q(3). Let i(l) be the third derivative of 1/160*l**6 + 0*l + 0 + 0*l**3 + w*l**5 + l**2 - 1/32*l**4. Factor i(a).
3*a*(a - 1)*(a + 1)/4
Let x(h) be the second derivative of 0*h**2 + 4*h + 0 - 27/20*h**5 + 7/4*h**4 + 1/2*h**6 - 1/14*h**7 - h**3. Determine d, given that x(d) = 0.
0, 1, 2
Let a(m) be the second derivative of -m**4/54 - 2*m**3/27 + 8*m**2/9 + 17*m. Factor a(y).
-2*(y - 2)*(y + 4)/9
Let t(k) be the first derivative of -121*k**3/12 - 55*k**2/2 - 25*k + 52. Determine j so that t(j) = 0.
-10/11
Let u(p) = -2*p**3 + 5*p - 2. Let m(t) = 52*t**3 - 528*t**2 + 16764*t + 35960. Let g(a) = -m(a) - 24*u(a). Factor g(l).
-4*(l - 67)**2*(l + 2)
Suppose -4*k - 15 = -7*k. Suppose 30 = k*m - 135. Solve m*h**2 - 3*h**4 + 6*h + 7*h**4 - 12*h**3 + 60*h**3 + 17*h**4 = 0 for h.
-1, -2/7, 0
Factor -2/11*z**3 + 0 - 8/11*z - 8/11*z**2.
-2*z*(z + 2)**2/11
Suppose 24*z + 18 = 25*z. Suppose -5*d - d + z = 0. Factor -7/3*n**d - 2/3 + 4*n**2 - n.
-(n - 1)**2*(7*n + 2)/3
Let r be (-64)/(-160) + (-46)/(-10) - (-57)/27. Let 16/9 + 100/9*j**2 + r*j + 76/9*j**3 + 28/9*j**4 + 4/9*j**5 = 0. Calculate j.
-2, -1
Let y(z) = -13*z**5 + 54*z**4 - 46*z**3 - z**2 + 29*z - 13. Let w(k) = -k**5 - k**2 - k + 1. Let q(l) = -10*w(l) - 2*y(l). Find j such that q(j) = 0.
-2/3, 2/3, 1
Let z(f) be the first derivative of -2*f**5/5 - 5*f**4/2 + 2*f**3/3 + 5*f**2 + 142. Suppose z(r) = 0. Calculate r.
-5, -1, 0, 1
Let q be (74/(-12) + 5)*(-8)/98. Let j(y) be the second derivative of q*y**7 - 2*y + 0*y**2 - 16/3*y**3 + 6/5*y**5 + 4/3*y**4 + 0 - 2/3*y**6. Factor j(h).
4*h*(h - 2)**3*(h + 1)
Suppose -4*n = 7*n + 9*n. Solve 4/11 - 2/11*r**3 + 6/11*r + n*r**2 = 0 for r.
-1, 2
Let w(n) = -n**2 - 14*n - 49. Let t = -305 - -298. Let k be w(t). Let k + 0*h**2 + 8/7*h - 2/7*h**3 = 0. What is h?
-2, 0, 2
Let g(o) be the third derivative of -o**7/105 + o**6/48 + o**5/8 - 5*o**4/12 + o**3/3 - o**2 + 513. Let g(j) = 0. What is j?
-2, 1/4, 1, 2
Let g be 8733/(-852) + (-11)/(-1). Factor -3/2 - 3/4*v + g*v**2.
3*(v - 2)*(v + 1)/4
Suppose 20 = -5*f + 10*f. Factor -92 - 7*k**2 - k**4 - k - 3*k**3 + 92 + f*k**2.
-k*(k + 1)**3
Let i = -7 - -7. Suppose -p + 4*v - 12 = i, 2*v - 4*v - 22 = -4*p. Find m such that 4*m**2 - 4*m - p - m + m = 0.
-1, 2
Let s be 1 + (-3)/3 + 12/3. Let w(h) be the second derivative of -5/16*h**5 + h + 2/3*h**3 + 0 + 5/48*h**s + 1/2*h**2. Factor w(k).
-(k - 1)*(5*k + 2)**2/4
Let z(q) be the first derivative of -q**6/12 + q**5/5 + 3*q**4/4 - 2*q**3/3 - 13*q**2/4 - 3*q - 383. Find u such that z(u) = 0.
-1, 2, 3
Let t(r) be the second derivative of r**4/84 - r**3/21 - 3*r**2/14 + 7*r + 13. What is s in t(s) = 0?
-1, 3
Let t(f) be the third derivative of -1/26*f**4 + 0 + 0*f + 1/390*f**5 + 3/13*f**3 + 8*f**2. Let t(p) = 0. Calculate p.
