2. Let m(d) be the first derivative of -1/3*d**v - 1/9*d**3 - 1/3*d + 7. Suppose m(w) = 0. What is w?
-1
Let w = -89/124 - -30/31. Solve s**3 - w - s - 5/4*s**4 + 3/2*s**2 = 0.
-1, -1/5, 1
Suppose -2*d - 60 = 5*l, 0 = 4*l + 2*d + d + 55. Let n be 6/(-9)*27/l. Factor n*j**2 - 12/5*j + 3/5.
3*(j - 1)*(3*j - 1)/5
Let y(u) be the first derivative of -16*u**3 + 0*u + 14 - 6*u**2 - 21/4*u**4. Determine p, given that y(p) = 0.
-2, -2/7, 0
Suppose -3*i + 2*h = 287, 3*i + 3*h = i - 213. Let q = i - -99. Factor -2*s**2 + 2/3*s + 2*s**3 + q - 2/3*s**4.
-2*s*(s - 1)**3/3
Let k be (-169)/(-55) + 6/(-15) - (-3)/(-11). Factor 0 + 0*h - 36/5*h**2 - 1/5*h**4 + k*h**3.
-h**2*(h - 6)**2/5
Let s(b) be the third derivative of b**4/24 - b**3/6 - 3*b**2. Let x be s(3). Determine k so that -3*k**4 + 3*k**2 + 5*k**3 + k**4 - x*k**4 - 4*k**2 = 0.
0, 1/4, 1
Let q(j) be the first derivative of 1/8*j**2 + 1/12*j**3 - 1/4*j + 2 - 1/16*j**4. Factor q(w).
-(w - 1)**2*(w + 1)/4
Let i = -9847 - -9847. Factor i - 2/3*n**2 - 10/3*n.
-2*n*(n + 5)/3
Let o(i) be the third derivative of 0*i + 11*i**2 + 1/100*i**6 - 4/15*i**3 + 0*i**4 + 0 + 7/150*i**5. Factor o(d).
2*(d + 1)*(d + 2)*(3*d - 2)/5
Suppose -47*l - 60 = -201. Factor 8/5 - 18/5*q**l + 14/5*q**2 + 8*q.
-2*(q - 2)*(q + 1)*(9*q + 2)/5
Let y = -41 + 39. Let a(d) = -d**4 + d**3 - d + 1. Let q(f) = -22*f**4 + 12*f**3 + 8*f**2 - 12*f + 14. Let b(u) = y*q(u) + 28*a(u). Factor b(c).
4*c*(c - 1)*(c + 1)*(4*c + 1)
Factor 3*p**3 - 4*p**3 + 0*p**3 + 22 - 12*p**2 - 72 - 6*p - 39*p.
-(p + 2)*(p + 5)**2
Let x(h) be the third derivative of h**5/30 + 71*h**4/12 - 128*h**2 - h. Let x(z) = 0. Calculate z.
-71, 0
Let k(u) be the second derivative of 5/2*u**4 - 5/2*u**2 - 11*u + 1/2*u**5 + 5/6*u**3 - 5/6*u**6 - 5/14*u**7 + 0. Determine c so that k(c) = 0.
-1, 1/3, 1
Let p(q) = -q**2 - 7*q - 5. Let l = -8 + 3. Let f be p(l). Solve 3*m + 3*m**3 - 10*m + m**3 + 8*m**2 - f*m = 0.
-3, 0, 1
Suppose 4*i + 15 = 7*l - 6*l, 15 = -5*i. Factor 2/5*q**l - 8/5*q - 16/5 + 4/5*q**2.
2*(q - 2)*(q + 2)**2/5
Let b(i) be the first derivative of -4/25*i**5 + 0*i**3 + 0*i + 1/15*i**6 + 1/10*i**4 + 0*i**2 - 18. Solve b(a) = 0.
0, 1
Let p(x) be the third derivative of 3*x**6/200 + 14*x**5/75 + 31*x**4/40 + 3*x**3/5 - 52*x**2 - 1. Factor p(f).
(f + 3)**2*(9*f + 2)/5
Let j be 18/12*(-2 + 28/6). Let i(a) be the second derivative of -5*a - 2/3*a**2 + 8/9*a**3 + 0 - 7/36*a**j. Solve i(q) = 0.
2/7, 2
Let m(v) be the third derivative of v**8/20160 + v**7/315 + 4*v**6/45 + 2*v**5/5 - 30*v**2. Let x(r) be the third derivative of m(r). Factor x(h).
(h + 8)**2
Let s be 3/(2/((-6)/(-3))). Determine t, given that -26*t - s*t**4 + 7*t**4 - 4*t**3 + 26*t = 0.
0, 1
Suppose -1/4*k + 1/4*k**3 + 7/4*k**2 - 7/4 = 0. What is k?
