b - 3)*(b - 2)
Let r = 16928/5 + -3399. Let v = r + 479/35. Factor 6/7*d**3 + 8/7 - 16/7*d + v*d**2.
2*(d - 1)*(d + 2)*(3*d - 2)/7
Let o(n) be the third derivative of -n**5/20 + 23*n**4/8 + 25*n**3 + 487*n**2 + 1. Determine u so that o(u) = 0.
-2, 25
Suppose -c = -5*u + 3*u - 2, -2*u - 4*c = 12. Let x be u/(-4) + 3/(-6). Let -1/2*r**2 + 1/2*r + 1/2*r**4 - 1/2*r**3 + x = 0. What is r?
-1, 0, 1
Let d(p) = -4*p**4 + 88*p**3 + 120*p**2 + 80*p + 52. Let a(m) = -m**4 - m**2 - m + 1. Let j(n) = -24*a(n) + d(n). Find q such that j(q) = 0.
-7/5, -1
Factor 1360/9*o**2 - 2888 - 12692/3*o - 4/3*o**3.
-4*(o - 57)**2*(3*o + 2)/9
Let v = -402 - -405. Let l(x) be the third derivative of 0 + v*x**2 + 0*x + 0*x**4 + 1/3*x**3 - 1/30*x**5. Solve l(b) = 0.
-1, 1
Let g be (-32)/(-10) - (2 - (-12 - -11)). Let 4/5*w + 0 - g*w**2 = 0. What is w?
0, 4
Let f be 24*((-32)/(-12) + 0). Solve -f*t**2 - 80*t + 26*t**2 + 33*t**2 - 320 = 0.
-8
Let i(h) be the first derivative of -h**6/21 - 4*h**5/35 + 3*h**4/14 + 8*h**3/21 - 4*h**2/7 - 46. Determine f, given that i(f) = 0.
-2, 0, 1
Let m(r) be the second derivative of 0 - 1/3*r**3 - 1/6*r**4 + 3*r + 0*r**2. Suppose m(j) = 0. What is j?
-1, 0
Let x(o) be the third derivative of o**6/280 + 87*o**5/140 + 2523*o**4/56 + 24389*o**3/14 - 44*o**2 - 1. Factor x(a).
3*(a + 29)**3/7
Let y(m) be the first derivative of 21 - 27/5*m**5 - 9/5*m**4 + 0*m + 7/5*m**3 + 3/5*m**2. Solve y(n) = 0.
-1/3, 0, 2/5
Factor 416*z**2 - 223*z**2 + 255*z - 203*z**2 - 100 - 25.
-5*(z - 25)*(2*z - 1)
Let n be 10/(-12) - (-43)/(2580/200). Solve -n*h**3 - 2 + 2*h + 5/2*h**2 + 1/2*h**5 - 1/2*h**4 = 0.
-2, -1, 1, 2
Solve 56/5*v**2 - 32/5*v**3 + 9/5*v**4 - 1/5*v**5 + 16/5 - 48/5*v = 0 for v.
1, 2
Let p = 44731 + -44728. Factor -8/5*w**2 + 2/5*w**p - 24/5*w + 0.
2*w*(w - 6)*(w + 2)/5
Let u(d) be the third derivative of d**7/5040 - d**6/4320 + 19*d**4/24 - 10*d**2. Let h(t) be the second derivative of u(t). Factor h(b).
b*(3*b - 1)/6
Let i(x) = -x**2 + 4*x + 4. Let a be i(3). Suppose a*s + 0*s = 14. Factor -12*b + b**2 + 3*b**s + 4 + 20*b.
4*(b + 1)**2
Let t be 5 - (3 - (-20)/10). Let y(r) be the second derivative of -1/21*r**4 - 2*r - 1/70*r**5 - 1/21*r**3 + 0 + t*r**2. Factor y(i).
-2*i*(i + 1)**2/7
Suppose 36 = 3*c + 27. Factor -79*n**3 + 5*n**2 - 5*n**4 + 3*n + 2*n + 74*n**c.
-5*n*(n - 1)*(n + 1)**2
Factor -11/4*x**3 + 13/4*x**2 - 1/4*x**4 + 11/4*x - 3.
-(x - 1)**2*(x + 1)*(x + 12)/4
Let 24*m - 5*m**3 - 5*m**4 - 4*m + 10*m**2 + 10*m**2 = 0. Calculate m.
-2, -1, 0, 2
Let p(j) = -j**2 + 22*j - 19. Let l be p(21). Factor 180*o**l - 179*o**2 + 0*o + 2*o.
o*(o + 2)
Let c(j) be the second derivative of j**4/6 - 7*j**3/3 - 8*j**2 - 305*j + 1. Factor c(o).
2*(o - 8)*(o + 1)
Let y = -117 + 120. Suppose 12 = f + 2*i, 7*i - 2*i - 19 = y*f. Solve 2/11*z**3 + 6/11*z + 2/11 + 6/11*z**f = 0.
