55 - 12*v**4/11 + 2939*v. Find x, given that t(x) = 0.
-2, 0, 36
Let o(z) be the third derivative of z**5/30 + 3*z**4/4 - 22*z**3/3 + 5*z**2 + 6*z. Factor o(y).
2*(y - 2)*(y + 11)
Suppose 5*m = 2*m + 4*j - 26627, -m + j = 8875. Let c = 12788 + m. Factor p**2 + p - 3915 + c.
p*(p + 1)
Let h(b) be the third derivative of 3*b**7/350 + 53*b**6/200 + 79*b**5/25 + 173*b**4/10 + 168*b**3/5 + 5297*b**2. Determine j, given that h(j) = 0.
-7, -6, -4, -2/3
Let p(w) be the first derivative of w**3 - 2061*w**2/2 - 1648. Factor p(l).
3*l*(l - 687)
Let b(k) = -124*k + 59*k + 57*k + 42. Let q be b(5). Solve 2*g**q + 0*g + 0*g**2 + 4*g = 0.
-2, 0
Let q(x) be the second derivative of -x**6/6 + 15*x**5/2 + 120*x**4 + 1520*x**3/3 + 235*x - 1. Factor q(j).
-5*j*(j - 38)*(j + 4)**2
Suppose 15517 = 48*t + 15421. Find v, given that 10*v + 2/3*v**t + 0 = 0.
-15, 0
Factor -4394*b**2 + 2205*b**2 + 242*b + 2191*b**2.
2*b*(b + 121)
Factor p**2 - 9167162*p - 141 + 9166829*p - 193.
(p - 334)*(p + 1)
Suppose 5 - 1/4*u**2 - 1/4*u = 0. What is u?
-5, 4
Let l be 1/(-11) + 195/330. Let h(f) be the first derivative of 1/3*f**3 - l*f**2 - f + 1/4*f**4 + 12. Factor h(b).
(b - 1)*(b + 1)**2
Determine v, given that 3/4*v**4 + 261/4*v**2 + 51/4*v**3 + 42 + 381/4*v = 0.
-8, -7, -1
Let u(l) be the second derivative of l**6/50 - 29*l**5/100 + 7*l**4/10 - 8*l**3/15 - 762*l - 1. Solve u(i) = 0 for i.
0, 2/3, 1, 8
Let d(n) = 1 - 83*n**2 + 41*n**2 + 5*n**3 + 41*n**2 - n. Let l be d(1). Determine b, given that -4*b**3 + l*b**3 + 17*b**2 + 18 + b**3 + 21*b - 9*b**2 = 0.
-3, -2
Let b be (-5 + -8 + 14)/(-1). Let c be b/((-77)/14) + 5/33. Factor 1/3*h**5 + 0*h**2 + 0*h - 2/3*h**3 + c*h**4 + 0.
h**3*(h - 1)*(h + 2)/3
Let z(t) be the third derivative of 26*t**2 + 5/8*t**4 + 6 + 0*t**3 + 0*t + 1/60*t**5. Factor z(h).
h*(h + 15)
Let d(p) = -p**3 + 9*p**2 + 78*p - 2700. Let q be d(-13). Factor -8/5*m**2 + 0 + 2/5*m**3 - 8/5*m + 2/5*m**q.
2*m*(m - 2)*(m + 1)*(m + 2)/5
Let v(x) = 4 + 152*x**2 - 154*x**2 - x**3 - 2*x + 1 + 10*x. Let m be v(-4). Suppose 1/4*c**4 + 1/4*c**3 + 0 - 1/4*c**2 - 1/4*c**m + 0*c = 0. Calculate c.
-1, 0, 1
Let a(f) be the third derivative of 7/6*f**5 + 5/6*f**3 + 125/336*f**8 - 31*f**2 + 15/8*f**4 + 1 - 17/12*f**6 - 5/14*f**7 + 0*f. Suppose a(o) = 0. Calculate o.
-1, -1/5, 1
Let c(d) be the second derivative of d**7/21 - 41*d**6/15 + 77*d**5/10 + 41*d**4/6 - 26*d**3 + 82*d + 6. Find g, given that c(g) = 0.
-1, 0, 1, 2, 39
Let c(o) = 6*o + 4. Let y(q) = 5*q + 4. Let w(x) = 2*c(x) - 3*y(x). Let t be w(-4). Factor 5*g - 11 + 2*g**2 + 0*g - 5*g**3 + 1 + t*g**2.
-5*(g - 2)*(g - 1)*(g + 1)
Let q(a) = -8 + 9 + 3*a**2 + 9*a + 6 + 8*a. Let k be 3 + -7 - 15/5. Let f(w) = -2*w**2 - 8*w - 3. Let j(z) = k*f(z) - 3*q(z). Factor j(m).
