t z be 8 + 9/((-54)/30). Solve 4/11*k**2 + 0 - 2/11*k**z + 0*k = 0 for k.
0, 2
Let r(v) be the second derivative of -v**7/126 - v**6/90 + v**5/30 + v**4/18 - v**3/18 - v**2/6 + 37*v. Factor r(h).
-(h - 1)**2*(h + 1)**3/3
Let f(s) be the third derivative of 7*s**8/120 + s**7/30 + s**6/180 + 25*s**3/6 - 27*s**2. Let u(b) be the first derivative of f(b). Factor u(a).
2*a**2*(7*a + 1)**2
Suppose -7*r - 9*r = -6*r. Let j(y) be the first derivative of 1/8*y**2 + r*y - 1 + 1/12*y**3. Factor j(n).
n*(n + 1)/4
Let t(o) = -3*o**2 - 24*o - 24. Let r(i) = i. Let n(h) = 3*r(h) - t(h). Factor n(u).
3*(u + 1)*(u + 8)
Let u be (2/7)/((-2000)/(-1750)*(-2)/(-16)). Suppose -4/5*i + 1/5*i**u + 3/5 = 0. What is i?
1, 3
Factor -2/9*u**2 + 38/9 - 4*u.
-2*(u - 1)*(u + 19)/9
Let x = -52 - -53. Let u be (-2)/x + 2 - (-22)/8. Factor 1/2*f + 0 - u*f**2 + 9/4*f**3.
f*(f - 1)*(9*f - 2)/4
Let d(x) be the first derivative of 3*x**5/5 + 3*x**4/4 - 6*x**3 + 65. Factor d(u).
3*u**2*(u - 2)*(u + 3)
Let a(i) be the second derivative of -1/15*i**6 + 0*i**2 + 1/21*i**7 + 0*i**3 + 0 - 1/10*i**5 + 1/6*i**4 - 11*i. Factor a(t).
2*t**2*(t - 1)**2*(t + 1)
Let f(i) be the first derivative of 10 - 7/90*i**4 + 2/5*i**2 + i - 19/45*i**3. Let u(p) be the first derivative of f(p). Factor u(t).
-2*(t + 3)*(7*t - 2)/15
Let w(s) be the second derivative of s**7/42 - 29*s**6/24 + 83*s**5/5 - 179*s**4/48 - 111*s**3/2 + 81*s**2/2 - 552*s. What is f in w(f) = 0?
-1, 1/4, 1, 18
Let l(r) be the first derivative of r**5/5 + 9*r**4/4 + 4*r**3 - 40*r**2 - 192*r - 43. Factor l(z).
(z - 3)*(z + 4)**3
Find d such that 496*d - 1974 + 4041 - 4717 - 12726 - 4*d**2 = 0.
62
Let q(w) be the first derivative of -50*w**6/21 + 44*w**5/7 + 8*w**4 + 16*w**3/7 + 9. Suppose q(z) = 0. What is z?
-2/5, 0, 3
Suppose -3 = -8*b + 13. Suppose 16 = z + b*n, -z - 2*n + 20 = 2*n. Factor z*j + 15*j - 32 - 2*j**2 - 11*j.
-2*(j - 4)**2
Let m(j) be the second derivative of j**6/75 + 3*j**5/50 - j**4/15 - 4*j**3/5 - 8*j**2/5 + 6*j - 12. Solve m(l) = 0.
-2, -1, 2
Let k(a) = 2*a**2 + a**2 - 2*a**2 + 40*a - 37*a. Let u be k(-4). Factor 15*r**u - 6*r**5 - 12*r**3 + 4*r**2 + 2*r**2 - 3*r**2.
-3*r**2*(r - 1)**2*(2*r - 1)
Find y, given that 2*y**2 + 6/5*y**3 + 0*y + 0 = 0.
-5/3, 0
Let x be (-347013)/(-594) - 1/(-6). Let z = x - 584. Factor 0*r**3 + 0 - 2/11*r**4 + 6/11*r**2 + z*r.
-2*r*(r - 2)*(r + 1)**2/11
Let o(h) = 10*h - 70. Let x(b) = b**2 - 1. Let t(j) = o(j) + 5*x(j). Suppose t(i) = 0. What is i?
-5, 3
Let v(y) be the first derivative of 3*y**4/4 + 21*y**3 + 441*y**2/2 + 1029*y + 362. Determine q, given that v(q) = 0.
-7
Let d(i) = 4*i - 120. Let w be d(15). Let r be 16/w*(-24)/16. Find x such that 0*x + 2/5*x**2 - r = 0.
-1, 1
Find w such that 4*w**3 + 4/3*w**4 + 0*w - 4*w**5 - 4/3*w**2 + 0 = 0.
