**5 + 34*u**4 - 46/7*u**2 + 8/7 + 134/7*u**3 - 32/7*u.
2*(u + 1)**3*(7*u - 2)**2/7
Factor -157/7*x**2 - 4/7 - 198/7*x**3 - 44/7*x - 81/7*x**4.
-(x + 1)**2*(9*x + 2)**2/7
Factor 4*x**2 - 10*x**2 - 9*x**5 - 6*x**2 + 32*x**3 - 15*x**4.
-x**2*(x + 3)*(3*x - 2)**2
Suppose 2*u = r - 7, -4*r + 12 = 2*u - 6*u. Let g = u + 6. Solve 0*h + 4*h - 2*h - g*h**3 = 0 for h.
-1, 0, 1
Let j(q) be the third derivative of q**5/570 + q**4/76 + 2*q**3/57 - 16*q**2 + q. Determine m, given that j(m) = 0.
-2, -1
Let n be 0 + (-4 - -3)/(-1). Let k(p) = 4*p**3 - 2*p**2 - 2*p - 6. Let o(l) = -l**3 + l**2 + 1. Let s(q) = n*k(q) + 6*o(q). Factor s(a).
-2*a*(a - 1)**2
Let u(k) = 16*k**2 - 67*k - 147. Let j(h) = -7*h**2 + 34*h + 74. Let t(a) = 13*j(a) + 6*u(a). Factor t(l).
5*(l + 4)**2
Let g(x) = 11*x + 398. Let m be g(-36). Let -24/7*q**3 + 2/7 + 0*q - 26/7*q**m = 0. What is q?
-1, -1/3, 1/4
Let i = -60 + 64. Factor -2/7*a**i + 0 + 0*a + 2/7*a**3 + 4/7*a**2.
-2*a**2*(a - 2)*(a + 1)/7
Let r be 54/(20/(-4) - -10). Find v such that r*v**4 - 4*v**2 + 14/5*v - 2/5 - 36/5*v**3 + 54/5*v**5 = 0.
-1, 1/3
Let z(o) be the second derivative of o**8/8400 + o**7/2100 + o**6/1800 + o**3/6 + 7*o. Let q(t) be the second derivative of z(t). Factor q(b).
b**2*(b + 1)**2/5
Let y(v) be the third derivative of 0*v - 3*v**2 + 0 + 1/15*v**5 + 0*v**4 - 2/3*v**3. Factor y(q).
4*(q - 1)*(q + 1)
Suppose 0 = 4*i - 7 - 13. Suppose 0 = -2*s - 3*w + 11, 1 = -w + 2. Determine y so that s*y**2 + y - i*y**3 - 8*y**4 - y**2 - y**3 = 0.
-1, -1/4, 0, 1/2
Let d(p) be the first derivative of p**6/2 + 6*p**5/5 - 15*p**4/4 - 6*p**3 - 14. Factor d(z).
3*z**2*(z - 2)*(z + 1)*(z + 3)
Let k(n) be the second derivative of -3/2*n**2 + 0*n**3 + n + 0 - 1/30*n**5 + 1/12*n**4. Let f(j) be the first derivative of k(j). Determine s so that f(s) = 0.
0, 1
Find j, given that -20/3 + 35/3*j**2 + 80/3*j - 215/3*j**3 - 15*j**5 - 65*j**4 = 0.
-2, -1, 1/3
Suppose 3 = -3*h - 4*w - 2, -4*w + 16 = -4*h. Let o be (1 - h) + 14/(-4). Suppose -o + q - 1/2*q**2 = 0. What is q?
1
Suppose 0 = 4*z - 8, o - 3*z + 4 = 1. Factor -1 - 2*a**2 + a**2 + o*a - 1.
-(a - 2)*(a - 1)
Let t(d) = 3*d - 6*d - 3*d + 8 - 8*d**2. Let w(n) = 15*n**2 + 11*n - 15. Let p(s) = 11*t(s) + 6*w(s). Factor p(q).
2*(q - 1)*(q + 1)
Let m(s) = -22*s**3 - 15*s**2 + 82*s - 38. Let t(c) = 7*c**3 + 5*c**2 - 27*c + 13. Let j(a) = -2*m(a) - 7*t(a). Factor j(d).
-5*(d - 1)**2*(d + 3)
Suppose -1 = -g + o, 5*o - o = 12. Suppose -2*t + g*t - 8 = 0. Determine c so that -3*c**5 + 4/3*c**2 + 8/3*c**3 + 0 + 0*c - c**t = 0.
-2/3, 0, 1
Let l(w) be the second derivative of -w**6/120 + 3*w**5/80 - w**4/48 - w**3/8 + w**2/4 - 34*w. Solve l(k) = 0 for k.
-1, 1, 2
Let v(j) be the second derivative of 1/3*j**3 - 1/12*j**4 - 1/2*j**2 - 2*j + 0. Let v(h) = 0. What is h?