3
Let c(x) be the second derivative of 0*x**2 + 0*x**4 - 5/6*x**3 + 0 + 8*x - 1/200*x**5 + 1/1800*x**6. Let d(z) be the second derivative of c(z). Factor d(j).
j*(j - 3)/5
Let x(a) be the first derivative of -2*a**3/57 + 10*a**2/19 - 50*a/19 + 128. Factor x(t).
-2*(t - 5)**2/19
Let d be (-4)/(-3)*-4*(-3)/16. Let m(c) be the first derivative of d + 1/20*c**5 - 1/12*c**3 + 0*c + 1/8*c**2 - 1/16*c**4. Determine z so that m(z) = 0.
-1, 0, 1
Find z such that 18*z**2 - 24*z + 3/4*z**4 - 6*z**3 + 12 = 0.
2
Let r = -14 + 8. Let f be 2/r + (-7)/(-3). Find n, given that 3*n**2 + 3*n - 6*n**3 + 5*n - 5*n**f - 4*n**4 + 2*n**5 + 10*n**2 = 0.
-1, 0, 2
Let o be ((-3)/9)/((-25)/375). Factor -d**o + 2*d**4 - 1/4*d**3 - 5/4*d**2 + 1/4 + 1/4*d.
-(d - 1)**3*(2*d + 1)**2/4
Suppose 9 = 11*p - 35. Suppose -w = p*w - 10. Let 2 + 1/2*s**w + 2*s = 0. Calculate s.
-2
Determine z, given that 30*z - 9*z**3 + 0*z**3 - 24*z + 3*z**5 - 3*z**2 + 3*z**4 = 0.
-2, -1, 0, 1
Suppose 0 = 4*t - 3 - 21. Suppose t*n = 26 - 8. Factor 27*i + 2*i**3 + 6*i**2 - 24*i + 0*i**n + i**3.
3*i*(i + 1)**2
Let h(a) be the second derivative of a**7/147 + 3*a**6/35 + 3*a**5/14 + a**4/6 + 17*a. Factor h(w).
2*w**2*(w + 1)**2*(w + 7)/7
Let w(n) be the first derivative of 0*n - 2/27*n**3 - 3 + 1/18*n**4 + 0*n**2. Factor w(c).
2*c**2*(c - 1)/9
Let j(z) be the first derivative of -z**6/24 - z**5/15 - z**4/30 - 16*z**2 - 12. Let b(s) be the second derivative of j(s). Factor b(l).
-l*(5*l + 2)**2/5
Determine u, given that -543/2*u**2 - 51/2*u + 99*u**5 + 9 - 987/2*u**4 + 1365/2*u**3 = 0.
-2/11, 1/6, 1, 3
Let p = 38 - 29. Let t(f) = -f**2 + 9*f + 2. Let i be t(p). Suppose -1/2 + 1/2*a**i + 1/4*a - 1/4*a**3 = 0. What is a?
-1, 1, 2
Let j = 15 + -4. Let d be 2/8 - j/(-4). Determine t, given that -3*t**5 + 22*t**4 - t**2 - t**d + 4*t**5 - 21*t**4 = 0.
-1, 0, 1
Suppose -5*r + j + 6 = 4*j, 2*j - 3 = -3*r. Let g(d) = 5 - 8*d**2 + 0 + r*d**2 - 3 - 4*d. Let p(m) = 11*m**2 + 7*m - 5. Let a(b) = 5*g(b) + 2*p(b). Factor a(s).
-3*s*(s + 2)
Let i = 26 + -16. Let p = i - 8. Factor y + y**4 + 2*y - y**2 + p*y - y**3 - 4*y.
y*(y - 1)**2*(y + 1)
Let x(s) = -22*s**2 + 1066*s - 246. Let p(m) = -21*m**2 + 1065*m - 249. Let o(u) = -6*p(u) + 5*x(u). Factor o(b).
4*(b - 66)*(4*b - 1)
Let l(q) be the third derivative of -q**8/1008 + q**7/315 + q**6/60 - 2*q**5/45 - 5*q**4/72 + q**3/3 - 95*q**2 - q. Determine u, given that l(u) = 0.
-2, -1, 1, 3
Let m(y) be the first derivative of y**6/16 - 27*y**5/40 + 39*y**4/16 - 17*y**3/4 + 63*y**2/16 - 15*y/8 + 292. Suppose m(p) = 0. Calculate p.
1, 5
Determine t so that 4*t**5 + 68/3*t - 16 + 274/3*t**2 - 128/3*t**3 - 34/3*t**4 = 0.
-3, -1/2, 1/3, 2, 4
Let z be 5/(-25)*30/(-3). Suppose -5*d**2 + z*d + 2*d**2 - d + 5*d = 0. What is d?
