pose 25*a = 16*a + 27. Determine k so that 0 + 2/9*k**a - w*k**2 - 2/9*k + 2/9*k**4 = 0.
-1, 0, 1
Let y(k) = -k**2 + 4*k. Let h(i) = -i**2 + 5*i. Let l(z) = -4*h(z) + 3*y(z). Let t be l(8). What is o in 2/3 + t*o - 2/3*o**2 = 0?
-1, 1
Let i(m) be the first derivative of -m**4/34 - 6*m**3/17 - 595. Factor i(k).
-2*k**2*(k + 9)/17
Let d be (1668/(-210) + 8)*(-40)/(-24). Factor 2/21*b**5 + 0 - 4/21*b**2 + 0*b**3 - d*b + 4/21*b**4.
2*b*(b - 1)*(b + 1)**3/21
Let w(d) be the third derivative of -5/336*d**8 - 1/120*d**6 + 0 + 0*d + 4/105*d**7 + 0*d**3 - 5*d**2 + 0*d**4 - 1/30*d**5. Determine x, given that w(x) = 0.
-2/5, 0, 1
Let a = 21659/18045 + -1/3609. What is u in 6/5*u + a*u**2 - 36/5 = 0?
-3, 2
Let o be 28/(-24) - (-190)/60. Factor 8/7*n - 8/7 - 2/7*n**o.
-2*(n - 2)**2/7
Let t = -26341/2 - -52687/4. Determine q, given that 2*q - t*q**4 - 1/4*q**5 + q**2 - 3/2*q**3 + 0 = 0.
-2, 0, 1
Let v = -372/7 - -13399/252. Let p(d) be the third derivative of -1/36*d**4 + 0*d + 0 + 0*d**3 - v*d**5 + 4*d**2 - 1/180*d**6. Suppose p(j) = 0. Calculate j.
-2, -1/2, 0
Factor -103*y - 142*y**2 - 153*y**3 - 5*y**2 + 256*y + 150 - 3*y**4.
-3*(y - 1)*(y + 1)**2*(y + 50)
Let s(m) be the third derivative of 0*m + m**2 + 0*m**5 + 0*m**6 + 0 + 0*m**4 + 1/1008*m**8 + 0*m**3 + 1/630*m**7. Factor s(i).
i**4*(i + 1)/3
Let b be 8/(-5)*(-155)/62. Suppose 9794*n**2 - 659*n**2 + 9065*n**3 + 1715*n**b + 14272*n + 5000 + 8715*n**2 + 1228*n = 0. Calculate n.
-10/7, -1
Let x(z) be the first derivative of -3*z**7/980 - z**6/180 + z**5/210 - 32*z**3/3 - 15. Let u(o) be the third derivative of x(o). Find p such that u(p) = 0.
-1, 0, 2/9
Find t, given that 0*t**2 + 0 + 4/3*t**5 + 20/3*t**4 + 0*t + 16/3*t**3 = 0.
-4, -1, 0
Let y(k) be the third derivative of k**5/30 - 7*k**4/12 + 10*k**3/3 - 83*k**2. Factor y(w).
2*(w - 5)*(w - 2)
Let 2/9*i**2 - 26/3*i + 148/9 = 0. What is i?
2, 37
Let g(z) be the second derivative of -1/6*z**4 + 0 + 1/5*z**6 - 5/3*z**3 - 10*z + 1/2*z**5 - 2*z**2. Factor g(m).
2*(m - 1)*(m + 1)**2*(3*m + 2)
Let k = -57 + 30. Let d = -14 - k. Let -4*s**5 + 3*s**5 + 0*s - 4*s - d*s**3 - 5*s**4 + 11*s**4 + 12*s**2 = 0. Calculate s.
0, 1, 2
Let p = -579/40 + 119/8. Let h(c) be the first derivative of c**4 + 2/3*c**3 + p*c**5 + 0*c**2 + 0*c - 5. What is d in h(d) = 0?
-1, 0
Let k = -16/69 - -13/23. Suppose k*p**2 - 2/3*p - 1 = 0. Calculate p.
-1, 3
Let v(k) be the first derivative of 6*k**2 - k**4 + 8/3*k**3 + 0*k + 37. Solve v(p) = 0 for p.
-1, 0, 3
Let s(z) = 36*z**3 + 46*z**2 + 20*z - 10. Let m(c) = 11*c**3 + 15*c**2 + 7*c - 3. Let i(r) = -10*m(r) + 3*s(r). Let i(u) = 0. What is u?
-5, -1, 0
Let u(g) be the second derivative of g**7/126 + g**6/30 - g**5/6 - 15*g - 10. Factor u(o).
o**3*(o - 2)*(o + 5)/3
Let p be 18/10 - ((-66)/55 - -1). Let j(v) be the second derivative of 0 - 2/13*v**p - 3/130*v**5 - 3*v - 7/39*v**3 - 4/39*v**4. Factor j(x).
