)/3
Let j = 38/11 - 1016/275. Let a = j + 104/225. Find t, given that 2/9*t**2 + 2/9*t - 2/9 - a*t**3 = 0.
-1, 1
Let z = 65 + -46. Let s = z + -19. Solve -9/5*j**2 + s - 2/5*j = 0.
-2/9, 0
Let a be (2 + -1)*(5 - 4). Suppose 3*l - 5 = a. Factor -1/4*q**3 + 1/4*q - 1/2 + 1/2*q**l.
-(q - 2)*(q - 1)*(q + 1)/4
Determine b so that 12/5*b**2 - 8/5*b**4 - 16/5 + 4*b**3 - 32/5*b = 0.
-1, -1/2, 2
Factor -10*z**3 + 24*z**2 + 46 - 8*z - 46.
-2*z*(z - 2)*(5*z - 2)
Let q be 9/(-15) + (-868)/(-1440). Let a(o) be the third derivative of 2*o**2 + 0 + 0*o**3 - 1/72*o**4 + 0*o + q*o**6 + 0*o**5. Find w such that a(w) = 0.
-1, 0, 1
Factor b**3 + 3*b**4 + 2*b**3 + 4*b - 4*b.
3*b**3*(b + 1)
Let p(m) be the third derivative of 0*m + 0 + m**2 - 1/6*m**5 + 7/12*m**4 - 2/3*m**3. What is b in p(b) = 0?
2/5, 1
Let o(t) be the third derivative of 0 + 1/210*t**5 + 1/42*t**4 + 0*t**3 - 6*t**2 + 0*t. Factor o(g).
2*g*(g + 2)/7
Let j(q) be the first derivative of -1/16*q**4 + 1/12*q**3 + 1/8*q**2 - 1/20*q**5 + 0*q + 1. Factor j(n).
-n*(n - 1)*(n + 1)**2/4
Let a(v) be the first derivative of 3721*v**3/3 - 122*v**2 + 4*v + 40. Factor a(b).
(61*b - 2)**2
Let d = 398 - 1192/3. Factor 0 - 4/3*i - d*i**2.
-2*i*(i + 2)/3
Let p(z) be the first derivative of -3*z**4 - 22*z**3/3 - 4*z**2 + 2*z + 19. Suppose p(k) = 0. What is k?
-1, 1/6
Factor 14/11*g**5 - 4/11*g**3 + 0 + 0*g + 0*g**2 - 10/11*g**4.
2*g**3*(g - 1)*(7*g + 2)/11
Let j(y) be the second derivative of y**8/224 + 3*y**7/140 + 3*y**6/80 + y**5/40 + 7*y**2/2 - 3*y. Let m(h) be the first derivative of j(h). Factor m(r).
3*r**2*(r + 1)**3/2
Let -88/7*x**2 + 0 + 8/7*x + 242/7*x**3 = 0. Calculate x.
0, 2/11
Let b(p) be the third derivative of -p**5/150 - p**4/30 + p**3/5 - p**2. Factor b(g).
-2*(g - 1)*(g + 3)/5
Suppose 4*c = -2*x + 2, 0*c = 4*c - 2*x - 14. Suppose -c*a - 4*g + 10 = -3*a, g - 9 = -3*a. Determine i, given that -2 + 2*i**3 + 2 - a*i**2 + 0*i**3 = 0.
0, 1
Let j(f) = f**3 - 9*f**2 + 3. Let q be j(9). Find k such that k**4 + k - k**3 + 0*k**3 - k**2 + 0*k**q = 0.
-1, 0, 1
Let j = 36 - 33. Let g(v) be the second derivative of -1/15*v**j + 0 + 1/15*v**4 - 1/75*v**6 + 1/25*v**5 - 1/5*v**2 - 2*v - 1/105*v**7. Solve g(n) = 0.
-1, 1
Let b(n) be the first derivative of n**9/6048 + n**8/3360 - n**7/1680 - n**6/720 + 5*n**3/3 - 2. Let k(f) be the third derivative of b(f). Factor k(i).
i**2*(i - 1)*(i + 1)**2/2
Let q(v) be the second derivative of -v**4/12 + v**3/2 - v**2 - 12*v. Determine h, given that q(h) = 0.
1, 2
Determine y, given that 8/11*y**2 - 6/11*y - 36/11 + 2/11*y**3 = 0.
-3, 2
Let z(s) be the second derivative of s**7/21 + s**6/15 - s**5/10 - s**4/6 + 3*s - 19. Factor z(x).