1
Let l be (8/(-6))/(4/(-12)). Solve b**5 + 6*b**4 + 5*b**l - 7*b**4 + 4*b**3 = 0.
-2, 0
Let f be (-43)/(-14) + 0 - 3. Let n(c) be the first derivative of 2 + 0*c + 1/7*c**2 - f*c**4 - 2/21*c**3 + 2/35*c**5. Factor n(i).
2*i*(i - 1)**2*(i + 1)/7
Let d be ((-16)/(-12))/(3/2). Let s = 91 + -817/9. Factor 2/3*y**2 + s + d*y.
2*(y + 1)*(3*y + 1)/9
Let 3/8*c**4 - 3/8*c**2 + 0*c**3 + 0*c + 0 = 0. Calculate c.
-1, 0, 1
Let f(w) = w**3 - w. Let x(m) = 4*m**4 + 12*m**3 - 16*m**2 - 36*m. Let d(i) = -4*f(i) + x(i). Determine q, given that d(q) = 0.
-2, 0, 2
Let y(n) be the first derivative of n**4/14 + 2*n**3/21 - 16*n**2/7 + 40*n/7 - 25. Factor y(p).
2*(p - 2)**2*(p + 5)/7
Let i(j) be the first derivative of j**6/2 + 3*j**5 + 15*j**4/2 + 10*j**3 + 15*j**2/2 + 3*j + 26. Suppose i(o) = 0. Calculate o.
-1
Let l = -117 + 587/5. Let x be (-11)/(-3) - 2/3. Factor 2/5*j**4 - l*j**x + 0 + 0*j**2 + 0*j.
2*j**3*(j - 1)/5
Let a be (-4)/20 + (-26)/(-5). What is n in -2*n**2 + 6*n**3 - 2 - 3*n + a*n + 12*n**2 = 0?
-1, 1/3
Suppose -3*o + 7*o + 16 = 0. Let a = o + 7. What is z in 0*z**a + 16 + z**3 + 12*z**2 + z**3 + 24*z = 0?
-2
Let r(d) be the first derivative of 0*d - 1/33*d**6 + 6 - 4/11*d**2 + 3/22*d**4 - 4/55*d**5 + 8/33*d**3. Determine h, given that r(h) = 0.
-2, 0, 1
Let z(v) = 3*v - 1. Suppose 0*u + u = -4, -5*o - 4*u = 11. Let g be z(o). Suppose 0 - 12/5*w**5 - 9*w**3 - 39/5*w**4 - 3/5*w - 21/5*w**g = 0. What is w?
-1, -1/4, 0
Let y(w) = w**3 + w**2 + w - 1. Let v(m) = 16*m**3 - 9*m**2 - 4*m + 4. Let l(p) = -v(p) - 4*y(p). Find c, given that l(c) = 0.
0, 1/4
Let j be (-739)/(-228) + (-6)/8. Let t = j + 16/19. Determine o so that 2/3 + 2/3*o**5 + 10/3*o**4 + 20/3*o**3 + 20/3*o**2 + t*o = 0.
-1
Find q such that -4225*q**2 - 15*q**5 - 5*q**3 + 20*q**4 + 4225*q**2 = 0.
0, 1/3, 1
Let v(p) be the first derivative of -p**3/24 + 3*p**2/8 - 9*p/8 - 7. Solve v(w) = 0 for w.
3
Let r = 157 + -155. Let b(p) be the first derivative of -2*p**r - 2/3*p**3 - 2 - 2*p. Factor b(g).
-2*(g + 1)**2
Suppose 48/5*z**3 - 3/5*z + 0 - 48/5*z**4 + 3/5*z**2 = 0. What is z?
-1/4, 0, 1/4, 1
Let l(a) = -a**4 - a + 1. Let p(b) = 3*b**5 - 18*b**4 + 58*b**3 - 50*b**2 + 8*b + 4. Let m(k) = -5*l(k) - p(k). Determine i, given that m(i) = 0.
-1/3, 1, 3
Determine s, given that 48*s - 169*s**3 + 24*s**2 - 84*s**2 - 57*s**2 - 4 = 0.
-1, 2/13
Let u be -2 + (5 - (-34)/(-18)). Determine t so that -20/9*t**3 + 10/9*t**5 + 4/9*t**4 + u*t + 4/9 - 8/9*t**2 = 0.
-1, -2/5, 1
Let z(d) be the second derivative of d**5/20 - d**4/6 + d**3/6 - 2*d. Let p be z(2). Factor -1/2*u**p + 0 + 0*u.
-u**2/2
Let t(d) = d**2 + 4*d - 32. Let o be t(-8). Let h(v) be the third derivative of 0*v + 1/6*v**4 - 1/3*v**3 + o - v**2 + 1/10*v**5. Let h(f) = 0. Calculate f.
