 Let o(l) = 4*l**3 + 34*l**2 - 36*l - 70. Let i(y) = 2*d(y) - o(y). Factor i(h).
-2*(h - 2)*(h + 1)*(h + 17)
Let r = -1/37 + 163/555. Let o(y) be the first derivative of 0*y**3 + 0*y**2 + r*y**5 - 2 + 0*y + 1/9*y**6 + 1/6*y**4. Factor o(h).
2*h**3*(h + 1)**2/3
Let a = 24 + -21. Let f = a + -1. Factor -33/5*i - 48/5*i**f - 6/5 - 21/5*i**3.
-3*(i + 1)**2*(7*i + 2)/5
Let i(g) be the first derivative of g**4/42 + 2*g**3/7 + 5*g**2/7 - 8*g - 22. Let h(v) be the first derivative of i(v). Factor h(u).
2*(u + 1)*(u + 5)/7
Suppose -8*s = -11*s + 12. Let w(y) be the third derivative of y**2 + 0 + 0*y - 1/8*y**s + 1/20*y**5 + 0*y**3. Find r such that w(r) = 0.
0, 1
Suppose 5*b - 3*b - 2 = 0. Let s be (-10)/35 - 23/(-7). Find c, given that -c + s*c + 0*c + b - 2*c**3 - c**2 = 0.
-1, -1/2, 1
Factor 6/7*n**3 - 2/7*n**2 + 2/7*n**5 + 0*n + 0 - 6/7*n**4.
2*n**2*(n - 1)**3/7
Let b = 50 - 37. Let t(r) = 35*r**3 - 40*r**2 + r + 17. Let o(z) = -17*z**3 + 20*z**2 - z - 8. Let k(v) = b*o(v) + 6*t(v). Factor k(h).
-(h - 1)**2*(11*h + 2)
Let s = -5/9 + 29/36. Suppose -4*u = -3*y - 3*u + 17, 0 = -4*y - 3*u + 1. Factor 1/2*i + 1/4*i**5 + 1/4*i**2 + 0 - 3/4*i**3 - s*i**y.
i*(i - 2)*(i - 1)*(i + 1)**2/4
Let w(o) be the third derivative of -1/10*o**3 + 6*o**2 + 0*o**4 + 1/100*o**5 + 0*o + 0. Factor w(y).
3*(y - 1)*(y + 1)/5
Let h(v) be the second derivative of v**5/20 + v**4/6 + v**3/6 + 3*v**2/2 + 12*v. Let o be h(0). Solve -1/3*c**o - 4*c + 2*c**2 + 8/3 = 0 for c.
2
Let v = -26 + 83. Find l such that -24*l**3 - v*l + 92*l**2 - 19*l + 2*l**4 - 78*l + 34*l + 50 = 0.
1, 5
Factor -s**3 - 72*s - 31*s**2 + 78*s - 36*s.
-s*(s + 1)*(s + 30)
Let q(g) be the first derivative of 3*g**5/20 - 45*g**4/16 + 61*g**3/4 - 63*g**2/8 - 147*g/2 + 105. Factor q(n).
3*(n - 7)**2*(n - 2)*(n + 1)/4
Let s = 313/1986 + 3/331. Let z(w) be the second derivative of 4*w - 1/36*w**3 + 1/72*w**4 - s*w**2 + 0. Solve z(a) = 0.
-1, 2
Let z(l) be the third derivative of -3*l**6/10 + 7*l**5/4 - 21*l**4/8 - l**3 + 21*l**2 - 6. Suppose z(u) = 0. Calculate u.
-1/12, 1, 2
Let p(r) be the third derivative of -r**8/840 - 2*r**7/525 + 101*r**2. Factor p(h).
-2*h**4*(h + 2)/5
Let t(j) = -4*j**3 - 8*j**2 - 12*j - 4. Let y(d) = 9*d**3 + 16*d**2 + 25*d + 8. Let u(k) = -5*t(k) - 2*y(k). Let u(p) = 0. Calculate p.
-2, -1
Let u be 4 + (4 + -5 - -1 - 0). What is w in -4*w**3 + 3*w**4 - 16*w**2 - 16*w**3 - 7*w**u = 0?
-4, -1, 0
Let h be ((-8)/(-30))/(14/(-35)*80/(-24)). Factor 0 - h*j - 3/5*j**2 + 3/5*j**4 + 1/5*j**3.
j*(j - 1)*(j + 1)*(3*j + 1)/5
Let x = -1 - -6. Let o = -10 + 12. Factor -2*u**o - 2*u**5 - x*u**4 + u + 3*u**2 - u**3 - 2*u**3.