5*m*(m + 1)
Let v(i) be the first derivative of 12/11*i - 1/11*i**6 + 9/11*i**4 + 25/11*i**2 + 24/11*i**3 - 4/55*i**5 - 169. Let v(k) = 0. Calculate k.
-1, -2/3, 3
Let y = -1/96 + 13/224. Let j(l) be the first derivative of -26 - y*l**3 - 3/14*l**2 + 0*l. Factor j(x).
-x*(x + 3)/7
Let z be ((-10)/(-8))/(6*(-6)/(-144)). Factor 3*c**5 + 21*c - 4*c**z + 64*c - 4*c**5 - 70*c**2 - 30 + 20*c**4.
-5*(c - 3)*(c - 1)**3*(c + 2)
Let m be ((-105)/24 + 5)/(51/(-1224) - (-22)/48). Factor 6*i**2 - 6*i - 24 + m*i**3.
3*(i - 2)*(i + 2)*(i + 4)/2
Let r(b) be the third derivative of -b**6/420 + b**4 - 160*b**3/21 + b**2 + 569*b - 2. Factor r(u).
-2*(u - 8)*(u - 2)*(u + 10)/7
Factor 94/5*o + 756/5 - 2/5*o**2.
-2*(o - 54)*(o + 7)/5
Suppose 0 = -8*p + 218 - 914. Let f = 90 + p. Factor -10*h + f*h**3 - 5*h**4 + h**5 + 6*h + 4*h**2 + h**4.
h*(h - 2)**2*(h - 1)*(h + 1)
Let u(m) = m**3 - 7*m**2 + 7*m - 4. Let k be u(6). Suppose 0 = -3*b + 4*q + 6, 2*b - 2*q = k + 2. Solve 2*h + b*h + h**2 - 5*h = 0.
0, 1
Let c(d) be the first derivative of -2*d**3/57 - 424*d**2/19 + 1704*d/19 - 988. Find r such that c(r) = 0.
-426, 2
Let f(i) be the second derivative of 2*i**7/945 + i**6/270 - 2*i**5/135 - 43*i**2/2 + i + 28. Let a(z) be the first derivative of f(z). Solve a(h) = 0 for h.
-2, 0, 1
Let x be 6/(1*12/54). Find i, given that x*i - 2*i**2 - 2*i**2 + 25*i - 48 = 0.
1, 12
Factor -7806*t**3 - 8*t**2 + 7811*t**3 + 3*t - 8*t**2.
t*(t - 3)*(5*t - 1)
Factor -1/2*x**2 - 13/2*x - 21.
-(x + 6)*(x + 7)/2
Let u(r) be the third derivative of r**5 + 19*r**4/6 + 8*r**3/3 - 1670*r**2. Determine i, given that u(i) = 0.
-1, -4/15
Determine y so that -325/6*y - 16/3*y**2 - 1/6*y**3 - 169 = 0.
-13, -6
Let c be (-1 + 0 + 119/(-85))*-5. Factor -35 + c*g**2 - 8*g**2 + 56*g - 25.
4*(g - 1)*(g + 15)
Let b(d) be the first derivative of -2*d**3/27 + 338*d**2/3 - 57122*d + 1087. Solve b(j) = 0 for j.
507
Let t(v) be the first derivative of 4/15*v**3 + 1/15*v**4 - 24 - 19*v - 6/5*v**2. Let x(u) be the first derivative of t(u). Factor x(p).
4*(p - 1)*(p + 3)/5
Let l(h) be the first derivative of 0*h + 7 - 11/20*h**5 - 3/8*h**2 - 5/12*h**3 + 19/16*h**4. Determine n so that l(n) = 0.
-3/11, 0, 1
Let s(r) be the third derivative of 0*r - 19/3*r**4 + 83*r**2 + 722/3*r**3 + 1/15*r**5 + 0. Suppose s(g) = 0. What is g?
19
Let m = 1391 + -5531/4. Let q(s) be the first derivative of 0*s**2 + m*s**4 + 1/2*s**6 + 0*s + 6*s**3 + 18/5*s**5 + 17. Let q(j) = 0. What is j?
-3, -2, -1, 0
Let 2/7*q**2 + 700928/7 - 2368/7*q = 0. What is q?
592
Let j(v) be the third derivative of 8/15*v**5 - 1/6*v**6 + 0 + 104*v + 4*v**3 - 4/105*v**7 + 17/6*v**4 - 2*v**2. Determine q so that j(q) = 0.
-3, -1, -1/2, 2
Let m(q) be the second derivative of -q**6/12 + 77*q**5/8 + 5*q**4/8 - 1145*q**3/12 - 385*q**2/2 - 12396*q. Solve m(v) = 0 for v.
