)/((-54)/(-8)) + (-32)/(-24). Let b(d) be the second derivative of y - 1/24*d**4 - d - 1/6*d**3 + 3/4*d**2. Determine i, given that b(i) = 0.
-3, 1
Let b(y) be the second derivative of y**5/10 - y**4 - 25*y**3/3 - 18*y**2 - 177*y. Let b(u) = 0. Calculate u.
-2, -1, 9
Suppose 25*d - 40*d = -25*d. Let c(y) be the second derivative of y + 1/48*y**4 + 9/8*y**2 + d - 1/4*y**3. Factor c(p).
(p - 3)**2/4
Determine j, given that -3/8*j**3 - 21/8*j**2 + 3/8*j + 3/8*j**4 + 9/4 = 0.
-2, -1, 1, 3
Let l = 9783 - 9783. Factor 0 + l*u**2 - 1/5*u**3 + 1/5*u.
-u*(u - 1)*(u + 1)/5
Let b(n) = -4*n - 1. Let q be b(-1). Suppose -q*x = -4*x + 2. Find o such that -o**x - o**3 + o**2 + 0*o**3 + o**4 + o - o**2 = 0.
-1, 0, 1
Let n(w) be the third derivative of w**8/336 - 2*w**7/105 - 3*w**6/20 - w**5/3 - 7*w**4/24 - 71*w**2. Factor n(r).
r*(r - 7)*(r + 1)**3
Let u(j) = 6*j - 4. Let n be u(1). Factor 18*r**n + 6 + 3*r - 29*r**2 + 8*r**2.
-3*(r - 2)*(r + 1)
Let c(g) be the third derivative of -g**6/480 + 13*g**5/240 + 5*g**4/24 - 7*g**3/2 - 56*g**2 + 7. Factor c(y).
-(y - 14)*(y - 2)*(y + 3)/4
Let u be 7/(-2) + 0 + 4. Let o(k) be the second derivative of -1/2*k**2 + 1/16*k**4 - 1/10*k**5 + k - 1/40*k**6 + 0 + u*k**3. Suppose o(f) = 0. What is f?
-2, 1/3, 1
Let r(a) be the first derivative of 8/21*a**3 + 1/7*a**4 - 8/35*a**5 - 1/7*a**6 + 0*a + 1/7*a**2 + 6. Suppose r(u) = 0. What is u?
-1, -1/3, 0, 1
Let s(r) be the third derivative of 392/3*r**3 - 4*r + 0 - r**2 + 14/3*r**4 + 1/15*r**5. Let s(f) = 0. Calculate f.
-14
Let w = 2 + -2. Let h be (w - 8)*2/(-4). Factor -h*o**3 - 7*o**2 + 7*o**2 + 5*o**3.
o**3
Factor 867/4*z**2 - 3/4*z**5 + 0 + 0*z - 969/4*z**3 + 105/4*z**4.
-3*z**2*(z - 17)**2*(z - 1)/4
Let z(f) be the third derivative of -1/24*f**6 + 0*f - 5/24*f**4 + 0*f**3 + 11*f**2 + 0 + 1/6*f**5. Determine k, given that z(k) = 0.
0, 1
Let v be ((-12)/21)/(-42 - -38). Factor -1/7 - v*q**4 + 0*q + 2/7*q**2 + 0*q**3.
-(q - 1)**2*(q + 1)**2/7
Let h(x) be the second derivative of x**8/6720 - x**6/720 + x**4/96 + x**3 + 3*x. Let k(a) be the second derivative of h(a). Factor k(r).
(r - 1)**2*(r + 1)**2/4
Let c(k) be the third derivative of 0 + 7/18*k**4 - 19*k**2 - 1/6*k**5 - 4/9*k**3 - 1/315*k**7 + 13/360*k**6 + 0*k. Suppose c(a) = 0. Calculate a.
1/2, 2
Let f(q) be the first derivative of -q**7/2100 - q**6/900 + q**5/150 + 8*q**3/3 + 2. Let i(z) be the third derivative of f(z). Factor i(y).
-2*y*(y - 1)*(y + 2)/5
Let c(y) be the third derivative of 5*y**8/336 - 37*y**7/21 + 1441*y**6/24 - 222*y**5 + 270*y**4 - y**2 - 102*y. Factor c(b).
5*b*(b - 36)**2*(b - 1)**2
Let m = 5 - 3. Let u be (29/(-9) - -3)/(2*1/(-3)). Let 1/3*x**m - 2/3*x + u = 0. What is x?
1
Determine s so that -56/3*s + 4*s**2 + 16 + 2*s**3 - 2/3*s**4 = 0.
-3, 2
Let i be 7/((-28)/12) - -8. Suppose i*j - 4*j**3 + 17 - 17*j + 12*j**2 - 13 = 0. Calculate j.