2*x**2*(x - 1)*(x + 1)**2
Let n(o) = o**4 + 9*o**3 + 12*o**2 - 25*o + 3. Let z(b) = b**4 + 9*b**3 + 11*b**2 - 25*b + 4. Let y(j) = 4*n(j) - 3*z(j). Factor y(m).
m*(m - 1)*(m + 5)**2
Let s(x) be the second derivative of -x**5/30 - x**4/6 - x**3/3 + 2*x**2 + 3*x. Let v(a) be the first derivative of s(a). Factor v(b).
-2*(b + 1)**2
Let l = -25 + 41. Solve 2*r**2 + 3*r**2 - 10*r**5 - 8*r**3 + 6*r**3 - l*r**4 - r**2 = 0 for r.
-1, 0, 2/5
Factor 23*u**2 - 10*u - 63*u**2 + 21*u**2 + 18*u**2 - 25.
-(u + 5)**2
Let c(k) be the first derivative of -3*k**4/2 - 5*k**3 + 33*k**2/2 - 12*k - 35. Factor c(a).
-3*(a - 1)*(a + 4)*(2*a - 1)
Let h(f) be the third derivative of -5/24*f**4 + 0*f - 1/60*f**5 + 0 - 8*f**2 - 2/3*f**3. Factor h(d).
-(d + 1)*(d + 4)
Let d(s) = -s**2 + 2*s - 2. Let t be d(3). Let r = 9 + t. Factor r*v**2 + v**2 - 5*v**2 - v**2.
-v**2
Let g(q) = q**2 - q + 1. Let r(a) be the second derivative of -5*a**4/4 - a**3/6 + 5*a**2/2 + 3*a. Let k(b) = 3*g(b) + r(b). Suppose k(w) = 0. What is w?
-1, 2/3
Let s(u) be the second derivative of u**6/90 - u**5/30 + u**4/36 + 12*u + 1. What is z in s(z) = 0?
0, 1
Let q(c) be the third derivative of -c**8/2016 + c**7/1260 + c**6/720 - c**5/360 + 19*c**2 - c. What is g in q(g) = 0?
-1, 0, 1
Let w(v) be the third derivative of -1/480*v**6 + 5*v**2 + 0*v - 1/120*v**5 + 1/96*v**4 + 0 + 1/12*v**3. Factor w(s).
-(s - 1)*(s + 1)*(s + 2)/4
Let f = 568369/13641 + 2/4547. Let q = f - 41. Determine l so that -10/3*l + 8/3*l**2 + 4/3 - q*l**3 = 0.
1, 2
Factor -2/13*r**3 + 0 + 4/13*r**2 - 2/13*r.
-2*r*(r - 1)**2/13
Factor 5 - 13 - 17*d - 3*d - 12 - 5*d**2.
-5*(d + 2)**2
Let f(y) be the first derivative of -7*y**5/15 + 5*y**4/8 - y**3/3 + y**2/2 + 1. Let i(q) be the second derivative of f(q). Factor i(n).
-(4*n - 1)*(7*n - 2)
Let u be -2*(1/1 + -3). Suppose -7*y = -9*y + u. Find p, given that 2/3*p**y + 8/3 + 8/3*p = 0.
-2
Let t(b) = -b + 6. Let u be t(5). Let z(s) = -u + 2*s + 0 + s**2 - s. Let g(k) = 4*k**2 + 2*k - 2. Let d(f) = g(f) - 2*z(f). Suppose d(v) = 0. Calculate v.
0
Let m(v) be the third derivative of -v**5/450 - v**4/60 + 14*v**2. Factor m(d).
-2*d*(d + 3)/15
Let o(x) be the first derivative of x**7/3780 - x**5/540 + x**3/3 - 1. Let i(p) be the third derivative of o(p). Suppose i(z) = 0. What is z?
-1, 0, 1
Let w be (1 - 2)/((-2)/8). Factor -w*k**2 - 2 + 6 - k + 2*k**3 - k.
2*(k - 2)*(k - 1)*(k + 1)
Suppose -10/13 + 2/13*r**2 + 8/13*r = 0. Calculate r.
-5, 1
Let z(n) = 72*n**3 + 48*n**2 + 9*n. Let u(q) = -9*q**3 - 6*q**2 - q. Let w(i) = 33*u(i) + 4*z(i). Factor w(t).
-3*t*(t + 1)*(3*t - 1)
Let i = -6760/7 + 966. Suppose -i*t + 2/7*t**2 + 0 = 0. Calculate t.
0, 1
Let f = 4/107 + -21/3424. Let v(u) be the third derivative of 0 + u**2 + 0*u + 1/12*u**3 + 1/240*u**5 + f*u**4. Determine p, given that v(p) = 0.
-2, -1
Factor -8*m**3 - 8*m + 58*m**2 - 14*m**4 - 27*m**2 - 29*m**2 + 28*m**3.