-1, 2, 77
Let v(n) be the third derivative of 0*n - 1/60*n**6 + 0 + 0*n**3 - 1/6*n**5 + 1/2*n**4 + 16*n**2. Determine a so that v(a) = 0.
-6, 0, 1
Let r be (-17)/(8721/38) + 83/27. Let k(d) be the second derivative of 0 - 4*d**r + 1/4*d**4 - 14*d + 24*d**2. Factor k(h).
3*(h - 4)**2
Let p(t) be the second derivative of -t**9/83160 - t**8/1155 - 64*t**7/3465 + 2*t**4/3 + t**3/3 + 242*t. Let s(q) be the third derivative of p(q). Factor s(l).
-2*l**2*(l + 16)**2/11
Let o(i) be the second derivative of 7*i + 3/5*i**5 - 16/3*i**3 - 2/15*i**6 + 2*i**4 + 0*i**2 + 0. Factor o(h).
-4*h*(h - 4)*(h - 1)*(h + 2)
Let h(j) = -3 + 24*j**2 - 47*j**4 - 27*j + 54*j**4 + 6 + 24*j**3 + 0. Let m(k) = k**4 + k**3 + 2*k**2 + 1. Let z(f) = 5*h(f) - 15*m(f). Factor z(a).
5*a*(a + 3)**2*(4*a - 3)
Let m(b) be the third derivative of -5*b**8/336 - b**7/42 + 13*b**6/12 - b**5/2 - 255*b**4/8 + 225*b**3/2 - 455*b**2 + 5*b. Let m(c) = 0. What is c?
-5, -3, 1, 3
Let i(w) = -2*w**2 - 176*w + 297. Let g(h) = 5*h**2 + 359*h - 591. Let p(s) = 3*g(s) + 7*i(s). Factor p(r).
(r - 153)*(r - 2)
Let p(w) be the third derivative of 5*w**8/1344 - 85*w**7/21 + 25651*w**6/16 - 721406*w**5/3 - 58485415*w**4/96 - 1354*w**2. Factor p(l).
5*l*(l - 227)**3*(l + 1)/4
Let i = -610302 - -6713420/11. Solve 6/11*l**3 + 40/11*l**2 - i*l**5 - 140/11*l**4 - 8/11*l + 0 = 0.
-1, 0, 2/7
Suppose -m - 57 = -y + 2*m, -2*m = y - 37. Solve -51*d**3 + d + y*d**3 + d**4 - 3*d**4 + 7*d = 0 for d.
-2, 0, 1
Factor 152/5*d**2 - 1/5*d**4 + 13/5*d**3 + 0 + 336/5*d.
-d*(d - 21)*(d + 4)**2/5
Let j(f) be the first derivative of 2*f**3/3 - 19*f**2 + 68*f + 990. What is a in j(a) = 0?
2, 17
Let y(d) be the second derivative of d**5/30 - 37*d**4/18 + 4*d**3 + 2*d + 1060. Suppose y(m) = 0. Calculate m.
0, 1, 36
Let x(v) be the third derivative of v**7/84 + 167*v**6/240 + 11*v**5/20 + 2*v**2 - 3401*v. Factor x(s).
s**2*(s + 33)*(5*s + 2)/2
Let j(y) be the first derivative of 4*y + 1/2*y**4 + 0*y**3 - 3*y**2 - 4. Solve j(h) = 0.
-2, 1
Factor -48*h + 2/7*h**3 + 0 - 106/7*h**2.
2*h*(h - 56)*(h + 3)/7
Let r be (-3)/(-18)*-5 + (-1)/6. Let p be r - -2 - 0 - (-5 + 3). Find z such that 21*z + z**p - 6 + 2 - 12*z - 6*z**2 = 0.
1, 4
Let m(g) = -5*g + 33. Let i be m(5). Suppose i*p**3 - 15*p**2 - 5*p**5 + p**3 - 4*p**3 + 10*p**4 + 5*p**2 = 0. What is p?
-1, 0, 1, 2
Let b = 19784/35 - 2822/5. Factor -6/7 - b*k**3 - 18/7*k**2 - 18/7*k.
-6*(k + 1)**3/7
Let p(v) = 8*v + 110. Let g be p(-16). Let m be -9 + (-4)/(8/g). Let -1/2 + m*x + 1/8*x**2 = 0. What is x?
-2, 2
Let u be (-18 - (-970)/25)*2/(-32)*-6. Determine p, given that -u*p**2 + 18/5*p**3 - 12/5 + 36/5*p - 3/5*p**4 = 0.
1, 2
Factor -200978 - 1268/3*w - 2/