0, 2
Let m(f) be the third derivative of f**5/270 + 85*f**4/108 + 28*f**3/9 - 126*f**2. Let m(r) = 0. What is r?
-84, -1
Let f(y) be the first derivative of -2*y**3/33 - 39*y**2/11 - 535. Factor f(h).
-2*h*(h + 39)/11
Let r(y) = 15*y**3 + 9*y**2 - 40*y + 16. Let k(g) = -46*g**3 - 28*g**2 + 120*g - 48. Let d(l) = 3*k(l) + 8*r(l). Factor d(o).
-2*(o + 2)*(3*o - 2)**2
Let n = 11 + -3. Suppose -10*s + 6*s + n = 0. Find z, given that s*z**4 + z**4 + 3 - z - 12*z**3 - 11*z + 18*z**2 = 0.
1
Find k such that 41/6*k**3 + 1078/3*k + 1372/3 - 1/6*k**4 - 91*k**2 = 0.
-1, 14
Let z = 67/210 + 1/70. Let x(s) be the first derivative of 1/27*s**3 + z*s + 10 + 2/9*s**2. Factor x(o).
(o + 1)*(o + 3)/9
Let z = 8/169 + 97/1521. Let d(p) be the second derivative of 0 - 1/18*p**6 + 0*p**2 - 1/10*p**5 + 4/9*p**3 + z*p**4 + 7*p - 1/126*p**7. Factor d(j).
-j*(j - 1)*(j + 2)**3/3
Suppose -h - 168 = -4*m, 0*h - 177 = h + 5*m. Let d be (-4)/(-5) - (h/60 + 3). What is o in d + 2/3*o**2 - 4/3*o = 0?
1
Let j(m) be the second derivative of -m**6/60 + 3*m**5/8 - 13*m**4/24 - 5*m**3/4 + 7*m**2/2 - 3*m + 5. Factor j(g).
-(g - 14)*(g - 1)**2*(g + 1)/2
Suppose 65 = 2*f + 57. Let z(w) be the first derivative of 2 + 0*w + 1/5*w**2 - 4/15*w**3 + 1/10*w**f. Solve z(v) = 0.
0, 1
Factor 1/2*s**3 + 0 + 7*s**2 + 13/2*s.
s*(s + 1)*(s + 13)/2
Let g = -1164 + 1164. Suppose -3*f - 3*d + 18 = 0, -4*f + 9 + 8 = -3*d. Suppose -44/5*r**3 + g*r + 64/5*r**4 + 0 - 28/5*r**f + 8/5*r**2 = 0. Calculate r.
0, 2/7, 1
Let x be (-17 - -15) + (-5)/(10/(-4)). Let m be (-8)/(-6)*-1 - -2. Factor 1/3*t**3 + 1/3*t - m*t**2 + x.
t*(t - 1)**2/3
Let n(f) be the second derivative of -2/3*f**2 - 3/10*f**5 - 26*f + 17/36*f**4 + 0*f**3 + 0 + 1/18*f**6. Factor n(k).
(k - 2)*(k - 1)**2*(5*k + 2)/3
Find u, given that 58/15*u**3 + 4/5*u**4 + 4/5 + 62/15*u + 32/5*u**2 = 0.
-2, -3/2, -1, -1/3
Factor 15*w + 5*w**4 + 48*w**3 + 39*w**3 - 62*w**3 + 35*w**2.
5*w*(w + 1)**2*(w + 3)
Let j(x) be the first derivative of 0*x - 2/7*x**2 - 2/21*x**3 + 12. Let j(d) = 0. Calculate d.
-2, 0
Let h = 174/23 + -778/115. Let r be 1*(-4)/(-2)*(-6)/(-4). Find x, given that -500 - h*x**4 - 400*x - 16*x**r - 120*x**2 = 0.
-5
Let j(o) be the second derivative of 23*o + 0*o**2 + 1/180*o**5 + 1/36*o**4 + 0 - 2/27*o**3. Let j(p) = 0. What is p?
-4, 0, 1
Let z = 2/3663 + -18437/223443. Let r = z - -71/122. Determine s so that 0 + r*s - 1/2*s**2 - 1/2*s**3 + 1/2*s**4 = 0.
-1, 0, 1
Factor -26410 - 39*x + 407*x - 4*x**2 + 2*x**2 + 9482.
-2*(x - 92)**2
Let a(b) be the second derivative of b**5/10 - 45*b**4/2 + 1496*b**3 + 4624*b**2 - 126*b. Factor a(v).
2*(v - 68)**2*(v + 1)
Let y = 6 - 6. Suppose -2*q + 4 = -3*m, 0 = q - 4*m - y*m + 8. Factor q + 3*z + 14*z - 5*z + 4*z**2.
4*(z + 1)