c(h) = j(h) - u(h). Factor c(o).
-o**2*(o + 1)**2
Let u(n) = -2*n**2 + 6*n + 23. Let b be u(5). Suppose 2*y = -2*z + b*z + 1, 2*z - 2 = 2*y. Factor 8/7*x + 1/7*x**z + 4/7 + 5/7*x**2.
(x + 1)*(x + 2)**2/7
Let u(y) be the second derivative of -y**7/70 - 3*y**6/20 - 9*y**5/20 + 8*y**2 + 19*y. Let a(n) be the first derivative of u(n). Factor a(g).
-3*g**2*(g + 3)**2
Suppose 0 = 17*m + 10*m - 27. Factor -1/5*i**2 - m - 6/5*i.
-(i + 1)*(i + 5)/5
Let t = -45 + 56. Let z(c) = c**2 - 10*c - 9. Let x be z(t). Solve -5/3*o**4 - 2/3*o - 1/3*o**x + 0 + 8/3*o**3 = 0.
-2/5, 0, 1
Let t(x) be the first derivative of 2*x**3/9 - 3*x**2 + 16*x/3 - 148. Suppose t(l) = 0. What is l?
1, 8
Find q such that -1/11*q**2 + 10/11 + 3/11*q = 0.
-2, 5
What is y in -1202/5*y**3 + 26*y**4 - 4/5*y**5 - 66*y + 2306/5*y**2 - 180 = 0?
-1/2, 1, 2, 15
Let y(g) be the first derivative of 15 - 3/8*g**2 - 1/16*g**4 - 1/3*g**3 + 0*g. Factor y(f).
-f*(f + 1)*(f + 3)/4
Let v(j) = -155*j**4 + 375*j**3 + 285*j**2 - 725*j - 660. Let i(x) = 7*x**4 - 17*x**3 - 13*x**2 + 33*x + 30. Let a(b) = 45*i(b) + 2*v(b). Factor a(h).
5*(h - 3)*(h - 2)*(h + 1)**2
Suppose -184*z = -199*z. Determine c, given that -2/7*c**2 + 2/7 + z*c = 0.
-1, 1
Let u = 102 + -102. Let k(m) be the first derivative of -4/5*m**5 + 3/2*m**4 + 3 + u*m + 1/2*m**2 - 4/3*m**3 + 1/6*m**6. Factor k(w).
w*(w - 1)**4
Let m(g) be the first derivative of -g**4/15 + 4*g**3/15 - 6*g - 7. Let c(q) be the first derivative of m(q). What is u in c(u) = 0?
0, 2
Let c(y) be the first derivative of y**5/20 + 9*y**4/16 + 25*y**3/12 + 27*y**2/8 + 5*y/2 - 117. Let c(a) = 0. What is a?
-5, -2, -1
Suppose -y = -3*y. Let l be 2 + 0/(-1 + y). Let 6*w - 2 - w + 11*w**3 - 3*w**l + w**4 - 12*w**3 = 0. Calculate w.
-2, 1
Suppose -12*b + 13*b + 2*d + 4 = 0, -4*b - 3*d + 4 = 0. Let f(c) be the third derivative of 0 + 1/480*c**5 + 1/96*c**b + 0*c - 6*c**2 - 1/16*c**3. Factor f(a).
(a - 1)*(a + 3)/8
Let g = 2084/5 - 14568/35. What is u in -4/7*u**2 - g - 10/7*u = 0?
-2, -1/2
Find s, given that 18/13*s - 2/13*s**2 + 0 = 0.
0, 9
Suppose 2*c + 77 = c + 5*f, -4*c - 350 = f. Let s = c - -87. What is r in 2/15*r**2 + s*r - 2/15 = 0?
-1, 1
Let k(b) be the third derivative of -b**5/15 - 11*b**4/6 - 56*b**3/3 - 460*b**2. Solve k(v) = 0.
-7, -4
Suppose -177 = -4*j + 459. Let -34*y**2 + 24*y + 31*y**2 + 12 - 42*y**2 - 45*y**5 - 147*y**4 - j*y**3 = 0. What is y?
-1, -2/3, 2/5
Factor -10*v**2 + 12*v**2 + 8*v - 6*v**2.
-4*v*(v - 2)
Let w = -1957 - -1959. Find q such that -w*q**4 + 2 + 3/2*q**2 + 13/2*q - 8*q**3 = 0.
-4, -1/2, 1
Let m(s) be the first derivative of 3*s**7/280 - 11*s**6/120 + 3*s**5/10 - s**4/2 - 2*s**3/3 + 2. Let b(p) be the third derivative of m(p). Factor b(d).
3*(d - 2)*(d - 1)*(3*d - 2)
Let z = -4/785 + 10213/1570. Factor 7/2*f**4 + 27/2*f**2 - 23/2*f**3 - z*f + 1.
(f - 1)**3*(7*f - 2)/2
Let j(q) be the third derivative of 0*q + 0*q**3 + 0*q**4 - 1/300*q**6 + 1/300*q**5 - 10*q**2 + 0 + 1/1050*q**7. Factor j(a).
a**2*(a - 1)**2/5
Let o = -1189/3 - -9566/15. Let r = o - 241. Let -r - 4/5*y + 2/5*y**4 + 0*y**2 + 4/5*y**3 = 0. What is y?
