u**3/4 - 243*u**2/4 - 19683*u/4 + 303. Factor c(g).
-3*(g + 81)**2/4
Let l(v) be the first derivative of -6*v**3 + 3*v**2/2 + 21*v - 240. Factor l(j).
-3*(j + 1)*(6*j - 7)
Suppose 7*s + 693 = -4*s. Let i = 63 + s. Factor -2*b**2 + 81/2*b**5 + i - 16*b**3 - 45/2*b**4 + 0*b.
b**2*(b - 1)*(9*b + 2)**2/2
Let y(x) be the second derivative of x**5/60 - x**4/2 + 16*x**3/3 - 64*x**2/3 - 36*x. Determine h so that y(h) = 0.
2, 8
Factor -41/4*t - 1/4*t**3 + 5 + 11/2*t**2.
-(t - 20)*(t - 1)**2/4
Let d = -7353 + 14707/2. Solve 0 - d*l**2 + 1/2*l**3 - 3*l = 0.
-2, 0, 3
Let -50 + 14*k**4 - 1366*k**3 + 56960*k - 39708*k**2 - 838*k**3 - 12750 - 42*k**4 - 2220*k**2 = 0. Calculate k.
-40, 2/7, 1
Suppose -7*l + 9 = -5. Factor -30*g**2 + 16*g - 8 - 25*g**3 + 20*g + 0*g**l.
-(g + 2)*(5*g - 2)**2
Let r(w) be the third derivative of 9/8*w**4 - 3/10*w**5 + 0 - 1/336*w**8 + 9/2*w**3 - 1/12*w**6 + 0*w + 3*w**2 + 1/30*w**7. Find g such that r(g) = 0.
-1, 3
Suppose 0 = -5*t - 4*s + 30, -5*t + 3 = -t - s. Suppose 8 = 2*q + 4. Find f, given that 2*f + 3*f**2 + 4*f - 3*f**t - 3*f**3 - 3*f**q = 0.
-2, 0, 1
Factor -15*q + 15*q**3 + 326 + 319 + 5*q**2 - 655 + 5*q**4.
5*(q - 1)*(q + 1)**2*(q + 2)
Let c = -193514/59 - -3280. Let l = c - -135/413. Solve l*m**2 + 3/7 + 6/7*m = 0.
-1
Let p = 1528 - 1524. Let f(k) be the second derivative of 0*k**3 + 1/18*k**p - 1/3*k**2 - k + 0. Factor f(c).
2*(c - 1)*(c + 1)/3
Let b(g) be the third derivative of -g**6/60 + 44*g**5/5 - 1452*g**4 + 17*g**2 + 2*g. Factor b(p).
-2*p*(p - 132)**2
Let b(p) = p**3 + 36*p**2 - 206*p + 9. Let o be b(5). Solve -138/5*y**3 + 212/5*y**o + 16*y**5 - 2/5*y + 12/5 - 164/5*y**2 = 0 for y.
-3, -1/2, -2/5, 1/4, 1
Suppose 11*h - 175 = 6*h. Let u be ((-30)/7)/((-5)/h). Solve -u*v**3 + 10*v**4 + 36*v**2 + 4*v**4 - 18*v**4 - 8*v - 21*v**4 = 0.
-2, 0, 2/5
Let 43/2*q**2 + 21/4*q**4 - 2 - q + 85/4*q**3 = 0. Calculate q.
-2, -1/3, 2/7
Let t = 1846 - 12920/7. Let r be (-2)/8 + (-15)/(-28). Factor 2/7*l + r + 2/7*l**5 - 4/7*l**2 - 4/7*l**3 + t*l**4.
2*(l - 1)**2*(l + 1)**3/7
Let a be 1288/345*21/28. Suppose a*q - 2*q**2 - 4/5 = 0. Calculate q.
2/5, 1
Let t(h) be the first derivative of -1/4*h + 1/2*h**2 + 10 - 1/20*h**5 + 1/4*h**4 - 1/2*h**3. Factor t(a).
-(a - 1)**4/4
Let m be (20 - 16)*26/60. Let w = 46/15 - m. Factor -4/3*d**3 + 4/3*d**2 + 0 + w*d - 4/3*d**4.
-4*d*(d - 1)*(d + 1)**2/3
Let t be 50/(3/(12/8)). Let r = -18 + t. Factor -4*o**2 - 3*o**4 + 0*o + 4*o**3 + 0*o - 4*o + r*o**4.
4*o*(o - 1)*(o + 1)**2
Let s(n) be the second derivative of 61*n**4/36 + n**3/3 + 3*n + 1. Find x such that s(x) = 0.
-6/61, 0
Let n(m) be the third derivative of -m**7/105 + m**6/18 - m**5/30 - m**4/3 + 23*m**3/6 + 32*m**2. Let a(p) be the first derivative of n(p). Factor a(f).
