irst derivative of -n**6/180 + n**5/30 + n**4/4 - 5*n**3/3 - 1. Let u(f) be the third derivative of l(f). Factor u(j).
-2*(j - 3)*(j + 1)
Let r(v) = v. Let n(d) = -3*d**2 + 11*d - 8. Let u(y) = -2*y**2 + 10*y - 7. Let q(f) = 3*n(f) - 4*u(f). Let h(c) = -q(c) - 4*r(c). Factor h(z).
(z - 1)*(z + 4)
Let c = 32 - 30. Factor -10*k + 298*k**4 - 303*k**4 + 21*k**2 - 6*k**c.
-5*k*(k - 1)**2*(k + 2)
Suppose -264 + 7*o**2 + 9*o**2 + 116 - 588*o = 0. What is o?
-1/4, 37
Let g(w) = 7*w**4 + 14*w**3 + 5*w - 5. Let x(q) = 11*q**4 + 21*q**3 + 8*q - 8. Let m(r) = -8*g(r) + 5*x(r). Factor m(b).
-b**3*(b + 7)
Suppose 3*x - 2 = -c + 4*x, 0 = -2*c + x + 6. Factor -12*t + 2*t**2 + 6*t**c - 9*t**3 + 3*t**5 - 12*t**2 - 14*t**2.
3*t*(t - 2)*(t + 1)**2*(t + 2)
Let k(j) be the second derivative of -j**9/432 + 3*j**8/560 - j**7/420 + 3*j**3/2 - 5*j. Let d(i) be the second derivative of k(i). Find x, given that d(x) = 0.
0, 2/7, 1
Let a(d) be the first derivative of d**6/42 + 41*d**5/35 + 249*d**4/14 + 270*d**3/7 - 11475*d**2/14 + 10125*d/7 - 41. Determine t, given that a(t) = 0.
-15, 1, 3
Suppose 0 = f - 5*o + 4, -5*f + 2 = -7*o + 4*o. Let n be 0/((-4)/6*3/f). Factor 1/2*j**2 + j + n.
j*(j + 2)/2
Let i(m) be the third derivative of 2*m**7/525 + 53*m**6/900 + 3*m**5/10 + 2*m**4/5 - 16*m**3/45 - 91*m**2. Find b, given that i(b) = 0.
-4, -1, 1/6
Let b = 287 - 197. Let p = b + -90. What is r in -3/2*r**2 + 1/2*r + p = 0?
0, 1/3
Let q be (14/21)/(-2) + (-104)/(-39). Factor 2 - q*u - u**2.
-(u + 3)*(3*u - 2)/3
Determine y, given that -16/7*y**4 - 10/7*y - 2/7*y**5 - 32/7*y**2 + 0 - 36/7*y**3 = 0.
-5, -1, 0
Let x(s) be the second derivative of -s**5/100 - 3*s**4/20 - 2*s**3/3 - 6*s**2/5 - 3*s + 19. Solve x(i) = 0.
-6, -2, -1
Let r(x) be the first derivative of 6*x**5/5 + 3*x**4/4 - 2*x**3 - 3*x**2/2 - 419. What is f in r(f) = 0?
-1, -1/2, 0, 1
Let b(g) be the first derivative of -g**3/21 + g**2/14 + 20*g/7 - 68. Determine o, given that b(o) = 0.
-4, 5
Factor -8/7*q**3 + 4/21*q + 2/3*q**4 + 0 + 2/7*q**2.
2*q*(q - 1)**2*(7*q + 2)/21
Let k = -1796/11 - -1798/11. Solve -16/11 + k*w**2 + 14/11*w = 0 for w.
-8, 1
Let s = -1094 - -1097. Let j(u) be the first derivative of -6*u**s - 7 + 0*u + 5/2*u**4 - 2*u**2. What is p in j(p) = 0?
-1/5, 0, 2
Let m(g) be the first derivative of 3*g**4/4 + 33*g**3/4 + 21*g**2 + 9*g - 68. Determine i so that m(i) = 0.
-6, -2, -1/4
Let h(k) be the third derivative of k**7/1155 - 7*k**6/660 + 3*k**5/110 + 7*k**4/132 - 10*k**3/33 - 63*k**2 + k. Determine f so that h(f) = 0.
-1, 1, 2, 5
Let p(k) be the third derivative of -k**8/840 + 13*k**7/525 - k**6/5 + 56*k**5/75 - 16*k**4/15 + 34*k**2 - 2*k. Let p(r) = 0. Calculate r.
0, 1, 4
Let n be ((-8)/80*16)/(-2). Let a be -1 - (0 + (-21)/15). Suppose -n*y - 2/5*y**2 - a = 0. What is y?
-1
Let z(o) = -o**2 + 41*o + 576. Let i be z(52). Let 0*g**2 + 0*g + 0*g**3 + 2/9*g**i + 0 = 0. What is g?