1
Let y(h) = -2*h + 41. Let p be y(-8). Factor -p*n - n**2 + 43*n + 12 + 3*n**2.
2*(n - 6)*(n - 1)
Let n(y) be the third derivative of -5/8*y**4 + 5/12*y**5 - 1/24*y**6 - 1/42*y**7 + 0*y**3 + 0 + 0*y - 33*y**2. Let n(c) = 0. What is c?
-3, 0, 1
Let h(t) be the second derivative of t**9/756 + t**8/240 + t**7/420 - t**6/360 - 13*t**3/6 + 5*t. Let c(k) be the second derivative of h(k). Solve c(f) = 0.
-1, 0, 1/4
Let j be (-1)/5 - 256/(-80). Suppose -8 = -j*u + 1. Solve -3/2*y + 0*y**3 - u*y**2 + 3/2*y**5 + 0 + 3*y**4 = 0 for y.
-1, 0, 1
Let v(a) be the second derivative of 3*a**5/20 + 7*a**4/20 + a**3/5 + 2*a - 14. Factor v(y).
3*y*(y + 1)*(5*y + 2)/5
Let 2/3*n**2 - 2/9*n**5 + 0*n - 2/3*n**4 + 2/9*n**3 + 0 = 0. Calculate n.
-3, -1, 0, 1
Let -5*w**4 - 11*w**2 + 7/2*w + 0 + 1/2*w**5 + 12*w**3 = 0. What is w?
0, 1, 7
Let j(h) = -h**2 - 5*h - 4. Let a be (-9)/(-15)*(-6 - -1). Let k be j(a). Solve -1/3*b**4 + b**3 + 0 + 1/3*b - b**k = 0 for b.
0, 1
Let b(x) be the second derivative of 0*x**6 + 1/21*x**7 + 0*x**2 + 0 + 10*x + 0*x**4 + 0*x**3 - 1/10*x**5. Suppose b(z) = 0. What is z?
-1, 0, 1
What is p in 3*p**2 - 3*p**4 + 0*p + 0 - 3/2*p**3 + 3/2*p**5 = 0?
-1, 0, 1, 2
Suppose -i = -3*r - 21, -546*i = -549*i + 5*r + 39. Factor -1/10*n + 1/10*n**i + 0*n**2 + 0.
n*(n - 1)*(n + 1)/10
Let z(t) be the second derivative of 1/4*t**2 + 0 - 1/60*t**6 + 0*t**4 + 12*t - 1/20*t**5 + 1/6*t**3. Find p such that z(p) = 0.
-1, 1
Let j(y) = -y**3 + 19*y**2 + 18*y - 6. Let i be j(20). Let u = 46 + i. What is k in 1/4*k + u - 1/4*k**2 = 0?
0, 1
Let p = -57 + 59. Factor 0*r**3 - 69*r**p + 5*r**3 - 11*r**2 + 400*r - r**3.
4*r*(r - 10)**2
Find k, given that 9*k**2 - 19*k**2 - 130*k + 4*k**2 + 3*k**2 + 8*k**2 + 845 = 0.
13
Let z(b) = 2. Let n(u) = -4*u**2 - 56*u + 52. Let y(x) = -n(x) - 4*z(x). Factor y(q).
4*(q - 1)*(q + 15)
Let s be 0 + 0 + 4 - (-684)/21. Factor 64/7*i - 144/7*i**2 - 4/7*i**4 + s + 44/7*i**3.
-4*(i - 4)**3*(i + 1)/7
Find f, given that 22*f**2 - 15*f + 5 + 30 - 5*f**3 + 3*f**2 + 80*f = 0.
-1, 7
Let j(p) = -65*p**3 - 2730*p**2 + 5550*p - 2785. Let f(t) = -9*t**3 - 390*t**2 + 793*t - 398. Let d(c) = 15*f(c) - 2*j(c). Factor d(x).
-5*(x - 1)**2*(x + 80)
Let o(q) be the second derivative of -q**4/18 + 101*q**3/9 - q - 74. Determine c so that o(c) = 0.
0, 101
Suppose -3*y = -3*b + 72, 4*b + 5*y - 45 = 60. Suppose 7*v + 4 = b. What is o in 0 + 2/3*o**2 + 4/3*o**v - 2/3*o**4 - 4/3*o = 0?
-1, 0, 1, 2
Let s(j) = j**2 + 2*j - 573. Let b be s(23). Factor 1/5*w**5 + 1/5*w**4 - 1/5*w**b + 0 - 3/5*w**3 + 2/5*w.
w*(w - 1)**2*(w + 1)*(w + 2)/5
Suppose 3*q + 6*k - 24 = 5*q, -4*q + 4*k - 16 = 0. Factor 1/4*v + q + 1/2*v**2 + 1/4*v**3.
v*(v + 1)**2/4
Let m(u) be the third derivative of 2*u**8/21 - 24*u**7/35 - u**6/4 + 281*u**5/30 + 5*u**4/4 - 75*u**3 + 462*u**2. Solve m(f) = 0.
