*s - 20, -5*s = -4*m - 20. Let r(t) = t**2 + 7*t + 10. Let g be r(m). Determine v so that 0*v + 1/5*v**4 + g*v**3 + 1/5 - 2/5*v**2 = 0.
-1, 1
Let s(r) = -2*r - 14. Let u be s(-9). Let b(c) be the first derivative of 19/6*c**3 - 2*c - 2 + 7/8*c**u + 2*c**2. Factor b(t).
(t + 1)*(t + 2)*(7*t - 2)/2
Factor -4/11*w + 10/11*w**4 - 18/11*w**3 + 14/11*w**2 - 2/11*w**5 + 0.
-2*w*(w - 2)*(w - 1)**3/11
Let u be 11 + 0 - (9 + -6). Let c = u + -6. Factor -4*j**2 - 5*j**c + 4*j**3 + 8*j - 3*j**2.
4*j*(j - 2)*(j - 1)
Let d(x) be the second derivative of -x**9/60480 - x**8/13440 - x**7/10080 + 9*x**4/4 - 2*x. Let p(l) be the third derivative of d(l). Factor p(h).
-h**2*(h + 1)**2/4
Let t = -24 - -27. Suppose 5*h + t = -5*q - 17, -4*h - 16 = -q. Find j such that q - 3/4*j - 9/4*j**5 - 3/2*j**2 + 3*j**3 + 3/2*j**4 = 0.
-1, -1/3, 0, 1
Determine u so that 42*u**3 - 56*u + u**5 + u**2 + 3*u**2 + 3*u**4 - 9*u**4 - 11*u**4 + 0*u**5 = 0.
-1, 0, 2, 14
Let v = -15287/24 - -637. Let f(j) be the first derivative of -11/6*j**3 - 9/8*j**4 + 6 - 7/20*j**5 - 13/8*j**2 - v*j**6 - 3/4*j. Factor f(t).
-(t + 1)**4*(t + 3)/4
Suppose 0*h + 3*h - 18 = 0. Find g such that -h*g**4 - 5*g**2 + 7*g**4 + 4*g**2 = 0.
-1, 0, 1
Let r(j) = j**3 + 4*j**2 + 3*j + 1. Let v be r(-2). Let n be (-23)/(-7) + (5 - (3 + v)). Factor 2/7*i**5 + 2/7*i**3 - 20/7*i**2 + 8/7*i**4 + n - 8/7*i.
2*(i - 1)**2*(i + 2)**3/7
Let g(k) = 7*k**2 - 48*k + 86. Let i(a) = -120*a**2 + 815*a - 1465. Let x(s) = 35*g(s) + 2*i(s). Factor x(c).
5*(c - 8)*(c - 2)
Let n be ((-36)/126)/(2/(-28)). Suppose -2*u = -n*d + 4, u = 6*d - d - 8. Find i, given that 3/4*i**3 + 1/2*i + 1/4*i**4 - 5/4*i**d - 1/4*i**5 + 0 = 0.
-2, 0, 1
Suppose -3*t + 5*t + 8 = -3*p, 0 = -2*p - t - 4. Factor p + 4*i**3 + 5*i**2 + 9*i**2 - 8 - 6*i**2 - 4*i.
4*(i - 1)*(i + 1)*(i + 2)
Let o = -89 - -89. Factor 11 - 14*s - 2*s + 4*s**2 + 1 + o.
4*(s - 3)*(s - 1)
Let p(l) be the third derivative of 0 - 2*l**3 + 25/12*l**4 + 37*l**2 + 0*l - 2/15*l**5. Factor p(a).
-2*(a - 6)*(4*a - 1)
Let b = 13 - 9. Suppose -b = 10*p - 14*p. Factor -p - 1 + 2 + 1 - j**2.
-(j - 1)*(j + 1)
Let s be 157358/(-39360) + -3*12/(-9). Let g(v) be the third derivative of 0 + 1/40*v**5 + 1/3*v**3 + 13*v**2 + 1/8*v**4 + s*v**6 + 0*v. Factor g(m).
(m + 2)**3/4
Let f(p) be the first derivative of 7*p**4/10 - 38*p**3/15 + 8*p**2/5 + 8*p/5 + 92. Factor f(x).
2*(x - 2)*(x - 1)*(7*x + 2)/5
Let s = -6 - -2. Let y = s - -7. What is i in -8*i + 21 + y + 12*i**2 + 3 - 28*i = 0?
3/2
Let a(u) be the second derivative of u**4/3 + 10*u**3/3 - 209*u + 1. Let a(o) = 0. What is o?
-5, 0
Let u(p) be the second derivative of -p**5/150 + 13*p**4/30 - 133*p**3/15 + 361*p**2/15 - 68*p + 7. Factor u(m).
-2*(m - 19)**2*(m - 1)/15
Factor -30*k**2 - 234*k + 178*k**2 - 40 - 6*k**3 + 56 + 76.
