b = 2/55 + -23/2145. Let h(m) be the first derivative of 3/26*m**4 + 0*m + 0*m**2 + b*m**6 + 4 - 2/39*m**3 - 6/65*m**5. Factor h(a).
2*a**2*(a - 1)**3/13
Let a(s) be the first derivative of -10/7*s**3 + 15/14*s**2 + 1 - 3/7*s**5 + 1/14*s**6 + 15/14*s**4 - 3/7*s. Let a(q) = 0. What is q?
1
Let y(q) be the first derivative of -4/7*q - 2/7*q**2 + 1/7*q**4 + 4/21*q**3 + 21. Factor y(g).
4*(g - 1)*(g + 1)**2/7
Let p be (-4 - 1) + -1*282/(-54). Determine r, given that 2/9*r + 0 - p*r**2 = 0.
0, 1
Let u(g) be the second derivative of 5*g**7/42 - g**6/2 - 25*g**5/4 - 35*g**4/4 + 2*g - 431. Determine o so that u(o) = 0.
-3, -1, 0, 7
Suppose 8*i - 19 = 221. Let q be 8/i - (-16)/40. Suppose 0*s + 0 - 2/3*s**4 + q*s**2 - 2/3*s**3 + 2/3*s**5 = 0. What is s?
-1, 0, 1
Let j(o) be the third derivative of -o**5/270 + o**4/9 - 35*o**3/27 + 5*o**2 + 7*o. Factor j(s).
-2*(s - 7)*(s - 5)/9
Let w(j) be the first derivative of j**6/2 + 6*j**5/5 - 3*j**4/2 - 8*j**3 - 21*j**2/2 - 6*j + 570. What is y in w(y) = 0?
-1, 2
Let m = -10/1143 + 13786/8001. Let -m*r**2 - 4/7*r**3 - 4/7 - 12/7*r = 0. Calculate r.
-1
Let a(h) be the second derivative of -h**5/20 - 7*h**4/12 - 5*h**3/2 - 9*h**2/2 + 42*h. Factor a(u).
-(u + 1)*(u + 3)**2
Suppose 0 = f - 5*i - 45, -4*f + 2*i + 41 = -139. Factor 12 - 9/2*y**4 - f*y**2 - 51/2*y**3 - 18*y.
-3*(y + 2)**3*(3*y - 1)/2
Suppose 2*y + 2*o + 64 = 0, -2*o - o + 84 = -3*y. Let g be (4/y)/((54/(-120))/9). Solve -22/3*f**3 - g*f**4 - 6*f**2 + 2/3 - 2/3*f = 0 for f.
-1, 1/4
Let n = 100 - 1499/15. Let z(d) be the first derivative of 0*d**4 + 0*d**2 + 1/9*d**3 + 0*d - n*d**5 + 1. Solve z(o) = 0.
-1, 0, 1
Let p(l) = -l**3 + 3*l**2 - 8*l - 6. Let d(t) = 2*t**3 - 6*t**2 + 15*t + 11. Suppose 24 = 3*z - 7*z. Let b(m) = z*d(m) - 11*p(m). Determine o so that b(o) = 0.
0, 1, 2
Let c(h) be the second derivative of h**5/80 + 7*h**4/48 - h**3/24 - 7*h**2/8 - 23*h. Factor c(j).
(j - 1)*(j + 1)*(j + 7)/4
Let v(j) be the third derivative of j**8/1008 - j**7/90 - j**6/360 + 7*j**5/180 + 273*j**2. Factor v(u).
u**2*(u - 7)*(u - 1)*(u + 1)/3
Let y(z) be the third derivative of -z**6/160 + 31*z**5/80 + 207*z**2. Factor y(d).
-3*d**2*(d - 31)/4
Let j(p) be the second derivative of -p**4/12 + 4*p**3 - 19*p**2/2 - 20*p. Let z be j(23). Factor 4/9*o**3 + 2/9*o**5 + 0 + 2/3*o**z + 0*o**2 + 0*o.
2*o**3*(o + 1)*(o + 2)/9
Let t(c) = 9*c**3 + 76*c**2 + 272*c + 244. Let j(z) = z**3 - z**2 + 3*z + 1. Let h(i) = -4*j(i) + t(i). Suppose h(g) = 0. What is g?
-12, -2
Let c(z) be the third derivative of 0*z + 13*z**2 - 3/16*z**3 + 9/160*z**5 + 0 - 1/80*z**6 + 5/32*z**4. Solve c(v) = 0.
-1, 1/4, 3
Let i(f) be the first derivative of -1/3*f**6 - 2*f**3 + 0*f - 1/2*f**4 - 9 + 2*f**2 + 6/5*f**5. Determine y, given that i(y) = 0.