-5/4, 1, 3
Let h(s) be the second derivative of s**5 - 9*s**4 + 80*s**3/3 - 24*s**2 + 724*s. Suppose h(w) = 0. What is w?
2/5, 2, 3
Let s(r) = 3*r**2 + r. Let p(o) = -8*o**2 - 46*o. Let f(d) = 2*p(d) + 6*s(d). Factor f(c).
2*c*(c - 43)
Let x(d) = -6*d**3 + 51*d**2 - 45*d - 18. Let h(f) = 3*f**3 - 26*f**2 + 23*f + 10. Let s(j) = 9*h(j) + 5*x(j). Factor s(b).
-3*b*(b - 6)*(b - 1)
Let -1/8*v**2 - 7/4*v + 9 = 0. Calculate v.
-18, 4
Let -20/3*m + 0 - 15*m**5 + 80/3*m**2 + 65/3*m**3 - 80/3*m**4 = 0. What is m?
-2, -1, 0, 2/9, 1
Suppose -18*q + 1 = -2*w - 23*q, q = -3*w + 5. Factor -121/2*u**w - 1/2 + 11*u.
-(11*u - 1)**2/2
Let i(l) = 15*l**2 + 4*l. Let k(h) = -16*h**2 + 0*h + 0*h - 4*h + 0*h. Let a(v) = -4*i(v) - 3*k(v). Factor a(q).
-4*q*(3*q + 1)
Let m = -70 + 74. Let d be -3 + m + -2 + 3. Solve 11/2*c**d + 6*c + 1/4*c**4 + 9/4 + 2*c**3 = 0 for c.
-3, -1
Solve 0 - 10/11*j - 2/11*j**3 - 12/11*j**2 = 0 for j.
-5, -1, 0
Let v be 3/(-3 - -6)*11. Let x = v + -8. Factor -x*r**2 + 8*r**2 - 2*r**4 + 2*r**3 - 2*r**2 + r**2.
-2*r**2*(r - 2)*(r + 1)
Let a = -20 + 25. Suppose -k - 16 = -a*k. Solve 40*t**4 - 60*t**4 - 45*t**2 - 15*t**3 - 10*t + 40*t**k = 0.
-1, -1/4, 0, 2
Let i(j) be the third derivative of -j**5/80 + j**4/4 + 176*j**2. Suppose i(p) = 0. What is p?
0, 8
Factor 2/5*l**3 + 682/15*l - 242/15 + 26/3*l**2.
2*(l + 11)**2*(3*l - 1)/15
Let b(k) be the second derivative of 5*k**4/72 - 235*k**3/12 + 175*k**2/3 - 214*k. Factor b(i).
5*(i - 140)*(i - 1)/6
Let j(b) be the third derivative of b**6/1380 + 13*b**5/345 + 209*b**4/276 + 484*b**3/69 + b**2 + 61*b. Suppose j(a) = 0. Calculate a.
-11, -4
Suppose 0 = -2*j + 21 + 9. Suppose -11*r = -j*r. Factor 1/4*z - 1/4*z**2 + r.
-z*(z - 1)/4
Let i(t) = -9*t**3 + 6*t. Let k(x) = x**5 + x**4 - 18*x**3 - x**2 + 12*x. Suppose 13 = -8*o - 11. Let h(r) = o*k(r) + 5*i(r). Suppose h(f) = 0. Calculate f.
-2, -1, 0, 1
Let u be (-9)/18*4/(-1). Suppose -2*j + j = u*h - 13, -4*j + 32 = 3*h. Determine r so that 8*r**h + 128/5 - 64*r + 64*r**2 - 4/5*r**5 - 32*r**3 = 0.
2
Let -2*d**2 + 3*d**3 + 5/2 - 1/2*d**4 - 3*d = 0. Calculate d.
-1, 1, 5
Let a(q) be the first derivative of q**6/2 - 12*q**5/5 + 9*q**4/2 - 4*q**3 + 3*q**2/2 - 101. Find d such that a(d) = 0.
0, 1
Factor 6/7 + 8/7*j + 2/7*j**2.
2*(j + 1)*(j + 3)/7
Let d be 25 + -1 - (-12 + 10). Let -16*h - 24*h**3 - d*h**2 + 3669*h**4 - 4*h**2 - 3 - 3676*h**4 = 0. Calculate h.
-1, -3/7
Find h, given that 12*h + h**3 + 2*h**5 - 14*h**4 - 34*h**2 - 9*h**3 + 42*h**3 = 0.
0, 1, 2, 3
Let s = -139 - -174. Let t = s + -35. Find n, given that -3/5*n**3 + t