**j - 2/3*l**3 + l**5 + 0 + 4/3*l**2 = 0 for l.
-1, 0, 1/3, 1
Let j = -162041/7 - -23149. Factor 12/7 - 2/7*u**2 + j*u.
-2*(u - 3)*(u + 2)/7
Determine f, given that 186 - 369*f**2 + 860*f**3 - 9*f**4 + 62*f + 37*f - 1151*f**3 = 0.
-31, -1, 2/3
Suppose -u - 10 = -21. Let m be (31/u - 26/(-143)) + 1. Determine z, given that 0 + 2/13*z**2 + 18/13*z**m + 0*z - 12/13*z**3 = 0.
0, 1/3
Suppose 3*q - 3 = -0. Let j be 145/(-116) - 26/(-8). Solve -13*u**j - 4*u**3 - 12*u - 2*u**3 - 5 + q - u**4 = 0.
-2, -1
Find d such that -4/7*d**2 + 16*d + 0 = 0.
0, 28
Let v(w) be the first derivative of 2*w**3/33 - 6*w**2/11 + 16*w/11 - 10. Suppose v(t) = 0. What is t?
2, 4
Let l(w) be the first derivative of w**4/2 - 4*w**3/3 - w**2 + 4*w + 98. Factor l(m).
2*(m - 2)*(m - 1)*(m + 1)
Let p(j) be the first derivative of -3*j**4/4 - 75*j**3 - 5625*j**2/2 - 46875*j - 239. Factor p(v).
-3*(v + 25)**3
Let v(n) be the first derivative of 2/5*n + 4/15*n**3 - 3/5*n**2 - 5. Suppose v(l) = 0. What is l?
1/2, 1
Let g(z) be the third derivative of z**8/11200 + z**7/12600 - z**6/1200 - z**5/600 - z**4/2 - 11*z**2. Let k(r) be the second derivative of g(r). Factor k(d).
(d - 1)*(d + 1)*(3*d + 1)/5
Let u(h) be the second derivative of -h**6/50 - 3*h**5/100 + 9*h**4/20 - 11*h**3/10 + 6*h**2/5 - 9*h - 3. Factor u(a).
-3*(a - 1)**3*(a + 4)/5
Factor 2*p**2 + 3*p**2 - 41 - 29 + 3*p**2 - 278*p.
2*(p - 35)*(4*p + 1)
Let l(s) = -2*s + 13. Suppose -20*z + 91 + 9 = 0. Let r be l(z). Determine w so that 8/5*w**2 + 6/5*w**r + 1/5 - 9/5*w**4 - 6/5*w = 0.
-1, 1/3, 1
Solve 288 + 287*f**3 + 198*f**4 + 13*f**5 + 5*f**5 + 57*f + 137*f**3 - 736*f**2 - 249*f = 0.
-6, -2/3, 2/3, 1
Let j(d) be the third derivative of -d**8/168 - d**7/35 + 13*d**6/60 + 47*d**5/30 + 4*d**4 + 16*d**3/3 - 75*d**2. Let j(k) = 0. Calculate k.
-4, -1, 4
Let -46/7*x + 0 + 1/7*x**3 + 45/7*x**2 = 0. Calculate x.
-46, 0, 1
Suppose -25 = -2*v + 25. Let q = -25 + v. Let -2/9*d + q - 2/9*d**2 = 0. What is d?
-1, 0
Suppose 4*s - 4*f + 12 = -4, 24 = 6*f. Factor 0 + 0*q**3 + 2/19*q**4 + s*q + 0*q**2.
2*q**4/19
Let c(s) be the second derivative of -s**9/2520 + s**8/2100 - 7*s**3/6 + 10*s. Let o(t) be the second derivative of c(t). Let o(i) = 0. What is i?
0, 2/3
Let u(c) be the second derivative of c**5/80 + c**4/8 + 11*c**3/24 + 3*c**2/4 + 14*c - 3. Factor u(g).
(g + 1)*(g + 2)*(g + 3)/4
Let f(x) = -6*x**3 + 3*x**2 + 3*x + 5. Let g(p) = p**3 - p - 1. Suppose 6*o = 2*o - 12. Let u(i) = o*f(i) - 15*g(i). Suppose u(q) = 0. What is q?
0, 1, 2
Let x(k) be the first derivative of 9*k**5/10 - 43*k**4/8 + 53*k**3/6 - 13*k**2/4 - 3*k + 81. Find g such that x(g) = 0.
-2/9, 1, 3
Let z(k) be the first derivative of -k**4/3 + 2*k**3 - 4*k**2 + 4*k + 2. Let b(o) be the first derivative of z(o). Factor b(x).