-4*(f - 2)*(f - 1)*(2*f + 1)
Let l be (828/(-36) - -21)*5/(-2). Factor -1/6*x**l - 3/2*x**3 - 1/3*x + 0 + 5/6*x**4 + 7/6*x**2.
-x*(x - 2)*(x - 1)**3/6
Let s(p) be the second derivative of -15/4*p**4 + 30*p**2 - 1/6*p**6 - 3/2*p**5 + 0 + 10/3*p**3 - 14*p. Suppose s(i) = 0. Calculate i.
-3, -2, 1
Suppose -r - 2*w - w = -2, 0 = -5*r - 4*w - 1. Let i be (r/3)/(9/(-297)). Suppose 7*u**2 + 3 + i*u**2 - u - 1 - 19*u**2 = 0. Calculate u.
-2, 1
Let i(l) = -l**2 - 5*l. Let m(v) = 20*v**3 - 319*v**2 - 100*v. Let u(d) = 4*i(d) - m(d). Factor u(o).
-5*o*(o - 16)*(4*o + 1)
Let p(w) = -2*w**2 + 2888*w + 210238. Let i(m) = -m**2 + 1155*m + 84095. Let k(f) = 12*i(f) - 5*p(f). Let k(a) = 0. Calculate a.
-145
Let i(b) be the first derivative of -b**8/8400 + b**7/4200 + b**6/1800 - b**5/600 - 22*b**3/3 - 1. Let j(w) be the third derivative of i(w). Solve j(u) = 0.
-1, 0, 1
Suppose 5*g - 9 = 6. Suppose -4*t + g*b + 11 = 0, -4*b + 22 = t + t. Suppose 0*u**2 - 1/5*u**4 - 1/5*u**t + 0*u + 0 + 0*u**3 = 0. Calculate u.
-1, 0
Let q(a) = -a**4 + 5*a**2 - 2*a + 2. Let r(v) = -v**2 - 1. Let w = 10 + -9. Let u(c) = w*q(c) + 2*r(c). Factor u(b).
-b*(b - 1)**2*(b + 2)
Find s such that -41/4*s + 21/2 - 1/4*s**2 = 0.
-42, 1
Let v(r) be the first derivative of -2*r**3/15 - 37*r**2/5 + 244. Find k, given that v(k) = 0.
-37, 0
Suppose -35*m + 11 = -33*m + 5*n, m - 3*n = 0. Let -75*z**m - 12 - 84*z - 180*z**2 + 375/4*z**4 = 0. What is z?
-2/5, 2
Let g be 7/(14/(-14)) - 74/(-10). Factor 2/5 - 2/5*z**2 + 2/5*z - g*z**3.
-2*(z - 1)*(z + 1)**2/5
Suppose 3*q + 4*j = -2*q + 12, -5*q = 2*j - 16. Factor 0*y**3 + 28*y**2 + 12 - 2*y**3 - 40*y - q*y**3 + 6*y.
-2*(y - 3)*(y - 1)*(3*y - 2)
Let y be 207/(-23) - -39*(-2)/(-6). Let b be 8/(-30)*(-3)/2. Factor 0*k**3 + b*k**2 - 2/15*k**y - 4/15*k + 0.
-2*k*(k - 1)**2*(k + 2)/15
Let i(s) be the second derivative of 1/6*s**4 + 1/6*s**3 - 3/80*s**5 - 4*s + 9/2*s**2 + 0. Let z(t) be the first derivative of i(t). Let z(j) = 0. Calculate j.
-2/9, 2
Suppose 2 - 1/2*p**2 + 1/2*p**3 - 2*p = 0. What is p?
-2, 1, 2
Let b = 2/405 - -1606/2835. Let j(g) be the third derivative of b*g**4 + 10*g**2 + 7/40*g**6 + 0 + 11/20*g**5 + 0*g + 2/7*g**3. Factor j(y).
3*(y + 1)*(7*y + 2)**2/7
Suppose 15*b + 1253 = 1313. Find i such that 0*i**3 - 1/2*i**b - 1/2 + i**2 + 0*i = 0.
-1, 1
Find f such that -2*f**5 + 3020*f - 932*f - 189*f**2 + 129*f**2 - 707*f**3 - 1296 + 72*f**4 + 65*f**3 - 160*f**2 = 0.
-2, 1, 18
Let y(j) be the third derivative of j**8/224 - 11*j**7/140 + j**6/2 - 11*j**5/10 - 2*j**4 + 16*j**3 + 2*j**2 - 21. Suppose y(m) = 0. What is m?
-1, 2, 4
Let p(n) be the second derivative of n**6/15 - 97*n**5/20 + 39*n**4/2 - 185*n**3/6 + 23*n**2 + 695*n. What is c in p(c) = 0?