-1, 0, 1, 2
Let k(v) be the first derivative of 5*v**6/72 + 7*v**5/24 + 5*v**4/12 + 8*v**3 - 3. Let z(t) be the third derivative of k(t). Let z(j) = 0. Calculate j.
-1, -2/5
Suppose 15*q - 2 = 14*q. Suppose -3*d = -2*d - 2*s + 8, q*d - 9 = -s. Factor d*n**3 + 2*n + 1/2 + 3*n**2 + 1/2*n**4.
(n + 1)**4/2
Let o(l) be the second derivative of -2*l**6/105 - l**5/35 + 2*l**4/21 + 17*l - 1. Factor o(v).
-4*v**2*(v - 1)*(v + 2)/7
Let h = -573 + 575. Factor 6/7*l**h - 4/7*l + 0 - 2/7*l**3.
-2*l*(l - 2)*(l - 1)/7
Let m(u) be the third derivative of 4/3*u**3 + 1/6*u**5 + 0*u + u**4 - 10*u**2 + 0. Factor m(r).
2*(r + 2)*(5*r + 2)
Suppose -2242*n**2 + 2239*n**2 - 4*n**3 + 2*n**4 - 3*n**4 = 0. What is n?
-3, -1, 0
Let a = -4119 - -16477/4. Determine m so that -a*m**2 + 5/4*m - 1 = 0.
1, 4
Let t(q) be the third derivative of q**6/90 - 11*q**5/45 - 2*q**4/3 + 14*q**2 + q. Solve t(o) = 0.
-1, 0, 12
Let h = 57 + -42. Factor 48*l - 15 - 23*l - h*l + 5*l**2.
5*(l - 1)*(l + 3)
Let x = -60 + 62. Factor -2*h**2 - 1783*h**3 + 1781*h**3 + h**x - h**4.
-h**2*(h + 1)**2
Let m(y) be the third derivative of -y**8/2016 - y**7/315 - y**6/240 - 110*y**2. Let m(d) = 0. Calculate d.
-3, -1, 0
Suppose c + 0*c = 5. Let i(s) = -20*s + 104. Let p be i(5). Factor -6*t**3 - 2 + 2*t**3 + 4*t**p - t**5 - 2*t**2 - t**c + t**5 + 5*t.
-(t - 2)*(t - 1)**3*(t + 1)
Suppose j = -3*j + 52. Let t = j - 11. Determine g so that 8/7*g - 2/7 - 6/7*g**t = 0.
1/3, 1
Suppose -185*z**3 - 16 + 770*z**3 - 338*z**4 - 996*z**2 + 533*z**3 + 232*z = 0. Calculate z.
2/13, 1, 2
Factor -274*l - 21*l**3 + 738*l - 72 - 39*l**2 + 3*l**4 - 335*l.
3*(l - 8)*(l - 1)**2*(l + 3)
Suppose 37 = -5*k - 33. Let b be (-2*(-2)/(-18))/(k/21). Factor 1/3*a + 0 - b*a**2.
-a*(a - 1)/3
Solve -4/5*p**3 + 0*p + 2/5*p**4 + 0 + 2/5*p**2 = 0.
0, 1
Let b = 509 + -509. Let 3/2*n**4 + 0*n**2 + 0*n**3 + 0 + b*n = 0. What is n?
0
Let l(c) be the first derivative of -c**5/15 - 5*c**4/54 + 2*c**3/27 + c**2/9 - 12*c + 3. Let u(k) be the first derivative of l(k). Solve u(o) = 0 for o.
-1, -1/3, 1/2
Factor -24*y**2 + 0 + 130/11*y**3 + 8/11*y.
2*y*(y - 2)*(65*y - 2)/11
Factor -3*h + 6*h**2 + 3*h**4 - 6*h**3 - 3/5*h**5 + 3/5.
-3*(h - 1)**5/5
Let k(f) = -51*f**2 - 51*f. Let m(r) = -5*r**2 - 5*r. Suppose -3*i - 75 + 12 = 0. Let l(q) = i*m(q) + 2*k(q). Let l(c) = 0. Calculate c.
-1, 0
Let t(x) = x**2 - x - 3. Let w be t(-3). Let r be 3 + w - (-1 + 3). Factor 4*n**3 - 2 + 2*n**5 - 6*n - 4*n**4 - 4*n**2 + r*n**4 + 0*n**3.
2*(n - 1)*(n + 1)**4
Let f(y) be the third derivative of -y**7/420 - 23*y**6/240 - 7*y**5/40 + 23*y**4/48 + 11*y**3/6 - 75*y**2 + 2*y. Factor f(r).
-(r - 1)*(r + 1)**2*(r + 22)/2
Determine h so that -1/4 - 6*h - 36*h**2 = 0.