-2*(x + 1)**2*(3*x + 2)/13
Let z(i) = 2*i**2 - 22*i - 20. Let a be z(12). Let o be a + 1/(-1) + 0/(-6). Find d, given that 0*d**2 + 2/15*d**4 + 0*d + 2/15*d**o + 0 = 0.
-1, 0
Let p(z) be the first derivative of -3/5*z**2 + 3/5*z**3 - 8 + 0*z - 3/25*z**5 + 0*z**4. Factor p(d).
-3*d*(d - 1)**2*(d + 2)/5
Let d(h) be the first derivative of h**6/39 - 66*h**5/65 - 105*h**4/26 - 214*h**3/39 - 36*h**2/13 - 381. Let d(o) = 0. What is o?
-1, 0, 36
Let v(f) be the third derivative of -1/10*f**5 + 5/8*f**4 + 0*f - 1/10*f**6 - 1/112*f**8 - 5*f**2 - f**3 + 0 + 2/35*f**7. Factor v(r).
-3*(r - 2)*(r - 1)**3*(r + 1)
Let o(y) be the third derivative of 0 - 2/21*y**7 - 5/24*y**6 - 1/6*y**5 - 5/336*y**8 + 0*y + 0*y**3 + 0*y**4 - 11*y**2. Find c, given that o(c) = 0.
-2, -1, 0
Let w = -536 + 963. Factor 4*h**3 + 6*h**3 - 36 + w*h + 5*h**4 + 11 - 60*h**2 - 357*h.
5*(h - 1)**3*(h + 5)
Let r be 5*(-44)/(-36) - (-42)/14. Let 32*a**5 + 2/3 - 862/9*a**3 - r*a + 410/9*a**2 + 176/3*a**4 = 0. Calculate a.
-3, 1/4, 1/3
Let b(d) = d**3 + d**2 - 3*d. Let v(n) = 4*n**3 + 14*n**2 - 24*n. Let z(s) = 6*b(s) - v(s). Solve z(u) = 0 for u.
0, 1, 3
Solve 1/6*a**2 - 8/3 + 1/6*a**3 - 8/3*a = 0 for a.
-4, -1, 4
Let u be (1/(-30))/((-9)/(-18)). Let s = u - -2/5. Factor 0*z - 5/3*z**3 + s*z**2 + 0 + z**4 + 3*z**5.
z**2*(z + 1)*(3*z - 1)**2/3
Let l(i) be the first derivative of i**4/48 + i**3/12 - 3*i**2/8 - 4*i - 12. Let g(o) be the first derivative of l(o). Factor g(h).
(h - 1)*(h + 3)/4
Let l be (0 - 6)/2 + 3. Suppose 2*v + l = -16. Let j(t) = 11*t**2 - 4*t + 17. Let p(n) = 4*n**2 - n + 6. Let r(q) = v*p(q) + 3*j(q). Factor r(k).
(k - 3)*(k - 1)
Let j(s) be the first derivative of -28*s**5/5 - 16*s**4 + 4*s**3 + 32*s**2 + 16*s + 154. Determine c so that j(c) = 0.
-2, -1, -2/7, 1
Suppose 3*o - 6*o = -3*q + 12, 2*o - 1 = -q. Solve -3*w**4 - 5 - 4 - q*w**2 + 15 - 9*w + 9*w**3 = 0 for w.
-1, 1, 2
Let q(w) be the first derivative of -3/4*w**2 - 1/6*w**3 + w - 13 - 1/10*w**5 + 3/8*w**4. Factor q(g).
-(g - 2)*(g - 1)**2*(g + 1)/2
Let -3*i**3 + 3*i**3 - 8*i**2 - 13*i - 6 - i**3 = 0. Calculate i.
-6, -1
Let p(o) = o**2 + 4*o - 11. Let z be p(3). Suppose 0 = 4*j - 10*r + 5*r + z, 0 = -5*j + 3*r - 6. Factor 0 + 1/2*l**4 + 1/2*l**2 + j*l - l**3.
l**2*(l - 1)**2/2
Suppose -4*c = -4 + 12. Let r be (2 + c)/(1 - 4). Factor 0*u + 0*u**2 - 2/3*u**3 + 0 + r*u**4 + 2/3*u**5.
2*u**3*(u - 1)*(u + 1)/3
Factor -143*s + s**3 + 73*s - 2*s**2 + 62*s.
s*(s - 4)*(s + 2)
Let p(n) be the third derivative of n**8/1344 + n**7/420 - n**6/96 - n**5/40 + 45*n**2. Factor p(y).
y**2*(y - 2)*(y + 1)*(y + 3)/4
Let l(m) be the second derivative of -5/6*m**3 + 0*m**2 + 0*m**4 + 1/2*m**5 - 17*m - 5/42*m**7 + 0 + 0*m**6. Factor l(u).