-2*(k - 23)*(k - 1)*(3*k - 2)
Let 0 + 3/2*m**2 - 45/2*m = 0. What is m?
0, 15
Suppose 5*t - 25 = -3*x, -3*x + 22 = 4*t - 1. Let z(i) be the second derivative of 3*i + 0 + 0*i**4 - 1/40*i**x + 0*i**2 + 1/12*i**3. Let z(g) = 0. Calculate g.
-1, 0, 1
Suppose 3*k = -3 + 18. Let q(o) = 7*o + 46. Let b be q(-6). Factor u**5 - 3*u**5 + b*u**4 - 2*u**k.
-4*u**4*(u - 1)
Let o(z) be the second derivative of -9/5*z**2 + 19*z + 1/4*z**4 + 7/10*z**3 + 0. Find h, given that o(h) = 0.
-2, 3/5
Let r(d) = d**2 + 2*d - 4. Let i be r(2). Solve 0*c**4 + c + 7*c**3 + 3*c**2 + 3*c**i - 2 + 0 - 4*c = 0.
-1, 2/3
Find j, given that -48*j**2 - 5578 + 35*j - 2*j**3 - 161*j + 5578 = 0.
-21, -3, 0
Determine s, given that -4*s**3 - 6 + 6*s**3 - 5*s**3 + 5*s**3 + 23*s - 14*s**2 - 5*s**3 = 0.
-6, 1/3, 1
Let c(n) = 8*n**2 - 5*n. Let o(v) = -2*v**2 + 2*v. Let a(h) = 2*c(h) + 7*o(h). Determine l so that a(l) = 0.
-2, 0
Let h = -1/867 + 7805/1734. Factor -6*y - 3/2 - h*y**2.
-3*(y + 1)*(3*y + 1)/2
Determine b so that -b**3 + 16*b + 8*b + 14*b**3 - 10*b**3 + 3*b**4 - 30*b**2 = 0.
-4, 0, 1, 2
Let -4 + 590*u**3 + 0*u + 6*u - 592*u**3 = 0. What is u?
-2, 1
Let h be 384/546 + 19/(2470/20). Determine z, given that -2/7*z**2 + h*z - 4/7 = 0.
1, 2
Let h(t) = -81*t - 30. Let i be h(-2). Let f = i - 132. Factor f*g**2 - g**5 + 0 + 0*g - 1/3*g**4 + 2/3*g**3.
-g**3*(g + 1)*(3*g - 2)/3
Let w = -97613/8 - -12202. Factor 3/2*i + w*i**2 + 3/2.
3*(i + 2)**2/8
Find d, given that 242 - 2*d**2 + 5*d + 5*d**2 - d**2 + 39*d = 0.
-11
Let 12*l + l**3 - 2*l**3 + 24 + 3*l**4 + 0*l**2 - 2*l**3 - 18*l**2 = 0. Calculate l.
-2, -1, 2
Let i(m) = -27*m**3 - 184*m**2 + 13*m + 198. Let f(x) = -8*x**3 - 62*x**2 + 4*x + 66. Let j(b) = 7*f(b) - 2*i(b). Factor j(u).
-2*(u - 1)*(u + 1)*(u + 33)
Let y(a) be the third derivative of 0*a - 3*a**2 + a**3 + 9/16*a**4 + 3/20*a**5 + 1/80*a**6 + 0. Suppose y(t) = 0. What is t?
-4, -1
Let u(m) = -3*m**3 - 23*m**2 - 45*m - 25. Suppose 0 = -0*i - 4*i - 8. Let z(s) = -9*s**3 - 70*s**2 - 135*s - 74. Let o(t) = i*z(t) + 7*u(t). Factor o(c).
-3*(c + 1)*(c + 3)**2
Factor -288/5*f + 5184/5 + 4/5*f**2.
4*(f - 36)**2/5
Let s be 2*(-4)/(-2)*4/24. Factor -s*b - 1/3 - 1/3*b**2.
-(b + 1)**2/3
Let x = -750 + 752. Factor -6/7*y - 2/7*y**x + 8/7.
-2*(y - 1)*(y + 4)/7
Let t be (-1)/(-1 + (-4)/(-8)). Suppose -2*z - 4*b + 20 = 0, -5*b - 15 = -t*z - 8*b. Factor 0*a**4 + 0*a**2 + z - 4/9*a**3 + 2/9*a**5 + 2/9*a.
2*a*(a - 1)**2*(a + 1)**2/9
Suppose -9 = 3*w, 0 + 2 = -2*k - 2*w. Let k*i**3 + 13*i**2 - 2*i**4 - 6*i**2 - 3*i**2 = 0. Calculate i.
-1, 0, 2
Let g(b) be the second derivative of b**6/45 - 11*b**5/30 + 4*b**4/9 + 20*b**3/9 + b - 6. Suppose g(h) = 0. What is h?