-1/12
Let u be 4/6 - (-4 + 56/12). Let o(d) be the third derivative of -1/20*d**5 + 1/2*d**4 + 0 + 4*d**2 - 2*d**3 + u*d. Factor o(m).
-3*(m - 2)**2
Suppose 18 = 127*x - 239*x + 121*x. Find n, given that 0 + 8/3*n**4 - 8/3*n + 17/3*n**3 - 2/3*n**x - n**5 = 0.
-1, 0, 2/3, 4
Let m(a) be the first derivative of 5 - 45/8*a**2 - 35/12*a**3 - 5/2*a. Factor m(k).
-5*(k + 1)*(7*k + 2)/4
Suppose 0 = -1130*l + 1152*l - 88. Factor -4/3*w**3 - 8/9*w**2 + 0*w + 20/9*w**l + 0.
4*w**2*(w - 1)*(5*w + 2)/9
Let h(l) = -l + 6. Let k be h(6). Suppose k = r + r - 4. Determine z, given that 3*z + 6*z + 5 - r + 3*z**3 + 4*z**2 + 5*z**2 = 0.
-1
Factor 50*z**4 + 32/9 + 2288/9*z**2 - 512/9*z - 640/3*z**3.
2*(z - 2)**2*(15*z - 2)**2/9
Let m = 1549 - 1546. Factor -m + 3*u - 3/4*u**2.
-3*(u - 2)**2/4
Suppose 0 = -25*q - 22*q + 52*q. Determine z, given that q - 1/7*z + 2/7*z**2 - 1/7*z**3 = 0.
0, 1
Let i = 8 + -5. Determine q, given that 0*q**5 - 94*q**2 - 74*q**i - 13*q**4 - 51*q + 1 - 12*q**4 - 10 - 3*q**5 = 0.
-3, -1, -1/3
Let r be (-357)/(-88) + 1/1. Let n = r + -39/8. Factor 0*z - n*z**2 + 2/11.
-2*(z - 1)*(z + 1)/11
Suppose -4*v + 6 = -v, v - 10 = -4*x. Let z(f) be the second derivative of 0 + 2/9*f**3 - 1/18*f**4 - 1/3*f**x - 4*f. Factor z(t).
-2*(t - 1)**2/3
Let r(g) be the third derivative of g**8/840 - g**7/420 - g**6/180 + g**5/60 - g**3 + 10*g**2. Let v(d) be the first derivative of r(d). Factor v(k).
2*k*(k - 1)**2*(k + 1)
Let g = 173/129 - 29/43. Let a(c) be the third derivative of 0*c**5 + 2/105*c**7 - 7*c**2 + 0*c + 1/15*c**6 - g*c**3 + 0 - 1/3*c**4. Factor a(o).
4*(o - 1)*(o + 1)**3
Let l(c) be the first derivative of 17 + 2/11*c**4 + 2/11*c**3 + 2/55*c**5 + 0*c**2 + 0*c. Factor l(h).
2*h**2*(h + 1)*(h + 3)/11
Suppose -2*z - 2*t = -4, 121*z - 4 = 118*z - 5*t. Solve 14/5*i + 12/5 - 14/5*i**z - 2/5*i**4 - 2*i**2 = 0 for i.
-6, -1, 1
Suppose 2*c - 11 = -4*n + 15, 4*c + 3*n = 42. Let b be -4 + 3/3 + c/2. Factor 9/2*y**3 + 0 + b*y**2 + 3/2*y**5 + 9/2*y**4 + 0*y.
3*y**2*(y + 1)**3/2
Let u(h) be the second derivative of -1/21*h**3 + 0 - 2*h + 1/70*h**5 + 0*h**2 + 0*h**4. Factor u(m).
2*m*(m - 1)*(m + 1)/7
Let w(s) be the second derivative of -4/5*s**2 + 1/25*s**6 + 1/30*s**4 - 4/25*s**5 + 0 - 8*s + 8/15*s**3. Find g such that w(g) = 0.
-1, 2/3, 1, 2
Factor -56/17*x**2 + 6/17*x**4 - 48/17*x + 0 + 2/17*x**5 - 12/17*x**3.
2*x*(x - 3)*(x + 2)**3/17
Let i(n) be the second derivative of -n**5/5 + 10*n**4 + 2*n**3/3 - 60*n**2 + 74*n. Determine c, given that i(c) = 0.
-1, 1, 30
Suppose u - 3*l - 12 = 0, 3*u = -l + 2*l + 44. Let -m + m**2 - 2*m**2 + 15 - u = 0. Calculate m.
-1, 0
Suppose 2*k - 444 = 2*p, 3*k - 850 + 192 = -p. Let t = 1984/9 - k. Factor -10/9*w**4 - t*w**2 + 0 + 0*w + 14/9*w**3.
-2*w**2*(w - 1)*(5*w - 2)/9
Let c(k) be the third derivativ