-7, -1, 1
Let p(w) be the second derivative of w**7/10080 + w**6/720 + w**5/120 + 5*w**4/6 - 11*w. Let v(z) be the third derivative of p(z). Factor v(g).
(g + 2)**2/4
Factor 979*t**2 - 981*t**2 + 0 + 1 + 10*t + 11.
-2*(t - 6)*(t + 1)
Determine z so that -2*z**3 + 1810 - 1666 - 20*z**2 - z - 23*z = 0.
-6, 2
Let l = -107 - -107. Let y = 64/3 - 21. Find q such that l + 1/3*q**4 + 0*q + y*q**3 - 2/3*q**2 = 0.
-2, 0, 1
Let c(x) be the third derivative of x**6/24 + 15*x**5/4 + 1125*x**4/8 + 5625*x**3/2 - 212*x**2. Solve c(r) = 0 for r.
-15
Let g(r) be the second derivative of 27*r**5/80 + 57*r**4/8 + 481*r**3/8 + 507*r**2/2 - 83*r. Factor g(c).
3*(c + 4)*(3*c + 13)**2/4
Let j = -2/117 - -4292/117. Let d = -27397 - -27411. Let 56/3*k - 8/3 - 34*k**2 + j*k**4 - d*k**5 - 14/3*k**3 = 0. Calculate k.
-1, 2/7, 1/3, 1, 2
Factor 251 + 5*m**2 - 22*m**2 - 3060 + 8*m**2 - 106*m + 8*m**2.
-(m + 53)**2
Suppose 588*z**5 - 5*z**2 + 837*z**2 + 44*z**2 + 108*z - 48 - 1821*z**3 - 1953*z**4 = 0. Calculate z.
-1, -1/4, 2/7, 4
Let v(j) be the third derivative of j**7/6300 - j**6/900 - j**5/100 + j**4/12 - 19*j**2. Let g(p) be the second derivative of v(p). Solve g(x) = 0 for x.
-1, 3
Let n(w) = 5*w + 3. Let x be n(1). Let f be (-364)/(-10) - 32/80. Suppose 20*g**2 + 11 - f*g + 16*g**3 + 12*g**3 - 28*g**4 + x*g**3 - 3 = 0. Calculate g.
-1, 2/7, 1
Let p(k) be the first derivative of 9*k**3 - 24*k**2 - 12*k - 435. Solve p(g) = 0.
-2/9, 2
Let k be (-8)/6*9/(-6). Let -k*c + 3*c - 2*c + 2*c**2 - c = 0. Calculate c.
0, 1
Let z be -2*(244/80 - (-3)/9). Let a = z + 43/6. Solve 2/5*s**3 + 0 + a*s + 4/5*s**2 = 0 for s.
-1, 0
Factor 624/5*a + 594/5*a**4 - 696/5*a**3 - 80*a**2 + 288/5 - 121/5*a**5.
-(a - 2)**3*(11*a + 6)**2/5
Let a(h) be the second derivative of 0*h**4 + 0*h**2 + 0 - 4/9*h**3 - 37*h + 1/30*h**5. Factor a(r).
2*r*(r - 2)*(r + 2)/3
Suppose n + 5*l + 14 - 43 = 0, 25 = 5*l. Suppose n*y - 6 = y. What is h in -15*h - 3 - 6*h + 6*h**y + 72*h**3 + 6*h = 0?
-1/3, -1/4, 1/2
Let z(l) be the first derivative of l**7/105 - l**6/20 - l**5/15 + l**4 - 8*l**3/3 + 5*l**2/2 - 13. Let y(a) be the second derivative of z(a). Factor y(w).
2*(w - 2)**2*(w - 1)*(w + 2)
Let a(q) be the second derivative of -q**6/40 + 3*q**5/80 + q**4/16 - q**3/8 + 2*q + 6. What is i in a(i) = 0?
-1, 0, 1
Let y = -101 + -9. Let o be (y/(-25) - 4) + 48/55. Suppose -2/11*a**4 - 10/11*a**3 - o*a - 4/11 - 18/11*a**2 = 0. Calculate a.
-2, -1
Let n be (4/(-12))/(24/(-504)). Let j(r) be the third derivative of -1/60*r**5 + 0*r**3 - 1/210*r**n + 0*r**4 + 2*r**2 + 0 + 0*r + 1/60*r**6. Factor j(g).
-g**2*(g - 1)**2
Let d(u) = u**3 - 8*u**2 + 2*u - 10. Let r be d(8). Factor o + 2 + 3*o**3 + 0 - r*o - 4*o**2.
(o - 2)*(o + 1)*(3*o - 1)
Let n(j) be the first derivative of -8*j**3/15 + 39*j**2/5 + 4*j - 61. Suppose n(b) = 0. Calculate b.
