o) be the first derivative of 1/4*o + 3/8*o**2 - 3/20*o**5 - 1/24*o**6 - 1/8*o**4 + 7 + t*o**3. Factor f(m).
-(m - 1)*(m + 1)**4/4
Let z = -85/36 + 28/9. Let x(g) be the first derivative of -z*g**2 + 3/8*g**4 - 6 + 0*g + 3/10*g**5 - 1/2*g**3. Factor x(k).
3*k*(k - 1)*(k + 1)**2/2
Let u(i) be the second derivative of i**5/4 - 65*i**4/6 + 545*i**3/6 - 210*i**2 + 127*i. Suppose u(j) = 0. What is j?
1, 4, 21
Let y(c) be the first derivative of -c**6/36 - 7*c**5/30 - 3*c**4/4 - 10*c**3/9 - 2*c**2/3 - 319. Suppose y(f) = 0. Calculate f.
-2, -1, 0
Let o(p) = -3*p**2 + 34*p - 6. Let u be o(11). Let y be 90/100 - 2/u. Let -y*g - 1/2*g**2 + 1/2*g**3 + 1/2 = 0. What is g?
-1, 1
Let b(i) be the third derivative of 0 + 0*i**3 - 1/30*i**6 - 3/2*i**4 - 2/5*i**5 - 9*i**2 + 0*i. Factor b(x).
-4*x*(x + 3)**2
Let r(c) be the third derivative of c**6/72 + c**5/4 + 25*c**4/24 + 3*c**3/2 + 19*c**2. Let w(d) be the first derivative of r(d). Factor w(g).
5*(g + 1)*(g + 5)
Let k = -6908780 - -6977869007/1010. Let u = 1/202 + k. Factor 0*s**3 + 0 + u*s**2 - 6/5*s**4 + 3/5*s - 3/5*s**5.
-3*s*(s - 1)*(s + 1)**3/5
Let h(x) be the third derivative of -x**6/60 - x**5/60 - x**4/24 + 5*x**2. Let j be h(-1). Factor j*s**2 - 6 + 3 - 6*s + 7.
2*(s - 2)*(s - 1)
Let a(c) be the third derivative of -c**7/105 + c**6/6 - 3*c**5/10 + 104*c**2 - 3*c. Determine s so that a(s) = 0.
0, 1, 9
Let n be ((-10)/(-4))/((-11)/(-22)). Determine z, given that -1 - 4*z**2 + 37*z**5 - 39*z**n + 5*z**4 + z**3 - 3*z**3 + 4*z = 0.
-1, 1/2, 1
Let x be -7 - (-6 - -2 - 11/3). Let g(o) be the third derivative of 1/15*o**5 + 0 - x*o**4 + 0*o + 8/3*o**3 + 10*o**2. Determine q so that g(q) = 0.
2
Let z = 8 - 33. Let o = 25 + z. Suppose 3/2*u**4 - 2*u**5 + o + 3/4*u**3 + 0*u - 1/4*u**2 = 0. What is u?
-1/2, 0, 1/4, 1
Suppose -7*u**2 + 56*u - 19*u**3 - 4*u**4 + 174*u**2 + 239*u**3 + 56*u**2 = 0. Calculate u.
-1/2, 0, 56
Suppose 5*o = -3*m + 21, 5 = -5*o - 4*m + 28. Suppose -2*k + 1 + o = 0. Factor 0*t**k + 1/2 - 3/4*t + 1/4*t**3.
(t - 1)**2*(t + 2)/4
Suppose -2*d + 11 - 5 = 0. Suppose 8*n = d*n + 10. Solve -4*m**4 + n*m**3 + 8*m**2 - 8*m**3 + 8*m + 3 - 3 + 2*m**5 = 0 for m.
-1, 0, 2
Suppose 7*l - l + 1710 = 0. Let t = -280 - l. Find y, given that 4/5*y**2 + 0*y + 0 + 2/5*y**t - 4/5*y**4 - 2/5*y**3 = 0.
-1, 0, 1, 2
Let j(f) = 3*f**3 - 22*f**2 - 12*f - 8. Let m(c) = -4*c**3 + 23*c**2 + 11*c + 6. Let g(s) = 3*j(s) + 4*m(s). Suppose g(d) = 0. What is d?
-2/7, 0, 4
Let -10/7*x**4 + 10/7*x**3 + 2/7*x**5 - 12/7*x + 0 + 10/7*x**2 = 0. What is x?
-1, 0, 1, 2, 3
Let g(b) be the second derivative of b**4/144 - b**3/72 - b**2/12 + b - 71. Factor g(v).
(v - 2)*(v + 1)/12
Let q(g) be the second derivative of g**7/231 + 9*g**6/55 + 119*g**5/110 + 205*g**4/66 + 52*g**3/11 + 4*g**2 - 4*g + 31. Determine j, given that q(j) = 0.