-5*u*(u - 1)**2*(u + 1)**2
Let d(q) = 2*q + 6. Let i be d(6). Suppose -2*v + i = 5*u + v, -2*u = -3*v - 3. Factor -4*p**5 + 3*p**5 - 2*p**5 - u*p**4.
-3*p**4*(p + 1)
Let x(u) be the third derivative of u**6/360 - u**5/20 + 13*u**4/36 - 4*u**3/3 + 578*u**2. Factor x(b).
(b - 4)*(b - 3)*(b - 2)/3
Let r(m) be the third derivative of -m**7/210 + 7*m**6/240 - 3*m**5/40 + 5*m**4/48 - m**3/12 - 75*m**2. Factor r(c).
-(c - 1)**3*(2*c - 1)/2
Suppose 43*v = 48*v - 10. Let i be (4/(-12))/(v*(-4)/12). Suppose 1/6*h + i*h**2 + 1/2*h**3 + 0 + 1/6*h**4 = 0. What is h?
-1, 0
Let k = 84838/9 - 9426. Factor 0 + 1/9*o**4 + k*o + 5/9*o**3 + 8/9*o**2.
o*(o + 1)*(o + 2)**2/9
Let j = -58 - -80. Suppose -24*v - j - 2*v**2 - 3*v**2 + 2*v**2 - 26 = 0. What is v?
-4
Let d(t) = -24*t**3 + 222*t**2 - 640*t - 206. Let v(l) = l**3 - 3*l**2 + l + 1. Let y(w) = -2*d(w) - 20*v(w). Determine z, given that y(z) = 0.
-2/7, 7
Find f such that -83 + 569*f + 1100*f - 4107*f**2 + 237*f - 109 - 130*f = 0.
8/37
Factor 2/3*n**2 - 10/9*n**3 + 2*n + 0 + 2/9*n**4.
2*n*(n - 3)**2*(n + 1)/9
Let u = 60 + -60. Suppose 0 = 2*c - 3*c. Factor 0*r - 2/11*r**5 + u - 4/11*r**3 + c*r**2 - 6/11*r**4.
-2*r**3*(r + 1)*(r + 2)/11
Let x(z) be the first derivative of 8 - 4*z**5 + 0*z**2 - 3*z**4 + 8/3*z**3 + 0*z. Factor x(f).
-4*f**2*(f + 1)*(5*f - 2)
Let i(y) be the third derivative of -y**9/12096 + y**8/576 - y**7/126 - y**6/9 + 11*y**5/60 + 13*y**2. Let m(w) be the third derivative of i(w). Factor m(v).
-5*(v - 4)**2*(v + 1)
Factor -15*s + 7 + 13 - 31*s + 31*s - 5*s**2.
-5*(s - 1)*(s + 4)
Let j be -18 - -12 - (1 + -1 + 78/(-12)). Factor 1/2*h**3 - 1/2 - j*h + 1/2*h**2.
(h - 1)*(h + 1)**2/2
Let y(c) be the first derivative of -c**7/2520 + c**6/135 - 2*c**5/45 + c**3/3 - 32. Let p(n) be the third derivative of y(n). Solve p(a) = 0.
0, 4
Let v be 18/(-54)*(-81)/9. Let -1/2*t**2 + 1/2*t**v + 0*t + 0 = 0. Calculate t.
0, 1
Let g(w) = 160*w - 2400. Let h be g(15). Factor 0 + l**2 + 1/4*l**4 + 5/4*l**3 + h*l.
l**2*(l + 1)*(l + 4)/4
Let f(u) be the third derivative of 2*u**7/315 + 7*u**6/90 + 16*u**5/45 + 2*u**4/3 - 126*u**2. Factor f(w).
4*w*(w + 2)**2*(w + 3)/3
Suppose -55 = -3*a - 5*t, a - 4*t + 8*t - 16 = 0. Suppose 30*z - 24*z**3 - z**3 + 8*z**5 - 3*z**5 + 5*z**2 + 10*z + a - 5*z**4 = 0. What is z?
-1, 2
Let i = -317/288 - -10/9. Let o(g) be the second derivative of -1/160*g**5 + 0 - 3*g + 1/48*g**3 + 1/240*g**6 - i*g**4 + 0*g**2. Suppose o(w) = 0. What is w?
-1, 0, 1
Let y(r) be the second derivative of -5*r**4/72 + 25*r**3/36 - 223*r. Find l such that y(l) = 0.
0, 5
Let z = -11 - -11. Suppose 4*i - 25 - 7 = z. Find p, given that 3*p**5 + 6*p + i*