-1, 1
Let y be (-15)/8 - (-23)/(-184). Let r be (4/9)/y + 2002/504. Factor r*c**3 + 9/4*c**5 + 0*c - 3/4*c**2 + 0 - 21/4*c**4.
3*c**2*(c - 1)**2*(3*c - 1)/4
Solve -9*f**4 - 3*f**2 - f**2 - 3*f**5 + 4*f**2 - 67*f**3 + 79*f**3 = 0.
-4, 0, 1
Let c = -1543 + 23161/15. What is v in -4/15*v**2 + c*v**4 + 0*v - 2/15*v**3 + 0 - 2/3*v**5 = 0?
-2/5, 0, 1
Let n be 0 + (-3 + 8/4)/(-1). Let k be (n/1)/((-15)/(-6)). Solve 4/5 + 28/5*q**3 + 12/5*q**4 + 32/5*q**2 + k*q**5 + 18/5*q = 0.
-2, -1
Suppose 5*j + 15 = 5*z, -2*j - 11 = -3*z + 3*j. Factor 4*o**3 + o - 9*o + 6*o - z*o**5.
-2*o*(o - 1)**2*(o + 1)**2
Factor 0*p**4 + 0 - 1/3*p**5 + 0*p**2 + 2/3*p**3 - 1/3*p.
-p*(p - 1)**2*(p + 1)**2/3
Let u(t) = 76*t**2 - 736*t - 67706. Let d(k) = 63*k**2 - 736*k - 67707. Let b(g) = 6*d(g) - 5*u(g). Factor b(o).
-2*(o + 184)**2
Let l(f) be the second derivative of -3*f**5/40 - 5*f**4/24 + f**3/6 - 43*f. What is p in l(p) = 0?
-2, 0, 1/3
Let i(c) = -143*c**2 - 254*c + 64. Let m(y) = 2000*y**2 + 3555*y - 890. Let z(q) = 55*i(q) + 4*m(q). Solve z(s) = 0.
-2, 4/27
Suppose -9*o + 40 = 166. Let d be -3 + (-16)/(-4) + o/18. Suppose d*a**3 - 2/9*a + 0*a**2 + 0 = 0. Calculate a.
-1, 0, 1
Suppose -11*f - 16*f**5 + f**3 + 22*f - f**2 - 11*f + 16*f**4 = 0. Calculate f.
-1/4, 0, 1/4, 1
Factor 18*l - 22*l**3 + 25*l**3 - 48*l - 9*l**2.
3*l*(l - 5)*(l + 2)
Let o(s) be the first derivative of -2/3*s**3 + 3*s**2 + 8*s - 32. Factor o(p).
-2*(p - 4)*(p + 1)
Suppose -b + 12 = b. Suppose -4*m + 31 = -5*r, 5*m + b*r - 5 = r. Suppose -m + 6*w + 2 + 0*w**2 + 6 + 2*w**2 = 0. Calculate w.
-2, -1
Let n(i) be the first derivative of -i**4/30 + 2*i**3/3 - 5*i**2 + 12*i - 1. Let t(p) be the first derivative of n(p). Let t(v) = 0. What is v?
5
Let p be ((-957)/(-145) - 7) + 0 + 12/5. Factor 2/5*c**3 - 1/10*c**4 + 0 + 1/2*c**p + 0*c.
-c**2*(c - 5)*(c + 1)/10
Let t(r) be the first derivative of r**5/80 - 5*r**4/48 + r**3/3 - r**2/2 - 6*r + 7. Let p(v) be the first derivative of t(v). Factor p(s).
(s - 2)**2*(s - 1)/4
Let p be (0/(-4))/(-4 - -3) + 2. Let x(j) be the first derivative of p + 1/7*j**2 - 4/7*j + 4/21*j**3 - 1/14*j**4. What is n in x(n) = 0?
-1, 1, 2
Let t(k) = k**3 + 12*k**2 - 46*k - 19. Let m be t(-15). Let j be (2/(2/(-40)*m))/2. Factor -1/2*i**4 - 27*i - 27/2 - j*i**3 - 18*i**2.
-(i + 1)*(i + 3)**3/2
Let i be 2/9 - 250/(-90). Factor -10*g**2 - 20*g**3 - i*g**4 + 36*g - g**4 - 2*g**2.
-4*g*(g - 1)*(g + 3)**2
Solve 3*t**3 - 48*t**2 - 36*t - 15*t - 4*t**3 + 4*t**3 = 0.
-1, 0, 17
Suppose -5*d = -6 + 26. Let w(l) = -l**2 - 4*l + 3. Let k be w(d). Let 5*m**2 + k*m**2 + 8*m**3 + 0*m**2 + 2*m**4 = 0. Calculate m.
-2, 0
Let n be 9 + 1108/(-136) + (-2)/4. Let n*u**2 + 8/17*u**3 + 0 - 2/17*u**4