-1, 0, 1/3, 1
Let v be -1 + (5 - 10) - 160/(-20). Suppose -5/3 - 4*a**v + 14/3*a + 2/3*a**3 + 1/3*a**4 = 0. Calculate a.
-5, 1
Let n(m) = m**4 - m**3 - m**2 + m - 2. Let g(o) = 2*o**5 - 10*o**4 + 16*o**3 + 10*o**2 - 18*o - 12. Let f(l) = 2*g(l) - 12*n(l). What is h in f(h) = 0?
-1, 0, 1, 2, 6
Let t(w) be the second derivative of 22*w**3 + 0 - 45*w + 7/3*w**4 - 20*w**2. Find q such that t(q) = 0.
-5, 2/7
Factor -5/3*x + 0 + 1/3*x**2.
x*(x - 5)/3
Let u = 61 + -58. Suppose y = -3*k + 9, u*k - 3*y + 8 - 5 = 0. Factor 0 + 1/2*r**k + 3/2*r.
r*(r + 3)/2
Let v(k) be the third derivative of -k**7/210 + 4*k**6/45 - 8*k**5/15 - 2*k**3 - 7*k**2. Let j(z) be the first derivative of v(z). Factor j(f).
-4*f*(f - 4)**2
Let z(h) = h**3 + 17*h**2 - 19*h - 8. Let u be z(-18). Let p = 5 - 3. Let -2*w + 7*w**4 - u*w**4 - 4*w + w**2 + 8*w**p = 0. Calculate w.
-2, 0, 1
Let w(o) be the second derivative of 15*o + 1/9*o**4 + 0*o**2 + 0 + 0*o**3 + 1/30*o**5. Suppose w(l) = 0. Calculate l.
-2, 0
Let a be 28/(-1008)*(-1 - 4/8). Let l(g) be the first derivative of -6 - a*g**4 + 1/3*g + 2/9*g**3 - 5/12*g**2. Factor l(r).
-(r - 2)*(r - 1)**2/6
Factor s**2 + 3*s**2 + 0*s**2 + 2*s**3 + 0*s - 3*s - 3*s.
2*s*(s - 1)*(s + 3)
Let p(v) be the first derivative of 3*v**4/4 + 26*v**3 + 48. Determine x, given that p(x) = 0.
-26, 0
Suppose 0 = 2*b + 4*w - 6*w, 3*b - 4 = 4*w. Let z be (1 - (-25)/b)/((-135)/80). Factor 98/9*n**2 + 2/9 + z*n.
2*(7*n + 1)**2/9
Suppose -207*j + 8 = -5*k - 203*j, 3*j = 2*k + 6. Factor -1/3*x + 1/3*x**2 + k.
x*(x - 1)/3
Let x be (-192)/(-40) + (-1)/(-5). Let m(i) be the third derivative of -8/15*i**3 - 1/15*i**4 + 0 + 0*i - 1/300*i**x - 6*i**2. Find l, given that m(l) = 0.
-4
Let u(c) be the first derivative of -8*c**4 + 208*c**3/3 + 183*c**2 + 144*c + 30. Factor u(g).
-2*(g - 8)*(4*g + 3)**2
Let i(h) be the third derivative of -h**7/735 - h**6/84 + 8*h**2 - 2. Factor i(c).
-2*c**3*(c + 5)/7
Let m(k) = k**3 + k**2 - k - 1. Let h(i) = 30*i**3 + 213*i**2 + 138*i - 45. Let u(f) = -3*f + 20. Let c be u(7). Let o(j) = c*h(j) + 3*m(j). Factor o(y).
-3*(y + 1)*(y + 7)*(9*y - 2)
Let h(r) = 5*r + 25. Let o = -34 - -33. Let l(g) = -g**2 - g - 1. Let b(q) = o*h(q) - 5*l(q). Solve b(y) = 0.
-2, 2
Let r(t) be the third derivative of 11/12*t**5 + 0 + 2/3*t**6 + 0*t + 12*t**2 + 0*t**3 + 1/6*t**7 + 5/12*t**4. Solve r(s) = 0.
-1, -2/7, 0
Let i be -11 + -21*30/(-54). Suppose 4/3*h**4 - 2/3*h + 4/3 - 8/3*h**2 + 4/3*h**3 - i*h**5 = 0. What is h?
-1, 1, 2
Let f(i) be the third derivative of -i**6/280 + i**5/28 - i**2 - 1. Determine u so that f(u) = 0.
0, 5
Let p(t) be the third derivative of t**8/84 - 43*t**7/315 - 43*t**6/180 + 11*t**5/45 + 4*t**4/9 - 578*t**2 + 2. Determine c, given that p(c) = 0.
