 Let p be o(8). Let y(i) be the first derivative of 2/3*i - 5 + 5/6*i**2 + 1/3*i**p. Factor y(r).
(r + 1)*(3*r + 2)/3
Factor -9/2*p**3 - 54*p + 0 - 27*p**2 - 1/4*p**4.
-p*(p + 6)**3/4
Let w(y) be the third derivative of y**6/30 - 2*y**5/15 - y**4/2 + 173*y**2. Solve w(a) = 0 for a.
-1, 0, 3
Let f be 5 - 23/3 - 18/24*-4. Factor 4/9*w - f*w**2 + 1/9 - 2*w**3.
-(2*w - 1)*(3*w + 1)**2/9
Let g(j) be the second derivative of 3/8*j**3 - 1/16*j**4 + 0 + 9*j - 3/4*j**2. What is c in g(c) = 0?
1, 2
Let v(g) be the second derivative of -g**7/189 - 4*g**6/45 - 23*g**5/45 - 10*g**4/9 - 25*g**3/27 - 465*g. Factor v(i).
-2*i*(i + 1)**2*(i + 5)**2/9
Let v(o) be the first derivative of o**5/5 - 37*o**4/4 + 156*o**3 - 1080*o**2 + 1728*o - 47. Factor v(l).
(l - 12)**3*(l - 1)
Let g(p) be the third derivative of -p**8/1008 - p**7/210 - p**6/360 + p**5/60 + p**4/36 - 39*p**2 - 2. Let g(w) = 0. What is w?
-2, -1, 0, 1
Let p(r) be the second derivative of r**5/4 - 7*r**4/12 + r**3/6 + 2*r**2 - 7*r. Let y(d) = 9*d**3 - 13*d**2 + d + 8. Let q(l) = -5*p(l) + 3*y(l). Factor q(s).
2*(s - 2)*(s - 1)*(s + 1)
Solve 26/5*o**3 + 0*o - 2*o**4 + 0 - 2/5*o**5 - 14/5*o**2 = 0.
-7, 0, 1
Let 0 + 3/4*k**2 - 75*k = 0. Calculate k.
0, 100
Let g be 2*1 + ((-14)/35)/((-9)/(-15)). Suppose 8*m - 20/3 - g*m**2 = 0. Calculate m.
1, 5
Suppose -4*f - 357 = 2*q - 1237, -5*q + 220 = f. What is h in 467*h**2 + 78*h + 480*h**3 - 67*h**2 + f*h**4 + 2*h + 35*h**5 = 0?
-2, -2/7, 0
Let v(a) = 2*a**2 - 8*a + 5. Let n(j) = j**2 - 7*j + 4. Let w = -23 - -18. Let f(y) = w*n(y) + 4*v(y). Factor f(r).
3*r*(r + 1)
Let c be (1 - 0)*3 + 1 + -221. Let u = c - -1955/9. Let -8/9*s + 10/9*s**2 - 4/9*s**3 + u = 0. Calculate s.
1/2, 1
Let u(r) = -r - 3. Let i be u(-14). Let y be (0/i)/(2 - 1). Factor y*l + 0 + 2/11*l**2.
2*l**2/11
Let z(f) be the third derivative of f**5/570 - 5*f**4/114 - 3*f**2 - 8*f. Let z(x) = 0. Calculate x.
0, 10
Let c(b) be the third derivative of 0 - 1/120*b**5 - 1/16*b**4 - 4*b**2 + 0*b - 1/6*b**3. Factor c(l).
-(l + 1)*(l + 2)/2
Suppose -2*f = 5*k - 11, -5*f - k - 2*k + 37 = 0. Factor 10*a**5 + 20*a**2 - 17*a**4 - 7*a + a**4 - f*a**3 + a + 4*a - 4.
2*(a - 1)**3*(a + 1)*(5*a + 2)
Suppose 78*u - 21 = 75*u - 5*d, -4*d = 3*u - 18. Factor 4/3 - 4/3*r**3 + 10/3*r + 2/3*r**u.
-2*(r - 2)*(r + 1)*(2*r + 1)/3
Factor -3/4*d**2 + 57/4 - 27/2*d.
-3*(d - 1)*(d + 19)/4
Find p, given that 16/3*p**2 + 2 + 22/3*p = 0.
-1, -3/8
Let x(u) be the second derivative of 2*u**7/21 + u**6/15 - u**5/5 - u**4/6 - 46*u. Solve x(z) = 0 for z.
-1, -1/2, 0, 1
Suppose 7*p = 21*p. Find u, given that p*u**2 + 2/5*u**3 + 2/5*u**4 + 0*u + 0 = 0.
-1, 0
Let n be (5 + -11 + 6)*(-1)/(-6). What is c in n*c + 0 - 1/4*c**2 = 0?
0
Find p such that -2/3*p**3 - 32/3*p + 14/3*p**2 + 8 = 0.