-1, 0, 2, 10
Let f(w) be the first derivative of -3/28*w**4 + 0*w - 3/7*w**3 + 10 + 6/7*w**2. Suppose f(g) = 0. What is g?
-4, 0, 1
Let f be -7*-3*(-10)/(-15). Suppose f*u - 30 = 4*u. Suppose 8/11*w**2 + 4/11 + 2/11*w**u + 10/11*w = 0. What is w?
-2, -1
Factor 622 + 75*l + 122*l + 951 - 21*l + 4*l**2 + 363.
4*(l + 22)**2
Let j(s) be the first derivative of -s**8/336 + s**6/30 - s**5/30 - s**4/8 + s**3/3 + 9*s**2 + 37. Let k(o) be the second derivative of j(o). Factor k(x).
-(x - 1)**3*(x + 1)*(x + 2)
Let 115*w**2 - 18*w - 55*w**3 + 13*w + 5 - 60*w = 0. Calculate w.
1/11, 1
Let z(s) = s**3 - 7*s**2 + 5*s + 25. Let b be z(5). Suppose 64*m - 60*m - 8 = b. Factor 4*c**m + 1 - 7/2*c - 3/2*c**3.
-(c - 1)**2*(3*c - 2)/2
Let q(f) be the first derivative of 1550*f**2 - 9*f**5 - 38 - 500*f - 5105/3*f**3 + 465/2*f**4. Factor q(u).
-5*(u - 10)**2*(3*u - 1)**2
Let r(p) be the first derivative of -3*p**7/280 - p**6/6 - 39*p**5/40 - 9*p**4/4 - 14*p**3/3 - 23. Let f(c) be the third derivative of r(c). Factor f(d).
-3*(d + 3)**2*(3*d + 2)
Let k(q) be the third derivative of -q**10/8064 + q**9/2520 - q**8/8960 - q**7/1680 + 7*q**4/8 - 6*q**2. Let i(g) be the second derivative of k(g). Factor i(a).
-3*a**2*(a - 1)**2*(5*a + 2)/4
Let u(i) be the third derivative of i**7/70 + 17*i**6/40 - 9*i**5/10 - 124*i**2. Factor u(t).
3*t**2*(t - 1)*(t + 18)
Let f(v) be the second derivative of 5*v**4/24 - 35*v**3/12 - 10*v**2 + 240*v - 2. Suppose f(u) = 0. What is u?
-1, 8
Let l(a) = -3*a**4 + 6*a**3 - 9*a**2 - 24*a. Let t(n) = n**4 - n**2 + n. Let k(u) = -l(u) - 6*t(u). Let k(x) = 0. Calculate x.
-3, -1, 0, 2
Suppose -5*f - 4 - 1 = 0, -5*f - 29 = -4*o. Suppose 14 = o*x + 2. Factor -5*u**3 - u**3 + x*u**2 - 2 - 2*u + 8*u**3.
2*(u - 1)*(u + 1)**2
Let d be 12/((-8)/60*-3*35). Let w(m) be the first derivative of 0*m**3 + 3/28*m**4 + d*m - 1 - 9/14*m**2. Factor w(y).
3*(y - 1)**2*(y + 2)/7
Let p be 20/(-7)*7/(-2). Factor -2*b - b**3 + 3 - 7*b - 3*b**2 + p*b.
-(b - 1)*(b + 1)*(b + 3)
Let o be -2*((-111)/15 - -1 - (0 + -6)). Let 4/5*p**4 + 4/5*p + 0 - 4/5*p**2 - o*p**3 = 0. What is p?
-1, 0, 1
Let m = -7687 - -7691. Factor 4*i**2 + 7/4*i**3 + 0 + 1/4*i**m + 3*i.
i*(i + 2)**2*(i + 3)/4
Suppose -5*w - 5*i + 5 = 0, -458*w + 454*w + 4*i = -12. Factor -4/13*x**w + 12/13 - 2/13*x.
-2*(x + 2)*(2*x - 3)/13
Suppose -4*r**5 + 12 - 88*r**4 - 52*r**3 + 76*r**2 + 20*r - 38*r**5 + 36*r**3 + 38*r = 0. Calculate r.
-1, -2/3, -3/7, 1
Suppose 0 = -30*k + 32*k + 4*a - 24, -3*a + 12 = 0. Find r, given that 4/9*r**2 + 2/9*r**3 - 1/3 - 2/9*r - 1/9*r**k = 0.
-1, 1, 3
Let y(m) be the third derivative of 1/30*m**4 - 1/3*m**3 + 0*m + 1/450*m**6 + 0 - 5*m**2 - 1/75*m**5. Let s(k) be the first derivative of y(k). Factor s(l).
4*(l - 1)**2/5
Let z(q) be the second derivative of 0*q*