-4*(x - 2)*(x - 1)
Let x(v) = 2*v**3 + 12*v**2 - 2*v - 10. Let l(z) = -4*z**3 - 25*z**2 + 4*z + 20. Let m(h) = 4*l(h) + 10*x(h). Factor m(t).
4*(t - 1)*(t + 1)*(t + 5)
Suppose -m + 2*j + 10 = 0, 0 = 5*m - 5*j - 25. Suppose 15/2*i**3 - 21/2*i**4 + 3*i**2 + m*i + 0 = 0. Calculate i.
-2/7, 0, 1
Let q = 4 + 8. Let u(o) = o - 4. Let t be u(q). Factor 12*g**3 - 6*g**4 - 16*g + t*g**2 + g**5 + g**5 - 4*g**4.
2*g*(g - 2)**3*(g + 1)
Factor -10*k**2 - 12 + 25*k**4 - 3 - 2*k**3 - 24*k - 28*k**3 - 5*k**5 + 59*k.
-5*(k - 3)*(k - 1)**3*(k + 1)
Let a(c) be the second derivative of -c**4/18 + c**3/3 + 4*c**2/3 + 25*c. Find j, given that a(j) = 0.
-1, 4
Let d(a) = 10*a**3 + 79*a**2 - 24*a - 58. Let i(t) = 3*t**3 + 26*t**2 - 7*t - 20. Let w(u) = 2*d(u) - 7*i(u). Find s, given that w(s) = 0.
-24, -1, 1
Let d(m) be the first derivative of 2*m**3/3 + 12*m**2 + 40*m - 77. Factor d(z).
2*(z + 2)*(z + 10)
Let s(w) = w**3 - w - 1. Let d(n) = -2*n**4 - 10*n**3 + 2*n**2 + 10*n + 12. Let u = -22 - -23. Let p(v) = u*d(v) + 12*s(v). Factor p(r).
-2*r*(r - 1)**2*(r + 1)
Suppose 6*l - 5*l = 20. Find k such that 5 - 14 - 3 - 4*k**2 - l*k + 4*k**3 = 0.
-1, 3
Let j(q) be the first derivative of q**5/180 + 5*q**4/72 + 2*q**2 + 12. Let h(o) be the second derivative of j(o). Factor h(r).
r*(r + 5)/3
Let l(v) = -14*v**2 + 12*v - 8. Let z(u) = u**2. Let k(i) = -l(i) - 10*z(i). Factor k(a).
4*(a - 2)*(a - 1)
Let a(q) = -q**2 - 13*q + 15. Let o be a(-11). Let n = 39 - o. Suppose 6 - 75/2*f**3 + 135/2*f**n - 36*f = 0. What is f?
2/5, 1
Factor -2/13*q**3 + 0 + 0*q + 0*q**2.
-2*q**3/13
Suppose -19 - 19 = -4*m + 2*s, 4*s + 55 = 5*m. Let p = -5 + m. Let -2*z**2 - 4 - 3*z**2 - 2 + 15*z - z**p = 0. What is z?
1/2, 2
Let g = -159 - -166. Let a(c) be the first derivative of 3/5*c**5 + 2*c**3 - 9/4*c**4 + 0*c**2 - g + 0*c. Suppose a(r) = 0. What is r?
0, 1, 2
Factor 20/7*m**2 + 0 - 4/7*m**3 + 0*m.
-4*m**2*(m - 5)/7
Let j(m) be the second derivative of -m**5/15 + 11*m**4/12 + 92*m**3/9 - 8*m**2 - 563*m. Factor j(b).
-(b - 12)*(b + 4)*(4*b - 1)/3
Let y be 15/9*30/25. Suppose -i + 7 = y*v, -v + 3*i - 1 = 3*v. What is h in 7/6*h**v + 1/3 + 3/2*h = 0?
-1, -2/7
Suppose -4*y = -a - 33, 1 = -2*a - 1. Suppose 6*x + 8 = 7*x. Factor -x + 3*z + 5*z + 6*z**2 - y*z**2.
-2*(z - 2)**2
Let t = -11 + 22. Let m = 13 - t. Factor g**3 + 7/2*g**m + 7/4*g**5 + 1/2 - 11/4*g - 4*g**4.
(g - 1)**3*(g + 1)*(7*g - 2)/4
Let k(f) = -f**3 - 25*f**2 + 14*f + 8. Let j(d) = -2*d**2 - d + 1. Let v(u) = 24*j(u) - 3*k(u). Factor v(t).
3*t*(t - 2)*(t + 11)
Let j(t) = -t**3 - 3*t**2 - 9. Let u be j(-4). Find x, given that -3*x**3 - 3*x**2 + 0 + 10*x**4 + 0 - u*x**4 + 3*x**5 = 0.
-1, 0, 1
Let y(x) be the third derivative of 1/105*x**5 + 8/21*x**3 + 0 - 2/21*x**4 + 18*x**2 + 0*x. Determine q so that y(q) = 0.