-1/4, 10
Let v(r) = -r**2 + r. Let l be v(1). Let h be ((-126)/(-165) + 68/(-187))*5. Factor l*j**h + 0 + 0*j**3 + 4/3*j**4 + 0*j.
4*j**4/3
Suppose 3*m - 27 = -3*x, -4*m - 4*x + 15 = -3*x. Factor -4/3*g**m - 100/3 + 40/3*g.
-4*(g - 5)**2/3
Let o = 80 + -83. Let j(s) = -s**3 - 3*s**2 - 5*s. Let z(c) = c**2 + c - 1. Let f be z(1). Let w(y) = -y. Let h(a) = f*j(a) + o*w(a). Factor h(i).
-i*(i + 1)*(i + 2)
Let q(o) = -5*o**3 + 116*o**2 - 24*o + 25. Let d be q(23). Let -2/5*g + 0 + 2/5*g**d = 0. What is g?
0, 1
Let l = -820 + 820. Let d(m) be the third derivative of -1/28*m**8 + 0 - 8/9*m**4 - 44/45*m**6 - 64/45*m**5 - 32/105*m**7 + 0*m**3 + 8*m**2 + l*m. Factor d(c).
-4*c*(c + 2)**2*(3*c + 2)**2/3
Factor 8*r**4 + 7*r**2 + 7*r**4 + 4*r**4 - 12*r**4 - 6*r**4 + 9*r**3 - 8 - 9*r.
(r - 1)*(r + 1)**2*(r + 8)
Let n(r) be the third derivative of 2*r**7/135 + r**6/9 + r**5/135 - 5*r**4/9 - 16*r**3/27 + 30*r**2 + 14*r. Suppose n(i) = 0. What is i?
-4, -1, -2/7, 1
Let z(r) be the second derivative of -r**7/5460 - r**6/780 - r**5/390 + 5*r**3/3 - 19*r. Let t(f) be the second derivative of z(f). Factor t(v).
-2*v*(v + 1)*(v + 2)/13
Let h(p) = -2*p + 53. Let q be h(25). Factor -2 + 16*y + y**q + y**2 - 9*y + 4*y**2 + 5.
(y + 1)**2*(y + 3)
Let h(p) = -p**3 + 8*p**2 - 4. Let n be h(8). Let v = 8 + n. What is l in -3 + 0 - v*l**2 - 1 + 5*l**2 = 0?
-2, 2
Factor -2 + 1/2*y**2 + 2*y - 1/2*y**3.
-(y - 2)*(y - 1)*(y + 2)/2
Find d, given that 0 - 1/5*d**2 - 13*d = 0.
-65, 0
Let z = 975/7 + -139. Suppose -16*i + 19*i - 5*h = 25, 0 = 3*i - 4*h - 20. Factor z*t**2 - 5/7*t**4 + 0 + i*t + 3/7*t**3.
-t**2*(t - 1)*(5*t + 2)/7
Let w be (63/45 - -3) + (-1 - 3). Let v(q) = q**3 + q**2 - q + 2. Let t be v(0). Factor 0*u + w*u**4 + 0 + 2/5*u**5 + 0*u**3 + 0*u**t.
2*u**4*(u + 1)/5
Let s be 12/8*(-60)/2. Let l be (s/(-5) + -3)/10. Factor 3/5*r**2 - 3/5*r**4 - 3/5*r + l*r**3 + 0.
-3*r*(r - 1)**2*(r + 1)/5
Let j(t) be the third derivative of 0*t**4 - 17*t**2 + 1/1320*t**6 + 1/660*t**5 - 17/2310*t**7 + 0*t + 5/1232*t**8 + 0*t**3 + 0. Let j(o) = 0. What is o?
-1/5, 0, 1/3, 1
Let d(m) = -5*m**2 + 2*m - 21. Let a(q) = 12*q**2 - 3*q + 41. Let f(y) = 3*a(y) + 7*d(y). Factor f(g).
(g - 3)*(g + 8)
Let y = 79 + -5924/75. Let n(t) be the second derivative of 0*t**2 - 6*t + 1/35*t**7 - 3/50*t**5 - 1/30*t**4 + 0 + 0*t**3 + y*t**6. Find h, given that n(h) = 0.
-1, -1/3, 0, 1
Let l = 72 - 69. Suppose -b = l*b + o - 12, -b = o - 6. Find n, given that -2/5*n**4 + 0*n - 2/5*n**b - 4/5*n**3 + 0 = 0.
-1, 0
Let r = -16390 - -213078/13. Find m such that 40/13*m**2 - r*m**3 + 12/13 + 46/13*m = 0.
-1/2, 6
Let m(o) be the first derivative of 0*o + 1/2*o**2 + 1/3*o**3 - 15