0
Let k(n) be the third derivative of 5*n**5/54 - 85*n**4/27 + 1156*n**3/27 - 82*n**2. Factor k(q).
2*(5*q - 34)**2/9
Let k(c) be the third derivative of 3*c**7/350 - 11*c**6/200 + 37*c**5/300 - c**4/8 + c**3/15 - 120*c**2. Factor k(l).
(l - 2)*(l - 1)*(3*l - 1)**2/5
Let m(a) be the third derivative of 1/36*a**4 - 1/180*a**5 + 0*a**3 + 0*a + 0 + 3*a**2. Factor m(w).
-w*(w - 2)/3
Let f = -2536/7 + 12736/35. Solve 2/5*l**3 + f*l - 2*l**2 + 0 = 0.
0, 1, 4
Let m be 38/60 - ((-274)/(-30) - (-171)/(-19)). Factor -m - 1/4*y**2 - 3/4*y.
-(y + 1)*(y + 2)/4
Let y be (7 - 15) + (6/2 - 1). Let z be (-5 - (y - -5)) + 7. What is r in 1/6*r**2 - 1/6*r**4 + 0*r**z + 0 + 0*r = 0?
-1, 0, 1
Suppose 0 = -j + 7*j - 1026. Let o = 1540/9 - j. Determine q, given that 0*q**2 + 0*q + 1/3*q**3 + o*q**4 + 0 = 0.
-3, 0
What is z in 0 + 2*z**2 + 1/6*z**4 + 4/3*z + z**3 = 0?
-2, 0
Factor 101*r - 208*r - 15*r**4 + 35*r**3 + 87*r.
-5*r*(r - 2)*(r - 1)*(3*r + 2)
Let q be 1/(435/219 + -2). Let l = 123 + q. Factor -38*v**2 + 5*v**5 + l*v**3 - 43*v**4 + 3*v**5 + 5*v + 9*v + 11*v**4 - 2.
2*(v - 1)**3*(2*v - 1)**2
Let z be (-9)/24*(-88)/36. Let h = -1/4 + z. Determine d so that 1/3*d**4 + 1/3 - h*d**2 + 0*d + 0*d**3 = 0.
-1, 1
Suppose 3561*l = 3566*l. Determine s, given that -8*s + 24*s**2 + l - 5/4*s**5 - 33/4*s**4 - 13/2*s**3 = 0.
-4, 0, 2/5, 1
Let i = 20 + -14. Let g(k) = 7*k**2 - 3 + 2*k - 3 + i. Let y(b) = -48*b**2 - 15*b. Let t(l) = 27*g(l) + 4*y(l). Let t(j) = 0. What is j?
-2, 0
Factor 0*q + 16/13*q**2 - 2/13*q**4 + 14/13*q**3 + 0.
-2*q**2*(q - 8)*(q + 1)/13
Suppose 21*c - 4*o - 6 = 24*c, -2*c + 5*o + 19 = 0. Let u(p) be the first derivative of p + 1/3*p**3 - p**c + 3. Factor u(n).
(n - 1)**2
Let b = -619/3 - -629/3. Factor -2/3*r**2 - b*r + 0.
-2*r*(r + 5)/3
Suppose 185 + 269 = 116*m + 106. Factor 2/9*j**m + 10/9*j - 8/9*j**2 - 4/9.
2*(j - 2)*(j - 1)**2/9
Let g(c) = -8*c**5 + 8*c**4 + 12*c**3 - 38*c**2 - 30*c - 6. Let d(w) = -w**5 + w**3 - w**2 + w + 1. Let s(t) = -20*d(t) + 2*g(t). Let s(r) = 0. Calculate r.
-2, -1, 2
Let t be (12/(-21))/(-2) - 36/28. Let r be (t + -1)/(((-192)/(-18))/(-8)). Solve -3*a**2 + 9/2*a - 3*a**3 - 3/2*a**5 + 9/2*a**4 - r = 0 for a.
-1, 1
Suppose -2*i - 21 = -5*w, -w - 3*w - 20 = 0. Let k be i/(-5) + (-3)/5. Solve -12*j**2 - 2*j - 10*j + 4*j - 4*j**k + 8*j**4 = 0.
-1, 0, 2
Suppose -57 = -5*c + 8. Suppose -5*p = -2*n - 4 + c, -n - p + 1 = 0. Factor 0 + 12/7*t**n + 18/7*t + 2/7*t**3.
2*t*(t + 3)**2/7
Let z(c) be the second derivative of c**6/6 - 10*c**5 + 2185*c**4/12 - 1805*c**3/3 - 3*c + 54. Let z(t) = 0. What is t?