-22, -2, -1
Let l be 0 - ((-5)/3 + 2/(-6)). Let o be (l/(-5))/((-3)/30). Suppose 0 + 5/2*a**o - a + 1/2*a**2 + 4*a**3 = 0. What is a?
-1, 0, 2/5
Let c(w) be the second derivative of w**7/420 - w**6/80 + w**5/40 - w**4/48 - 5*w**2 + 6*w. Let m(z) be the first derivative of c(z). What is t in m(t) = 0?
0, 1
Factor -110*f**2 - 186*f**2 - 132*f**2 - 136*f**2 - 19600 + 20160*f + 4*f**3.
4*(f - 70)**2*(f - 1)
Let y(v) be the first derivative of 3*v**4/28 - 11*v**3/7 + 36*v**2/7 + 108*v/7 + 674. What is d in y(d) = 0?
-1, 6
Factor 16226 + 285*o + 2*o**2 - 409*o - 304*o + 6672.
2*(o - 107)**2
Suppose 0 + 6*l**2 - 16/15*l**3 - 2/15*l**4 - 24/5*l = 0. Calculate l.
-12, 0, 1, 3
Let z = 88 + -86. Solve 9*l**3 - 3*l**4 + 2*l**2 - l**2 - 7*l + 6 - 2*l - 4*l**z = 0.
-1, 1, 2
Let n(l) = 3*l - 9 - 9*l**3 - 17*l**2 + 22*l**3 + 6*l**3 + 14. Let m(a) = 10*a**3 - 9*a**2 + 2*a + 3. Let s(h) = 5*m(h) - 3*n(h). What is c in s(c) = 0?
-1/7, 0, 1
Let x(l) be the third derivative of 4/15*l**5 + 1/6*l**3 + 0*l + 0 - 10*l**2 + 1/3*l**4. Factor x(w).
(4*w + 1)**2
Let x(h) be the second derivative of -19*h**5/40 + 5*h**4/3 - 23*h**3/12 + h**2/2 - h + 17. Factor x(f).
-(f - 1)**2*(19*f - 2)/2
Let w(d) be the second derivative of 0 - 3/2*d**2 + 1/8*d**4 + 3*d + 1/4*d**3. Find u such that w(u) = 0.
-2, 1
Let f(n) = -n + 7. Let q be f(6). Let d(g) = -2*g**3 + 12*g**2 - 10*g - 8. Let b(a) = a**3 - a**2 + a + 1. Let w(u) = q*d(u) + 8*b(u). Factor w(x).
2*x*(x + 1)*(3*x - 1)
Let j(y) be the second derivative of 0*y**2 + 0*y**3 - 1/40*y**5 + 9*y - 1/240*y**6 - 1/24*y**4 + 0. Factor j(i).
-i**2*(i + 2)**2/8
Let t be 6 + (-1)/1 + 0. Let k = -386 + 391. Factor -b**5 - 2*b**5 + b**3 - 3*b**k + 5*b**t.
-b**3*(b - 1)*(b + 1)
Suppose 4/7*k**2 + 264/7*k + 260/7 = 0. What is k?
-65, -1
Let h = 2/18857 - -75406/207427. What is i in 6/11*i**3 - 6/11*i - 2/11*i**2 - 2/11*i**4 + h = 0?
-1, 1, 2
Let p(l) = l**3 - 6*l**2 + 4*l + 5. Let x be p(5). Suppose -d + 2 + 1 = x. Find b such that d*b**2 - 2*b**2 - 3*b**4 + 2*b**2 = 0.
-1, 0, 1
Factor 0*y**2 + 8/9*y**3 - 8/9*y + 4/9 - 4/9*y**4.
-4*(y - 1)**3*(y + 1)/9
Let g(o) be the first derivative of -3*o**5/20 + 21*o**4/4 - 60*o**3 + 150*o**2 + 1500*o - 328. Let g(s) = 0. Calculate s.
-2, 10
Let t be -2*(21/(-6) + 3). Let s(d) = 3*d + 1. Let a be s(t). Find w such that 6*w + 2*w**3 + 4*w**a - 4*w**2 - 2*w - 6*w**3 = 0.
-1, 0, 1
Let d = 40 - 3. Suppose 16*z - 17*z + d = 0. Factor 2*j**2 + 2*j**2 - j**3 + 5*j**3 + 29*j - z*j.
4*j*(j - 1)*(j + 2)
Let f be (14 + 3)/(-1*(-1)/2). Factor -30*d**2 - 5*d + 8*d**5 + f*d**2 - 6*d**4 + 12*d**3 + d - 14*d**4.