-1
Factor 8*v + 24 + 10*v - 4*v**3 + 2*v**3 + 2*v + 2*v**2 + v**3.
-(v - 6)*(v + 2)**2
Let r(s) be the third derivative of -5*s**6/32 - 17*s**5/120 - s**4/32 - 363*s**2. Let r(z) = 0. What is z?
-1/3, -3/25, 0
Let p(t) be the first derivative of -t**4/4 - t**3 + 19*t - 13. Let u(q) be the first derivative of p(q). Factor u(s).
-3*s*(s + 2)
Let t(s) be the third derivative of 0 - 4/9*s**3 + 0*s - 99/35*s**7 - 53/10*s**6 + 40*s**2 - 16/9*s**4 - 25/6*s**5. Solve t(g) = 0.
-1/3, -2/9, -2/11
Let h(a) be the third derivative of -1/21*a**4 - 17*a**2 + 0 - 1/210*a**5 + 0*a - 4/21*a**3. Factor h(s).
-2*(s + 2)**2/7
Let y(d) = 21*d**2 - 5*d - 6. Let j be y(-3). Solve 198 + r**2 - j - r**3 = 0.
0, 1
Determine x, given that -18/5*x + 14/5*x**2 + 0 = 0.
0, 9/7
Suppose 0 = 23*z - 18*z - 855. Find y, given that 5*y**3 - z*y**2 + 199*y**2 + 3*y**3 - 12 + 0 + 8*y = 0.
-3, -1, 1/2
Let s(k) = -4*k**2 + 6*k - 2. Let p be (-1102)/95 - 3/(-5). Let z = p - -8. Let m(x) = 4*x**2 - 5*x + 1. Let w(r) = z*s(r) - 2*m(r). Factor w(h).
4*(h - 1)**2
Let d = 49766 + -49764. Let 12/7 - 3/7*x**d + 9/7*x = 0. Calculate x.
-1, 4
Factor -14*q**5 - 9*q**3 + 38*q**2 - 12*q**4 + 17*q**5 + 24*q - 8*q**2.
3*q*(q - 4)*(q - 2)*(q + 1)**2
Determine d so that -22/5*d**2 + 24/5*d + 14/5*d**4 - 24/5*d**3 + 8/5 = 0.
-1, -2/7, 1, 2
Factor 466/7*m + 132/7 + 2*m**2.
2*(m + 33)*(7*m + 2)/7
Let s be (-2 + 24/9)*(1 - -5). Suppose s*l - 7 - 1 = 0. Factor 0 + 1/3*n**l - n.
n*(n - 3)/3
Let p(w) = -17*w**3 + w**2 + w + 1. Let o be p(-1). Solve 15*u**2 - 4*u**2 + o*u + 15 - 8*u**2 = 0.
-5, -1
Let g(y) = y**3 - 38*y**2 + 314*y - 48. Let l be g(26). Let 3*f + 45/2*f**2 + 0 + 99/2*f**3 + 27/2*f**5 + 87/2*f**l = 0. Calculate f.
-1, -2/9, 0
Let x(l) be the second derivative of 3*l**5/10 + 13*l**4/4 + 5*l**3/2 - 9*l**2 + 3*l + 1. Suppose x(k) = 0. Calculate k.
-6, -1, 1/2
Let s(x) be the second derivative of -x**4/90 + x**3/15 - 2*x**2/15 - 37*x. Factor s(g).
-2*(g - 2)*(g - 1)/15
Let j = 25 + -20. Let l(a) = 3*a**2 - 3*a - 2. Let o(b) = -b - 1. Let h(q) = j*l(q) - 10*o(q). Find c, given that h(c) = 0.
0, 1/3
Let s(l) = 4*l**2 + 2*l + 1. Let p be s(-1). Let 4 - 3*a - p*a - 8*a**3 + 14*a - 4*a**4 = 0. What is a?
-1, 1
Let g(n) be the third derivative of 3*n**8/112 + 8*n**7/35 + 3*n**6/5 + 3*n**5/10 - 11*n**4/8 - 3*n**3 - 115*n**2. Solve g(r) = 0.
-3, -1, 2/3
Factor 110*g**3 + 8 + 120*g - 145*g**2 - 65*g**3 - 28.
5*(g - 2)*(g - 1)*(9*g - 2)
Let y(o) be the third derivative of -5/336*o**8 - 14*o**2 + 0 + 0*o - 1/21*o**7 + 0*o**4 + 0*o**3 - 1/24*o**6 + 0*o**5. Factor y(u).
-5*u**3*(u + 1)**2
Let y(f) = -5*f**2 - 5*f + 5. Let m(a) = -7*a**2 - 8*a + 8. Let r = -21 + 13. Let s(k) = r*y(k) + 5*m(k). Factor s(t).