2
Let b(d) = -2*d**3 + d**2 + d + 1. Let n(t) = -13*t**3 - 3*t**2 - 4*t + 7. Let q(y) = -28*b(y) + 4*n(y). Factor q(r).
4*r*(r - 11)*(r + 1)
Let g(s) be the third derivative of -s**5/360 + s**4/3 - 16*s**3 - 62*s**2. Factor g(t).
-(t - 24)**2/6
Let s(h) be the first derivative of h**4/2 - 4*h**3 + 5*h**2 - 247. Factor s(g).
2*g*(g - 5)*(g - 1)
Suppose -2*b - 6 + 12 = 0. Let -r**2 + r - 6 + b*r + 2*r**2 - 3*r = 0. What is r?
-3, 2
Let r(g) be the second derivative of -g**5/80 + g**4/16 - g**3/8 - 15*g**2/2 - 11*g. Let l(h) be the first derivative of r(h). Factor l(k).
-3*(k - 1)**2/4
Factor 4*z**2 - 32*z + 0 - 1/8*z**3.
-z*(z - 16)**2/8
Let x be (4860/(-40))/27*-2*1. Let c(g) be the second derivative of 0*g**4 + 1/16*g**3 - 1/8*g**2 + 0 + x*g - 1/160*g**5. Find h, given that c(h) = 0.
-2, 1
Factor -3*x**3 + 5*x**5 - 50*x - 190*x**2 + 25*x**4 - 19*x**3 - 165*x - 75 - 8*x**3.
5*(x - 3)*(x + 1)**3*(x + 5)
Let d be (6 - 0) + -15*10/(-50). Let z be (-10)/(-72)*3*24/d. Factor -2/3*f**2 + z*f - 4/9.
-2*(f - 1)*(3*f - 2)/9
Factor -3570 + 3560 + 0*t - 2*t**2 + 5*t + 7*t.
-2*(t - 5)*(t - 1)
Let r(u) be the first derivative of 0*u - 12 + 7/16*u**4 - 1/4*u**3 + 0*u**2 - 1/4*u**5 + 1/24*u**6. Factor r(w).
w**2*(w - 3)*(w - 1)**2/4
Let n(v) be the second derivative of -25*v**4/3 + 80*v**3/3 - 32*v**2 - 237*v. What is f in n(f) = 0?
4/5
Let b = 5 - -3. Suppose -20*s = -19*s - b. Let -1 - 4*h**2 - 3 + 0*h + s*h = 0. Calculate h.
1
Let m(h) be the second derivative of 0*h**3 + 2/33*h**4 + 0 + 1/110*h**5 + 6*h + 0*h**2. Factor m(y).
2*y**2*(y + 4)/11
Let g = 122 - 487/4. Let j(u) be the first derivative of 1/12*u**6 + 0*u - g*u**4 + 1/10*u**5 + 0*u**3 - 4 + 0*u**2. Factor j(y).
y**3*(y - 1)*(y + 2)/2
Let z(o) be the second derivative of -o**4/72 - 3*o**3/4 - 77*o - 1. Factor z(j).
-j*(j + 27)/6
Suppose -56 = 4*a - 2*t - 2*t, -3*t = -12. Let z be (-11)/22 - (2 - (-49)/a). Solve -12/5*l**2 + 0 - 4/5*l - z*l**3 - 4/5*l**4 = 0.
-1, 0
Suppose -59*i + 40 + 47 + 31 = 0. Let h = -1/45 - -16/45. Factor -5/3*o + 1/3*o**3 + h*o**i + 1.
(o - 1)**2*(o + 3)/3
Let g(u) = -u**2 - 3*u + 20. Let t = 29 - 35. Let p be g(t). Solve 2/3*y**4 - 8/3*y + 2*y**3 + 0 + 0*y**p = 0.
-2, 0, 1
Let t(q) = -5*q**2 + 3*q - 14. Let h(s) = -12*s**2 + 3*s - 28. Let n(f) = 2*h(f) - 5*t(f). Find d such that n(d) = 0.
2, 7
Let o(d) = -d**2 - 14*d - 10. Let n be o(-13). Suppose -2*p + p = -n. Suppose 3*w**3 - 5*w**2 - 6*w**3 + w**p - w**2 - 4*w = 0. What is w?
-2, -1, 0
Let d(o) be the first derivative of -5 - 4/25*o**5 + 1/4*o**4 + 0*o + 1/30*o**6 - 2/15*o**3 + 0*o**2. Let d(u) = 0. What is u?
0, 1, 2
Let x(p) = 729*p**3 - 6322*p**2 + 18244*p - 17576. Let r(y) = -2*y**2 - 4*y. Let o(f) =