-u*(u + 1)**3*(2*u - 1)
Let n(x) be the second derivative of x**5/20 - 16*x. Let i(p) = -6*p**3 + 16*p**2 - 40*p + 32. Let h(t) = i(t) + 4*n(t). Determine j so that h(j) = 0.
2, 4
Let o = 1395/119 + -192/17. Factor 4/7*b**3 - 4/7*b - o*b**2 + 4/7 - 1/7*b**4.
-(b - 2)**2*(b - 1)*(b + 1)/7
Let z(a) be the third derivative of a**8/6720 - a**7/280 + 3*a**6/80 + a**5/4 - 11*a**2. Let d(i) be the third derivative of z(i). Factor d(g).
3*(g - 3)**2
Let u(a) be the third derivative of 0*a + 1/1890*a**7 - 4*a**2 + 1/540*a**5 + 0*a**4 + 0 - 1/540*a**6 + 0*a**3. Factor u(o).
o**2*(o - 1)**2/9
Factor -28 - 55 + 169*d + 43*d**2 - 23*d**2 - 85 - 21*d**2.
-(d - 168)*(d - 1)
Suppose -6*c = 1 - 13. Factor o + o**5 - 126*o**2 - o**4 + 60*o**c - 3*o**4 + 62*o**2 + 6*o**3.
o*(o - 1)**4
Let r(l) be the third derivative of -1/30*l**6 - 6*l**2 + l**3 + 2/15*l**5 + 2/3*l**4 + 0 + 0*l. Let z(s) be the first derivative of r(s). Factor z(n).
-4*(n - 2)*(3*n + 2)
Let a = 12605 - 12601. Determine j, given that 0*j**2 - 4/7*j**5 + 0*j + 0 + 4/7*j**3 + 0*j**a = 0.
-1, 0, 1
Let v(g) be the third derivative of -g**9/11340 + g**8/5040 - g**7/7560 + 13*g**4/12 - 35*g**2. Let i(m) be the second derivative of v(m). Factor i(p).
-p**2*(2*p - 1)**2/3
Let f(i) = -4 + 2 + i + 0*i. Let b be f(4). What is t in 0 + b*t**3 - t**5 + 0*t**5 - t - t**4 + 0*t**2 - 1 + 2*t**2 = 0?
-1, 1
Factor -12/7 + 6/7*s**3 - 6/7*s**2 + 2/7*s**4 - 22/7*s.
2*(s - 2)*(s + 1)**2*(s + 3)/7
Let t(o) be the first derivative of 3*o**8/112 - o**7/28 - o**6/9 + o**5/4 - 5*o**4/24 - 4*o**3 - 19. Let w(f) be the third derivative of t(f). Factor w(a).
5*(a - 1)*(a + 1)*(3*a - 1)**2
Let w(a) = -11*a**2 + 225*a - 6498. Let r(d) = 36*d**2 - 674*d + 19494. Let n(j) = -3*r(j) - 10*w(j). Determine g, given that n(g) = 0.
57
Let d(b) be the second derivative of b**7/273 - 2*b**6/195 - 3*b**5/65 + 2*b**4/39 + b**3/3 + 6*b**2/13 - 49*b. Determine v, given that d(v) = 0.
-1, 2, 3
Factor 2*v - 16/3 + 1/3*v**2.
(v - 2)*(v + 8)/3
Let k(z) be the second derivative of z**6/15 + z**5/35 - 2*z**4/3 - 8*z**3/21 - 6*z - 3. Solve k(a) = 0 for a.
-2, -2/7, 0, 2
Let z be (-4)/270*-6 + 70/630. Let m(q) be the first derivative of 2/15*q**3 - 5 - z*q**2 + 1/10*q**4 - 2/5*q. Determine u so that m(u) = 0.
-1, 1
Let w(v) = -22 + 15 + 106 - 4*v - 35. Let q be w(15). Factor 9/7*l**3 - 9/7*l - 6/7 + 3/7*l**q + 3/7*l**2.
3*(l - 1)*(l + 1)**2*(l + 2)/7
Let x(f) be the third derivative of 3*f**5/20 + 217*f**4/8 + 36*f**3 + 96*f**2 - 2*f. Factor x(l).
3*(l + 72)*(3*l + 1)
Factor -38*b**3 - 7*b**2 + 6*b**2 - 11*b**2 + 120 + 15*b**3 + 14*b + 21*b**3.
-2*(b - 3)*(b + 4)*(b + 5)
Let k(g) be the second derivative of g**5/50 + 17*g**4/60 - 29*g**3/30 + g**2 - 358*g. Let k(o) = 0. Calculate o.
-10, 1/2, 1
Let i(t) be the first derivative of -t**3/9 + 14*t**2/3 - 196*t/3 - 84. Factor i(j).