4*d*(d - 1)**3*(2*d + 1)
Let k = -38012/5 - -7604. Solve 4/5*x**4 - 16/5*x**2 + 2/5*x**5 + 0*x - k*x**3 + 0 = 0.
-2, 0, 2
Let c(q) be the second derivative of q**6/6 + 4*q**5 + 235*q**4/6 + 200*q**3 + 1125*q**2/2 + 27*q. Suppose c(u) = 0. What is u?
-5, -3
Suppose 0*n = -2*n + 4. Suppose 0 = i - 0*i - n. Let 5*m + 4*m**3 - i + 0 - 16*m**2 - 1 + 8*m = 0. What is m?
1/2, 3
Let w(m) be the third derivative of -m**7/70 - 3*m**6/20 - 11*m**5/20 - 3*m**4/4 - 8*m**2 - 10*m. Factor w(s).
-3*s*(s + 1)*(s + 2)*(s + 3)
Let b(h) be the third derivative of -h**8/3864 + 3*h**7/805 - h**6/92 - 5*h**5/138 - 2*h**2 + 63*h. Find n, given that b(n) = 0.
-1, 0, 5
Let d(y) be the first derivative of -y**5/30 - y**4/6 + y**3 - y**2 - 6. Let b(a) be the second derivative of d(a). Solve b(i) = 0 for i.
-3, 1
Let m be 1*4/(-4) - -2. Suppose 4 = 3*g + m. What is j in -5 + 3*j + 10*j**4 - 3*j**3 + 9*j**2 - 13*j**4 - g = 0?
-2, -1, 1
Let q(p) be the first derivative of 2*p**3 + 44*p**2 + 59*p + 34. Let l(y) = -6*y**2 - 88*y - 60. Let b(i) = 3*l(i) + 4*q(i). What is o in b(o) = 0?
-14, -2/3
Let a(f) be the first derivative of 27*f**4/4 + 70*f**3 + 141*f**2/2 - 42*f - 9. Suppose a(w) = 0. What is w?
-7, -1, 2/9
Let i(y) be the first derivative of -y**3/4 - 5*y**2/2 - 3*y - 182. Factor i(b).
-(b + 6)*(3*b + 2)/4
Let a = -40 + 65. Factor a*u**4 + 0*u**5 - 5*u**5 - 18*u**4 - 2*u**3.
-u**3*(u - 1)*(5*u - 2)
Let r(n) be the first derivative of 3*n**6/20 - n**5/20 - 3*n**4/8 + n**3/6 + 6*n - 19. Let f(o) be the first derivative of r(o). Factor f(a).
a*(a - 1)*(a + 1)*(9*a - 2)/2
Let j(c) = 4*c - 48. Let b be j(21). Let t be 8/b - 8/(-18). Factor t*y**4 + 8/3*y**3 + 4/3*y + 0 + 10/3*y**2.
2*y*(y + 1)**2*(y + 2)/3
Let l(k) be the second derivative of k**8/140 + k**7/14 + 11*k**6/40 + k**5/2 + k**4/2 + k**3/3 - 13*k. Let n(y) be the second derivative of l(y). Factor n(b).
3*(b + 2)**2*(2*b + 1)**2
Suppose -10*k**3 + 5*k**2 - k**2 + 2*k**5 + 3*k**3 + k**3 = 0. What is k?
-2, 0, 1
Let b(n) be the third derivative of n**7/280 + n**6/24 + 7*n**5/40 + 3*n**4/8 - 11*n**3/6 - 13*n**2. Let w(u) be the first derivative of b(u). Factor w(x).
3*(x + 1)**2*(x + 3)
Let b(m) be the first derivative of m**6/240 - m**5/60 + m**4/48 + 17*m**2/2 + 30. Let c(z) be the second derivative of b(z). Factor c(l).
l*(l - 1)**2/2
Suppose -21 = -4*j - 13. Let k(w) = w**2 - 4. Let b be k(j). Find t such that -4/7*t - 18/7*t**3 - 2/7*t**5 - 2*t**2 + b - 10/7*t**4 = 0.
-2, -1, 0
Let l(w) = 4*w**2 - 38*w + 5. Let d(a) = -5*a**2 + 39*a - 6. Let b(c) = -5*d(c) - 6*l(c). Suppose b(i) = 0. What is i?
-33, 0
Find c, given that -5/4*c**3 + 27/2*c - 33/4*c**2 - 4 = 0.
-8, 2/5, 1
Let r be 2 + (-8)/(-4) - 2. Factor -2*b**3 + 30*b + 38*b - 64*b - 2*b**r.
-2*b*(b - 1)*(b + 2)
Let o be (-20)/15 - (92/(-6) - 2). Let h be (3/30)/(8/o). Factor -1/5*d**