-1, -1/2, 0, 2/3, 8
Let y be ((-2)/1)/(0 - 3/6). Suppose 0 = 44*p - 42*p - y. Factor -1/2*b**2 + p*b - 2.
-(b - 2)**2/2
Let y(f) = f**2 + 25*f - 1102. Let h be y(-48). Determine a so that 12/11 + 6/11*a**h - 2*a = 0.
2/3, 3
Let i be 48/288*768/40. Suppose 0 + 4/5*u + i*u**3 + 14/5*u**2 + 6/5*u**4 = 0. What is u?
-1, -2/3, 0
Let x(a) be the first derivative of 0*a**3 - 1/2*a**2 + 1/270*a**5 + 3 + 0*a**4 + 0*a. Let b(r) be the second derivative of x(r). Find q such that b(q) = 0.
0
Let p(o) be the second derivative of -26/27*o**4 + 8/27*o**3 + 0*o**2 + 5/27*o**6 + 0 + o**5 - 125/189*o**7 + 27*o. Factor p(y).
-2*y*(y + 1)*(5*y - 2)**3/9
Solve 10*j - 3*j**4 - 7*j**2 - 11*j**3 + j**5 + 6*j**4 - 6*j**4 + 2*j**4 + 8 = 0.
-2, -1, 1, 4
Determine o so that -14/5 - o**3 - 1/5*o**4 + o + 3*o**2 = 0.
-7, -1, 1, 2
Let j(d) be the third derivative of 0*d - 1/6*d**6 - 1/42*d**7 - 1/3*d**5 + 0*d**4 + 0 + 34*d**2 + 0*d**3. Suppose j(c) = 0. Calculate c.
-2, 0
Let j(n) be the third derivative of -n**7/840 - 7*n**6/480 - n**5/40 + n**4/3 + 4*n**3/3 - 12*n**2. Factor j(r).
-(r - 2)*(r + 1)*(r + 4)**2/4
Let o = 340/4103 - -3/373. Let v(z) be the second derivative of 0 + 1/11*z**4 - 2/55*z**5 + 1/165*z**6 - 4/33*z**3 + o*z**2 + 4*z. Solve v(d) = 0.
1
Let o(b) = -18*b**2 - 18*b + 53. Let v(s) = -116*s**2 - 116*s + 344. Let m(r) = -32*o(r) + 5*v(r). Factor m(q).
-4*(q - 2)*(q + 3)
Let i(w) be the first derivative of 1/7*w**2 + 0*w - 6/35*w**5 + 11 - 10/21*w**3 + 1/2*w**4. Let i(s) = 0. Calculate s.
0, 1/3, 1
Let d = -63 - -63. Suppose 16*m + 0 + 0 = d. Let -3/5*b**2 + 0 + m*b = 0. What is b?
0
Factor 101*x**3 + 2797 + 245*x**2 - 51*x**3 - 55*x**3 + 83 - 3120*x.
-5*(x - 24)**2*(x - 1)
Let 263*b**3 - 40*b**2 + 33*b - 5*b**2 + 7*b - 258*b**3 = 0. What is b?
0, 1, 8
Let f(i) be the first derivative of 2*i**5/5 - 5*i**4/2 + 4*i**3 - 59. Factor f(c).
2*c**2*(c - 3)*(c - 2)
Find j such that -1/6*j**4 + 1/6*j**2 + 0 - 7/6*j**3 + 7/6*j = 0.
-7, -1, 0, 1
Suppose 3*q - 20 = -5. Suppose -z = -4*z - 5*r, 0 = z + q*r. Find h such that -4/3*h**2 + 2/3*h + 0*h**3 + 4/3*h**4 - 2/3*h**5 + z = 0.
-1, 0, 1
Factor 5*p**5 + 458856 - 1446635*p + 574040*p**2 + 285529 + 26389*p**2 + 60481*p**2 + 40550*p**3 + 785*p**4.
5*(p - 1)**2*(p + 53)**3
Suppose -2*u - 2*q - 7 - 3 = 0, 5 = -q. Let d be (-1)/3*u + 4. Factor 7*o - o + 2 - o**d + 9*o**4 - 6*o**3 - 10*o**2.
2*(o - 1)**2*(o + 1)*(4*o + 1)
Let v(h) be the second derivative of h**5/10 + 19*h**4/18 + 11*h**3/3 + 3*h**2 - h - 35. Determine x so that v(x) = 0.
-3, -1/3
Let t(b) = -2*b + 9. Let i be t(6). Let o(f) = f + 3. Let v be o(i). Factor k**5 - 2*k**2 - 5*k**4 + 7*k**4 + k**3 + v*k**3 - 2*k**5.
-k**2*(k - 2)*(k - 1)*(k + 1)
Let a(n) = n**5 + 2*n**4 + n**2. Let l(j) = -9*j**5 