0, 2, 19
Let c(l) = l**3 + 7*l**2 - 33*l + 1. Let g be c(-10). Suppose -17 = -16*f + g. Factor 0 + 5/2*o**2 + o**f - o - 5/2*o**4.
-o*(o - 1)*(o + 1)*(5*o - 2)/2
Let c = 2/2455 + 483/9820. Let t(d) be the first derivative of -1/16*d**2 - 1/12*d**3 + 1/48*d**6 + c*d**5 + 0*d**4 + 0*d + 3. Factor t(r).
r*(r - 1)*(r + 1)**3/8
Factor -4/5*j**2 + 48/5 + 44/5*j.
-4*(j - 12)*(j + 1)/5
Suppose 19*v**2 + 307*v**3 - 25*v + v**2 - 302*v**3 = 0. Calculate v.
-5, 0, 1
Let q = 23/136 + -3/68. What is l in -2*l - 1/2 + 1/2*l**3 + q*l**2 = 0?
-2, -1/4, 2
Suppose k - 3*g + 0*g - 18 = 0, 0 = 5*g + 10. Factor -40*u + k*u + 23*u - 10*u**2 - 5*u**3.
-5*u*(u + 1)**2
Let a(y) = y**3 - 20*y**2 - 17*y - 70. Let k be a(21). Let s(p) be the second derivative of 0 - 6*p**2 - k*p**3 + 5*p - 49/4*p**4. Solve s(b) = 0.
-2/7
Let n(s) be the first derivative of 18*s**5/5 + 282*s**4 - 2698*s**3/3 + 1036*s**2 - 520*s - 537. Find y, given that n(y) = 0.
-65, 2/3, 1
Let q = 564 + -808. Let d = q + 247. What is w in -2/7*w**2 + 2/7*w**d + 0 + 0*w = 0?
0, 1
Let r(d) = -19*d - 1. Let q be r(-1). Let h = q - 15. Factor 2/3*j**4 + 2*j**h + 2*j**2 + 0 + 2/3*j.
2*j*(j + 1)**3/3
Let d(t) = -5*t**3 - 38*t**2 + 81*t - 40. Let f(s) = -51*s**3 - 381*s**2 + 810*s - 399. Let j(u) = -21*d(u) + 2*f(u). Factor j(m).
3*(m - 1)**2*(m + 14)
Let s(w) be the second derivative of w**6/120 + w**5/80 - w**4/48 - w**3/24 + 195*w. Suppose s(q) = 0. Calculate q.
-1, 0, 1
Suppose 8 = -132*i + 134*i. Find x such that 1/4*x**4 - i*x + 0 - 3*x**2 + 0*x**3 = 0.
-2, 0, 4
Suppose -10560*u - 236*u**2 - 30976/3 - 4/3*u**3 = 0. Calculate u.
-88, -1
Let n be 2/(-11) - 6222/(-1309). Factor -64/7 - n*w - 4/7*w**2.
-4*(w + 4)**2/7
Let z(r) = -2*r**2 + 6*r + 3. Let q = -17 - -19. Let p(a) = 17 + 4*a**2 - 9*a**q - 6*a**2 + 10*a + 25*a. Let l(o) = -6*p(o) + 34*z(o). Factor l(k).
-2*k*(k + 3)
Let i = 587/238 - -4/119. Determine a, given that -5/4*a**2 - 5/4*a**4 + 0*a + 0 - i*a**3 = 0.
-1, 0
Let w(s) be the third derivative of s**10/30240 + s**9/15120 - s**8/3360 - 7*s**4/12 - 16*s**2. Let g(z) be the second derivative of w(z). Factor g(v).
v**3*(v - 1)*(v + 2)
Find b, given that -6/19*b**2 + 0*b + 2/19*b**3 + 6/19*b**4 + 0 - 2/19*b**5 = 0.
-1, 0, 1, 3
Factor -9/5 + 29/5*m**2 - 33/5*m + 13/5*m**3.
(m - 1)*(m + 3)*(13*m + 3)/5
Let h be -11*(7 - 385/60). Let i = h - -23/3. Let i*q**3 + 3/4*q**2 - 1/4*q - 1/4 + 1/2*q**4 = 0. Calculate q.
-1, 1/2
Let m = -293/116 - -95/29. What is d in 0 - 3/4*d - 3*d**2 - 3*d**4 - 9/2*d**3 - m*d**5 = 0?
-1, 0
Suppose 35*a + 330 = 46*a. Let o be 5 - 9/(54/a). Factor 0 + 0*n**2 + o*n + 2/13*n**4 + 0*n**3.
2*n**4/13
Let o be (12/(-2) - -1)/(2/(-34)). Let z(k) = 15*k**3 - 155*k**2 + 85. Let v(b) = b**3 - 11*b**2 + 6. Let f(m) = o*v(m) - 6*z(m). Let f(j) = 0. What i