5*t**2
Suppose 54*s + 56 = 58*s. Let g be 4/(-14) + 60/s. Factor -2/9*q**g + 0*q - 2/9 + 4/9*q**2 + 0*q**3.
-2*(q - 1)**2*(q + 1)**2/9
Let f be 70/(-120) + (-3)/4 - 700/(-140). Factor -2*v**2 - 2 - 1/3*v**3 - f*v.
-(v + 1)*(v + 2)*(v + 3)/3
Let d(n) be the first derivative of -n**3/12 - 81. Factor d(g).
-g**2/4
Let l(v) be the first derivative of 2*v**5/15 - v**4/2 - 10*v**3/9 + v**2 + 8*v/3 - 315. Factor l(c).
2*(c - 4)*(c - 1)*(c + 1)**2/3
Let x(l) = -3*l**3 + 12*l**2 - 50*l + 62. Let s(b) = -b**3 - b - 1. Let f(m) = -2*s(m) + x(m). Factor f(o).
-(o - 4)**3
Let v(t) = -t**2 + 12*t + 47. Let m be v(-3). Let 2/3*g**m + 2/3*g + 0 = 0. What is g?
-1, 0
Suppose 0 = 3*m - 3*a - 21, m - 13 = -2*m + a. Suppose -m*z = z. Suppose -98/5*u**3 + 8/5*u + 0 + z*u**2 = 0. What is u?
-2/7, 0, 2/7
Solve 3/2*b**3 - 3/4*b - 12 + 24*b**2 - 3/4*b**5 - 12*b**4 = 0 for b.
-16, -1, 1
Let w(f) = 2*f**4 - f**3 - f**2 + 2*f - 1. Let b(g) = -5*g**4 + 60*g**3 + 200*g**2 + 235*g + 105. Let r(z) = b(z) + 5*w(z). Suppose r(x) = 0. Calculate x.
-5, -4, -1
Suppose -23*o = 122 - 214. Let g(y) be the second derivative of -5*y - 1/10*y**5 + 1/3*y**3 + 1/6*y**o - y**2 + 0. Suppose g(d) = 0. What is d?
-1, 1
Let h(n) be the third derivative of -n**6/360 - n**5/40 + n**4/6 - 17*n**3/6 + 43*n**2. Let l(r) be the first derivative of h(r). Factor l(x).
-(x - 1)*(x + 4)
Let p(r) be the first derivative of 0*r + 7 + 3/7*r**3 - 6/7*r**2 + 3/28*r**4. Factor p(x).
3*x*(x - 1)*(x + 4)/7
Let z be 16 - -5 - (-3 + 2). Let r = -14 + z. Factor -33*l**3 + 11*l**3 - l**2 + r*l**3 - l**4 + 12*l**3.
-l**2*(l + 1)**2
Let c(k) = -4*k**3 + k**2 - k - 1. Let i(r) = -39*r**3 + 105*r**2 - 6*r - 105. Let f(z) = -9*c(z) + i(z). Find h, given that f(h) = 0.
-1, 1, 32
Suppose -4/11 - 1/11*v**2 - 5/11*v = 0. Calculate v.
-4, -1
Let o = 237 + 15. Let i = o - 250. Solve 2/5 + 0*m - 2/5*m**i = 0 for m.
-1, 1
Let y(n) = -n**3 - n**2 + 2*n. Suppose 13 = -3*l + 4. Let c be y(l). Factor 7*a**3 - c*a**2 - 3*a**3 + 8*a + 4*a - 4.
4*(a - 1)**3
Let q(g) be the third derivative of g**5/150 + 2*g**4/5 - 5*g**3/3 - 47*g**2. Factor q(k).
2*(k - 1)*(k + 25)/5
Let b(w) = w**4 - w**3 + w**2 + w. Let c(u) = -12*u**4 + 54*u**3 - 33*u**2 - 3*u. Let s(x) = 3*b(x) + c(x). Factor s(p).
-3*p**2*(p - 5)*(3*p - 2)
Suppose 3*v + 51 = 3*q - 2*v, -12 = -4*v. Suppose -17*u + q*u = 0. Solve u + 0*l**2 + 3/5*l**3 - 3/5*l = 0.
-1, 0, 1
Let s(j) = -2*j**2 + 18*j - 22. Let y be s(7). Suppose -2*v + 7*a = 9*a - y, -2*v - 3*a = -7. Find n, given that -25*n - 125/2 - 5/2*n**v = 0.
-5
Factor -10*w**4 + 1 + 1 + 4*w**3 + 20*w**4 - 4*w - 12*w**4.
-2*(w - 1)**3*(w + 1)
Let l be (-4)/26 + 2159/1105 - 1. Factor 8/5*g - 4/5*g**2 - l.
-4*(g - 1)**2/5
Let x(s) be