-(j - 14)**2/3
Determine u so that -3436*u**3 + 280*u + 1699*u**3 - 240 - 15*u**2 + 5*u**4 + 1707*u**3 = 0.
-3, 1, 4
Let h(r) = 100*r + 4400. Let p be h(-44). Factor 3/4*l**2 + 9/8*l - 3/4 + p*l**4 - 3/2*l**3 + 3/8*l**5.
3*(l - 1)**3*(l + 1)*(l + 2)/8
Let c = -2110 - -2115. Solve 1/7*m**3 + 0*m + 1/7*m**4 - 2/7*m**c + 0 + 0*m**2 = 0 for m.
-1/2, 0, 1
Let k be (-7)/(28/(-12)) + 0. Let u be 6/9*k - -2. What is n in 0 - 2/5*n**3 + 2/5*n - 2/5*n**2 + 2/5*n**u = 0?
-1, 0, 1
Let t(u) = -235*u**3 - 170*u**2 + 65*u. Let s(o) be the first derivative of -9*o**4/2 - 13*o**3/3 + 5*o**2/2 + 8. Let f(j) = -40*s(j) + 3*t(j). Factor f(z).
5*z*(z + 1)*(3*z - 1)
Let t(q) be the first derivative of -1/5*q**5 - 7 + 0*q + 0*q**3 - 1/4*q**4 + 0*q**2. Let t(l) = 0. What is l?
-1, 0
Let b(c) be the third derivative of c**7/42 + c**6/45 + c**5/150 - c**3/3 - 15*c**2. Let x(z) be the first derivative of b(z). Let x(s) = 0. Calculate s.
-1/5, 0
Factor -2*j**2 + 3933 - 11*j - 3849 - 11*j.
-2*(j - 3)*(j + 14)
Let f(a) = a**2 + 87*a + 1838. Let k be f(-51). Factor 1/2*t + 0 - 1/2*t**k.
-t*(t - 1)/2
Let y(k) = 12*k**5 - 23*k**4 + 6*k**3 + 5*k. Let v(q) = 6*q**5 - 12*q**4 + 4*q**3 + 2*q. Let c(b) = 9*v(b) - 4*y(b). Factor c(t).
2*t*(t - 1)**3*(3*t + 1)
Let h = -4149 + 37343/9. Factor h*y**4 + 10/9*y**2 + 0 - 4/9*y - 8/9*y**3.
2*y*(y - 2)*(y - 1)**2/9
Let f(b) be the first derivative of 19*b**3/3 + b**2 + 564. Factor f(r).
r*(19*r + 2)
Factor 0 - 15/2*t**2 + 93/8*t**3 - 21/4*t**4 + 9/8*t.
-3*t*(t - 1)**2*(14*t - 3)/8
Let y = -10295/24 - -429. Let o(h) be the first derivative of 1/6*h**3 + 1/8*h**4 + 1/4*h + y*h**6 - 3/8*h**2 - 3/20*h**5 + 7. Factor o(t).
(t - 1)**4*(t + 1)/4
Let f(s) = -96*s + 290. Let w be f(3). Let q(i) be the first derivative of 0*i + 0*i**w + 1/6*i**3 - 6 + 1/4*i**4 + 1/10*i**5. Factor q(h).
h**2*(h + 1)**2/2
Let z(d) be the second derivative of -d**5/120 + d**4/48 - 27*d**2/2 - 3*d + 10. Let n(m) be the first derivative of z(m). Factor n(t).
-t*(t - 1)/2
Factor 5*d**2 + 16*d**2 - 48*d - 63*d**2 - 36 + 21*d**2 - 3*d**3.
-3*(d + 2)**2*(d + 3)
Let 72*s - 459/2 + 3/2*s**2 = 0. What is s?
-51, 3
Suppose 1233 = 5*k + r - 469, 0 = -5*k - 5*r + 1710. Let a be 16/5 + (-7 - k/(-50)). Determine n so that 1/8 + 3/4*n**2 + 1/8*n**4 - 1/2*n**a - 1/2*n = 0.
1
Let j = -270177/5 + 54036. Determine t so that -j*t**2 - 21/5*t - 18/5 = 0.
-6, -1
Let p(h) be the third derivative of -h**6/3600 - 7*h**5/600 - 49*h**4/240 + 4*h**3/3 + 37*h**2. Let m(q) be the first derivative of p(q). Factor m(n).
-(n + 7)**2/10
Let -96 - 216*v**3 + 145*v + 125*v + 27*v**5 + 325*v - 6*v**4 + 48*v**2 - 163*v = 0. What is v?
-2, 2/9, 2
Let u(g) be the third derivative of -g**6/180 + 11*g**3/6 - g**2. Let o(c) be the first derivative of u(c). Find r such that o(r) 