-1, 1/3
Solve -2*x**3 + 2*x**2 - 4*x + 0*x**3 + 8*x = 0.
-1, 0, 2
Let d = 12 - 10. Suppose 1/4*u**d + 0*u - 1/4 = 0. What is u?
-1, 1
Let p be 2*(-2 + (-29)/(-11)). Let i be (2/(2/(-3)))/((-77)/42). Determine q, given that -i*q + 4/11 + p*q**2 = 0.
2/7, 1
Let l = 681/16 + -85/2. Let b(h) be the second derivative of 1/24*h**3 + l*h**4 + 0 + 0*h**2 - h. Let b(c) = 0. Calculate c.
-1/3, 0
Let g(r) be the third derivative of -r**7/1680 - r**6/360 - r**3/3 - 2*r**2. Let b(p) be the first derivative of g(p). Let b(i) = 0. Calculate i.
-2, 0
Let x(a) be the second derivative of 0 - 1/54*a**4 + 0*a**3 + 4/135*a**6 + a + 1/30*a**5 + 0*a**2. Find r such that x(r) = 0.
-1, 0, 1/4
Let q = -22 + 25. Factor 3/2*a**q + 0 + 3*a + 9/2*a**2.
3*a*(a + 1)*(a + 2)/2
Determine i, given that 0 + 2/7*i**3 + 10/7*i**2 - 2/7*i**4 + 6/7*i = 0.
-1, 0, 3
Let z(u) be the first derivative of -u**6/2 + 3*u**4/4 - 12. Factor z(r).
-3*r**3*(r - 1)*(r + 1)
Suppose 0 = -251*a + 259*a - 96. Factor a*y**2 - 21/2*y - 9/2*y**3 + 3.
-3*(y - 1)**2*(3*y - 2)/2
Let l(i) be the third derivative of 0*i**3 + 0 + 3*i**2 + 0*i - 1/630*i**7 + 0*i**4 - 1/360*i**6 + 0*i**5. Determine r, given that l(r) = 0.
-1, 0
Let c be (-4)/(-16) - (-3 - 33/(-20)). Factor 6/5*o + 0*o**4 - 4/5*o**2 + 2/5*o**5 - c*o**3 + 4/5.
2*(o - 2)*(o - 1)*(o + 1)**3/5
Let f(o) = 13*o - 62. Let g be f(5). Determine k, given that 0 - 2/13*k**2 + 0*k + 2/13*k**g = 0.
0, 1
Suppose -2/9*p**2 - 2/9*p**3 + 0 + 0*p = 0. What is p?
-1, 0
Let p(b) be the first derivative of 4*b**5/15 + 5*b**4/12 - b**3/3 - 5*b**2/6 - b/3 - 31. Factor p(q).
(q - 1)*(q + 1)**2*(4*q + 1)/3
Find h, given that -1/3 - 2*h**2 - 1/3*h**4 - 4/3*h**3 - 4/3*h = 0.
-1
Let u(p) be the third derivative of p**6/15 - p**5/5 - p**4/3 + 29*p**2. Suppose u(a) = 0. Calculate a.
-1/2, 0, 2
Let o(q) be the first derivative of 3*q**5/5 - 9*q**4/4 + q**3 + 9*q**2/2 - 6*q + 11. Factor o(k).
3*(k - 2)*(k - 1)**2*(k + 1)
Let q = -949 + 1901/2. Factor q*i - 3/2*i**2 + 0.
-3*i*(i - 1)/2
Let u(r) = -r**2 + r - 4. Let v be u(0). Let o be (v/(-1))/1 + -1. Factor -x**o - 1/3*x**2 - x**4 - 1/3*x**5 + 0 + 0*x.
-x**2*(x + 1)**3/3
Let k(m) be the third derivative of -m**6/6 - m**5/12 - 17*m**2. Solve k(r) = 0.
-1/4, 0
Let x = -2 - -4. Let u = 41/148 - 1/37. Factor -1/2*q**x + 1/2*q**4 - 1/4*q**5 + 0 + 0*q**3 + u*q.
-q*(q - 1)**3*(q + 1)/4
Let b be 4/(-6)*(-3)/6*1. Find r, given that -b*r**4 + 0*r + 1/3*r**2 + 1/3*r**5 - 1/3*r**3 + 0 = 0.
-1, 0, 1
Let k(s) = 3*s**2 - 3*s + 2. Let z(w) = 4*w**2 - 4*w + 2. Let m(y) = 5*k(y) - 4*z(y). Find l such that m(l) = 0.
-1, 2
Let w be 5*(-56)/(-30)*-3. Let p be (-21)/w*(-2)/(-3). Factor -1/2*t**2 + 1 - p*t.
-(t - 1)*(t + 2)/2
Let v(f) be the third der