1/2, 1, 46
Let q(l) be the first derivative of l**5/160 + 5*l**4/64 + 3*l**3/8 + 31*l**2/2 + 5. Let m(g) be the second derivative of q(g). Factor m(j).
3*(j + 2)*(j + 3)/8
Let a(x) be the second derivative of -x**6/15 + 7*x**5/10 - 8*x**4/3 + 4*x**3 - 84*x - 2. Factor a(z).
-2*z*(z - 3)*(z - 2)**2
Let s(w) = -w**2 + 22*w + 27. Let h be s(23). Let m = -83 - -86. Let 2/11*d**5 + 0*d**m + 0*d**2 + 0*d + 0 - 2/11*d**h = 0. What is d?
0, 1
Let a(d) be the second derivative of -2*d**7/21 + 4*d**6/15 + 8*d**5/5 + 65*d. Determine f so that a(f) = 0.
-2, 0, 4
Factor 1/4*j**3 + 5/2*j**2 + 0*j + 0.
j**2*(j + 10)/4
Let q(y) = -y**4 + y**3 - y**2 - y + 1. Suppose 6*w - 5 - 13 = 0. Let n(l) = 6*l**4 + 51*l**3 + 155*l**2 - 159*l - 51. Let k(u) = w*n(u) + 6*q(u). Factor k(z).
3*(z - 1)*(z + 7)**2*(4*z + 1)
What is k in 2028*k - 552*k - 452*k - 216*k**2 - 928 - 112*k - 4*k**3 = 0?
-58, 2
Suppose m - 1 = -5. Let p(l) = -l**2 + 3*l. Let i(j) = 3*j + 22 + 27 - 49. Let z(y) = m*i(y) + 3*p(y). Factor z(c).
-3*c*(c + 1)
Let x(b) be the second derivative of 5*b**7/42 + b**6/2 + b**5/2 - 24*b + 2. Let x(q) = 0. What is q?
-2, -1, 0
Let p(j) = -5*j**5 + 18*j**4 - 20*j**3 - 2*j**2 + 2*j + 2. Let c(k) = -10*k**5 + 35*k**4 - 40*k**3 - 5*k**2 + 5*k + 5. Let g(x) = -2*c(x) + 5*p(x). Factor g(u).
-5*u**3*(u - 2)**2
Let b be (-2)/(-12) + 8/(-48). Let g be (27/(-60))/((-3)/4). Solve b*n - g + 6/5*n**2 - 3/5*n**4 + 0*n**3 = 0.
-1, 1
Let j(m) = -m**2 - 10*m + 27. Let p be j(-12). Factor -p*s**4 + 243*s - 237*s + 12*s**3 - 15*s**2 + 0*s**4.
-3*s*(s - 2)*(s - 1)**2
Let x(s) be the third derivative of -2*s**8/21 - 2*s**7/105 + 8*s**6/15 + 2*s**5/15 - 4*s**4/3 - 2*s**3/3 - 8*s**2 + 5*s. Suppose x(a) = 0. Calculate a.
-1, -1/8, 1
Let m(g) be the first derivative of g**6/2700 + g**5/450 + g**4/180 + 4*g**3/3 - 8. Let v(u) be the third derivative of m(u). Determine t, given that v(t) = 0.
-1
Let m(j) be the third derivative of -j**5/15 - j**3/3 + 18*j**2. Let q(v) = -13*v**2 - 7. Let s(r) = -14*m(r) + 4*q(r). Suppose s(d) = 0. What is d?
0
Let a(x) be the second derivative of -x**6/10 + 39*x**5/20 - 35*x**4/4 - 49*x**3/2 - x - 14. Factor a(w).
-3*w*(w - 7)**2*(w + 1)
Let w(s) be the third derivative of -s**6/60 + 3*s**4/4 - 157*s**2. Factor w(j).
-2*j*(j - 3)*(j + 3)
Factor 136*z - 289/2*z**2 - 32.
-(17*z - 8)**2/2
Suppose 3*d + 9 = f, 2*d = 5*f - 2*d - 23. Suppose l + f*k - 3 = 7*k, 5*l - 15 = -k. Find y such that -4/3*y**2 + 10/3*y**l + 0 - 2*y**4 + 0*y = 0.
0, 2/3, 1
Factor 0 - 5*b**3 - 37/4*b**2 - 1/4*b**4 - 9/2*b.
-b*(b + 1)**2*(b + 18)/4
Let y(s) be the first derivative of -s**7/5880 + s**6/1260 + s**5/168 - s**4/28 + 19*s**3/3 + 12. Let o(u) be the third derivative of y(u). Factor o(c).
-(c - 3)*(c - 1)*(c + 2)/7
Let x(n) be the third derivative of n*