-2*m*(m - 1)**2*(7*m + 4)
Let w(b) be the first derivative of b**4/16 + b**3/6 + 19. Let w(z) = 0. What is z?
-2, 0
Let t = -201 - -201. Factor 0*v - 1/6*v**5 + 0 + 0*v**2 + t*v**4 + 1/6*v**3.
-v**3*(v - 1)*(v + 1)/6
Let i(z) be the first derivative of -z**4/4 - 5*z**3/3 + 27. Factor i(r).
-r**2*(r + 5)
Let s = 5 + -2. Factor 84*n**4 + s*n**3 - 81*n**4 + 0*n**3.
3*n**3*(n + 1)
Suppose 5 - 1 = -4*o, -o - 4 = -a. Determine u so that -4/5*u**2 + 0*u - 2/5*u**a + 0 = 0.
-2, 0
Let y = 174 + -1564/9. Let r = 2 - 2. Factor r*g**3 + y*g**4 + 0*g - 2/9*g**2 + 0.
2*g**2*(g - 1)*(g + 1)/9
Let d(y) be the second derivative of y**4 + 0 + 3/5*y**5 + 2/3*y**3 + 0*y**2 - 5*y + 2/15*y**6. Factor d(z).
4*z*(z + 1)**3
Factor 0*w**2 + 0*w**4 - 6/5*w**3 + 3/5*w + 0 + 3/5*w**5.
3*w*(w - 1)**2*(w + 1)**2/5
Let q be (4 - 4)*(-2)/(-6). What is a in 2*a**2 - 2*a - 4 + 0*a + q*a**2 = 0?
-1, 2
Let i(v) be the second derivative of v**6/15 - 3*v**5/10 + v**4/2 - v**3/3 - 4*v. Factor i(u).
2*u*(u - 1)**3
Let z = -3 + 2. Let q be z/(3/(-12)) + 0. Find y such that -y + y**2 - q + 4 = 0.
0, 1
Let q = -6 - -10. Suppose -q*z - 10 = -l - 0*z, -2*z = 5*l - 50. Factor -u**5 + 4*u**3 - u**5 - 4*u**5 + u + 8*u**4 - l*u**2 + u**5 + 2.
-(u - 1)**3*(u + 1)*(5*u + 2)
Let h be 123/63 - -1 - 0. Let t = h + -16/7. Factor 1/3*f**4 - t*f**2 + 0*f + 1/3 + 0*f**3.
(f - 1)**2*(f + 1)**2/3
Let b = -85/2 - -43. Find o, given that -b*o**3 + 1/2*o - 1 + o**2 = 0.
-1, 1, 2
What is d in 24 - 8*d + 2/3*d**2 = 0?
6
Let r(u) = u**5 - 2*u**4 + 2*u**3 - u + 2. Let s(j) = 6*j**5 - 11*j**4 + 10*j**3 - 5*j + 11. Let h = -10 + 21. Let m(t) = h*r(t) - 2*s(t). Solve m(c) = 0 for c.
-1, 0, 1
Let i(z) be the second derivative of 10*z**7/21 - 59*z**6/6 + 285*z**5/4 - 2125*z**4/12 - 625*z**3/6 - 3*z + 11. Factor i(l).
5*l*(l - 5)**3*(4*l + 1)
Let y(i) = -i**3 + i**2 + i - 9. Let j be y(0). Let p be (-3)/j + 0/1. Determine l, given that l**2 - p*l**3 - 4/3 + 0*l = 0.
-1, 2
Let z(c) be the third derivative of -c**8/840 - c**7/140 - c**6/180 + c**5/20 + c**4/6 + c**3/3 - 3*c**2. Let x(k) be the first derivative of z(k). Factor x(q).
-2*(q - 1)*(q + 1)**2*(q + 2)
Find a, given that 28*a - 35*a + 5*a**2 + 10 + 22*a = 0.
-2, -1
Let k be (2 - (-15)/(-5))*(-1 - 1). Factor -2/5*s**k + 2/5 + 0*s.
-2*(s - 1)*(s + 1)/5
Let o(c) = c**2 - 5*c + 6. Let l(f) = -f**2 + 4*f + 4. Let w be l(4). Let a be o(w). Solve 2/3*d**a - 4/3*d + 0 = 0 for d.
0, 2
Let r(n) be the third derivative of 1/112*n**8 + 1/40*n**6 + 0 - 1/35*n**7 + 4*n**2 + 0*n**4 + 0*n**5 + 0*n**3 + 0*n. Factor r(l).
3*l**3*(l - 1)**2
Let q(i) be the first derivative of i**5/20 + i**4/6 + i**3/6 - 2*i + 2. Let h(m) be the first derivative of q(m). Factor h(