2, 3
Let g(u) = -2 + 2 + 24 - 2*u. Let t be g(11). Factor -1/2 - 2*x - 1/2*x**4 - 3*x**t - 2*x**3.
-(x + 1)**4/2
Let a(t) = -2*t**4 + 14*t**3 + 2*t**2 - 26*t + 18. Let x(y) = 6*y**4 - 41*y**3 - 6*y**2 + 79*y - 55. Let z(j) = 17*a(j) + 6*x(j). Suppose z(n) = 0. Calculate n.
-2, 1, 2, 3
Let r(i) = 54*i**2 - 4*i - 14. Let y(a) = 11*a**2 - a - 3. Let j be 2/(-6)*(2 - 11). Let x(m) = j*r(m) - 14*y(m). Find q, given that x(q) = 0.
-1/4, 0
Let w(u) be the third derivative of 1/504*u**8 + 0*u - 8*u**2 - 1/90*u**5 - 1/180*u**6 + 1/315*u**7 + 0 + 0*u**4 + 0*u**3. Factor w(q).
2*q**2*(q - 1)*(q + 1)**2/3
Let q be ((-16)/(-12))/(-2)*108/(-204). Factor 0 - q*d - 2/17*d**3 - 8/17*d**2.
-2*d*(d + 1)*(d + 3)/17
Suppose -a + 4*r + 23 = 0, 14*r - 2 = -4*a + 12*r. Factor -125*b**a - 3*b**2 + 3*b + 3*b + 122*b**3.
-3*b*(b - 1)*(b + 2)
Let v(c) be the third derivative of -c**7/630 + c**6/360 + 7*c**5/180 - c**4/72 - c**3/3 + 220*c**2. Solve v(i) = 0 for i.
-2, -1, 1, 3
Let i(c) be the third derivative of c**6/90 + 11*c**5/45 + 19*c**4/18 + 2*c**3 + 3*c**2 + 34. Factor i(t).
4*(t + 1)**2*(t + 9)/3
Find r such that -2/15*r**2 - 3362/15 - 164/15*r = 0.
-41
Let c(i) be the second derivative of -13*i + 121/3*i**2 - 44/9*i**3 + 2/9*i**4 + 0. Determine d so that c(d) = 0.
11/2
Suppose 5*y = 81 - 21. Let v be (y/20)/(18/20) - 0. Factor 0*z**2 - 4/3*z + v*z**4 + 4/3*z**3 - 2/3.
2*(z - 1)*(z + 1)**3/3
Suppose x - 10 = -2*a - 0*a, -5*a = 4*x - 28. Factor -24*g**a + 85*g**3 + 4*g**4 + 6*g - 80*g**2 + 9*g.
-5*g*(g - 3)*(g - 1)*(4*g - 1)
Suppose 13 = -w + 3*z, 2 = -4*w + 3*z - 5. Factor -325*m**2 + 325*m**w - 4*m + 4*m**3.
4*m*(m - 1)*(m + 1)
Let f(d) = -d - 2. Let b(x) = -2*x - 5. Let z(m) = -3*b(m) + 7*f(m). Let n be z(0). Solve -n - 2*w**3 - w**3 + 3*w**4 + 1 = 0 for w.
0, 1
Let z = -59 + 63. Let p = -2 + 3. Let -59*s**3 + 7*s**3 + p - 35*s**z - 2*s - 19*s**2 - 1 = 0. Calculate s.
-1, -2/7, -1/5, 0
Let o(x) be the second derivative of -5*x**4/12 - 25*x**3 - 145*x**2/2 + 187*x. Factor o(d).
-5*(d + 1)*(d + 29)
Let q(x) be the third derivative of 0*x + 2/7*x**3 + 0 - 1/21*x**4 - 26*x**2 - 1/105*x**5. Factor q(j).
-4*(j - 1)*(j + 3)/7
Let v be (-31)/(-5) - (-4 - -5 - -5). Solve 0 + v*d**3 - 1/5*d**4 - 1/5*d + 1/5*d**2 = 0 for d.
-1, 0, 1
Suppose t = -2*t + 12. Let y = -311 + 313. Solve 2*k**4 + 4*k**t + k**4 + y*k - 12*k**3 + 3*k**2 = 0.
-2/7, 0, 1
Suppose 0 = 2*o + 11 - 5. Let r = o + 8. Let v(u) = -6*u**3 - 11*u**2 + u + 11. Let h(f) = 9*f**3 + 16*f**2 - 2*f - 16. Let a(b) = r*h(b) + 7*v(b). Factor a(y).
3*(y - 1)*(y + 1)**2
Let z be (-4*3/6)/((-3)/(-54)). Let q be 1/(-4) + (-9)/z. Factor q + 1/4*h - 1/4*h**2.
-h*(h - 1)/4
Let n(u) = 3*u**2 + 21*u - 43. Let h(m) = m**2 + 11*m - 22. Let p(o) = -5*h(o) + 2*n(o). Let f be p(11). Solve -18/7 + 10/7*g**f - 2/7*g**3 - 6/7*g = 0.
-1, 3
Let y(a) be the second derivative of a**2 + 2*a + 0 - 1/24*a**4 - 1/9*a**3 - 1/180*a**5. Let v(m) be the first derivative of y(m). Suppose v(g) = 0. What is g?
-2, -1
Let u be 2/((-5)/(60/(-8))). Let f(g) be the first derivative of -3*g**3 + 7 + 2*g + g**2 + g**u + g**2. Factor f(d).
-2*(d - 1)*(3*d + 1)
Let g be (2/(-2 - 10))/((-116)/(-36)). Let c = 131/290 + g. Factor -2/5*b**2 + 2/5*b**4 - c*b**3 + 2/5*b + 0.
2*b*(b - 1)**2*(b + 1)/5
Let s(r) be the third derivative of -r**7/1050 - 9*r**6/200 - 18*r**5/25 - 18*r**4/5 - 269*r**2. Factor s(v).
-v*(v + 3)*(v + 12)**2/5
Suppose -3*z + 65*n = 70*n - 15, -4*z = -n + 3. Suppose -2*m = -8 - 2. Let 0 + v**m + 16/3*v**3 + z*v + 4/3*v**2 + 13/3*v**4 = 0. What is v?
-2, -1/3, 0
Let y be 1/4*8 + -1 + 4. Find i such that 7*i**5 - 2*i**3 + 12*i**4 + 3*i - 4*i**y + 5*i**3 + 12*i**2 + 15*i**3 = 0.
-1, 0
Let o = 9/176 + 659/880. Factor -3/5*v**3 - o + 4/5*v + v**2.
-(v - 2)*(v + 1)*(3*v - 2)/5
Let o(n) be the first derivative of n**6/9 - 4*n**5/5 + 7*n**4/3 - 32*n**3/9 + 3*n**2 - 4*n/3 + 104. Factor o(c).
2*(c - 2)*(c - 1)**4/3
Let o(a) be the first derivative of -2*a**5/5 - 5*a**4/4 + 38*a**3/3 - 14*a**2 - 24*a - 621. Factor o(g).
-(g - 2)**2*(g + 6)*(2*g + 1)
Let g(m) be the third derivative of m**6/30 - 2*m**5/15 - 2*m**4/3 + 16*m**3/3 - 20*m**2. Factor g(o).
4*(o - 2)**2*(o + 2)
Let o(r) be the second derivative of 2/21*r**4 + 0 - 1/70*r**5 + 0*r**2 - 1/7*r**3 + 12*r. Factor o(l).
-2*l*(l - 3)*(l - 1)/7
Suppose -24 = -4*y + 16. Factor -y*s - 18*s**3 - 22*s**2 - 10*s - 6*s + 22*s.
-2*s*(s + 1)*(9*s + 2)
Let w(d) be the third derivative of d**8/192 + d**7/42 + d**6/48 - d**5/12 - d**4/3 + 7*d**2. Let z(q) be the second derivative of w(q). Factor z(m).
5*(m + 1)**2*(7*m - 2)
Let m be (0 + (-3 - -1))/(2/(-28)). Let x be m/(-70) - 6/(-10). Factor -2/5 - x*j + 1/5*j**2.
(j - 2)*(j + 1)/5
Let c(o) be the first derivative of -64*o - 484/3*o**3 + 176*o**2 + 21. Solve c(s) = 0.
4/11
Determine d, given that 0 + 57/2*d**2 - 3/2*d**3 + 63*d = 0.
-2, 0, 21
Factor -3/8*d**5 + 3/8 - 9/8*d**4 + 3/4*d**2 - 3/4*d**3 + 9/8*d.
-3*(d - 1)*(d + 1)**4/8
Let y(s) = -2*s**3 + 9*s**2 + 5*s - 6. Let r(a) = -8*a**3 + 26*a**2 + 14*a - 20. Let m(i) = 3*r(i) - 10*y(i). Factor m(x).
-4*x*(x + 1)*(x + 2)
Suppose -b - 19*i = -17*i + 8, 3*i = b - 12. Let p(o) be the second derivative of 4*o - 5/3*o**4 + b*o**2 + 4/5*o**5 + 0 + 2/3*o**3. Factor p(s).
4*s*(s - 1)*(4*s - 1)
Let v be 6 + 155/(-25) - 211/(-30). Let k = v + -197/30. Suppose -2/15*s**3 + k*s**2 - 16/15 + 8/15*s = 0. What is s?
-2, 2
Suppose -4*i = 4*x - 12, -4*x + 5*i - 3 - 3 = 0. Let r(u) = 2*u**3 + 2*u - 1. Let h be r(x). Factor -9*p**4 -