
Let j(k) be the first derivative of -12 + 0*k**2 - 1/4*k**3 - 1/16*k**4 + 0*k. Factor j(t).
-t**2*(t + 3)/4
Let t(k) be the second derivative of -k**4/6 - 101*k**3/9 - 22*k**2 - 2*k + 7. Determine o so that t(o) = 0.
-33, -2/3
Let g = 8 + -6. Let k be -3*(1 + 0 - g). Factor -2*a**k + 5*a - a - 2*a.
-2*a*(a - 1)*(a + 1)
Solve -36/7 + 264/7*s - 39/7*s**3 - 27*s**2 = 0 for s.
-6, 2/13, 1
Let p = 2930 + -14648/5. Find b such that b**2 + 2/5*b - p*b**4 + 1/5*b**3 + 0 = 0.
-1, -1/2, 0, 2
Let z(c) be the first derivative of -3*c**4/4 + 153*c**3 - 23409*c**2/2 + 397953*c - 290. Suppose z(j) = 0. What is j?
51
Let 5/4*g + 9/4*g**2 - 1 = 0. Calculate g.
-1, 4/9
Let u(x) = -17*x**4 - 12*x**3 + x**2 - 17*x - 13. Let q(i) = 4*i**4 + 3*i**3 + 4*i + 3. Let g be -1 + 1 + (7 - 13). Let s(p) = g*u(p) - 26*q(p). Factor s(m).
-2*m*(m + 1)**3
Suppose -g + 7 = a, 0*g = 4*g - 4*a - 4. Let q = 6642 - 6642. Factor 2/9*k + q - 2/9*k**2 - 2/9*k**3 + 2/9*k**g.
2*k*(k - 1)**2*(k + 1)/9
Let q = -44 - -104. Suppose 72 - q = 4*s. Factor 2/7*l**2 + 0 + 2/7*l**s + 0*l.
2*l**2*(l + 1)/7
Let k(v) be the first derivative of -2*v**3/69 - 4*v**2/23 - 6*v/23 - 181. Solve k(s) = 0 for s.
-3, -1
Let g = 20 + -20. Suppose 520*z + 3 = 521*z. Factor g + 0*i + 0*i**2 - 2/3*i**z + 2/3*i**4.
2*i**3*(i - 1)/3
Let i(h) be the second derivative of -h**6/120 - h**5/80 + h**4/16 + 5*h**3/24 + h**2/4 - 6*h - 1. Factor i(x).
-(x - 2)*(x + 1)**3/4
Let y(u) be the third derivative of u**7/1260 + u**6/240 - 7*u**5/360 - 5*u**4/48 + u**3/2 - 819*u**2. Factor y(f).
(f - 2)*(f - 1)*(f + 3)**2/6
Let j = -12 + 15. Factor -3 + 3*g**3 + 3*g - 5*g + g + j*g**2 - 2*g.
3*(g - 1)*(g + 1)**2
Let a be (-10)/(-55) - 4/22. Factor -5*r + 5/2*r**4 + a*r**2 + 5*r**3 - 5/2.
5*(r - 1)*(r + 1)**3/2
Let p(o) be the second derivative of o**7/42 + 2*o**6/15 + 3*o**5/20 - 170*o. Solve p(m) = 0.
-3, -1, 0
Factor -16*h**4 - 20*h**4 - 4*h**3 + 31*h**4 + 14*h**3.
-5*h**3*(h - 2)
Let g = -11889 + 11889. Factor 1/2*i + g + 2*i**2 + 2*i**4 + 1/2*i**5 + 3*i**3.
i*(i + 1)**4/2
Let k(j) be the second derivative of -j**5/110 - 7*j**4/66 - 14*j**3/33 - 8*j**2/11 + 538*j. Let k(b) = 0. Calculate b.
-4, -2, -1
Find a such that -9/2 - 1/8*a**4 + 5/4*a**3 + 15/2*a - 37/8*a**2 = 0.
2, 3
Suppose 9*k + 1 + 44 = 0. Let w be 9*3*k/(-45). Factor -3 + w*m**2 + 3/2*m - 3/2*m**3.
-3*(m - 2)*(m - 1)*(m + 1)/2
Let j(c) be the second derivative of c**7/120 - c**6/30 + c**5/40 + c**4/12 + c**3/2 + 26*c. Let g(h) be the second derivative of j(h). Factor g(z).
(z - 1)**2*(7*z + 2)
Let l(d) = d**2. Let j(p) = 5*p**3 - 21*p**4 - 4*p**3 + 3*p + 22*p**4 - 8*p**2. Let f(c) = -5*j(c) - 15*l(c). Factor f(a).
-5*a*(a - 1)**2*(a + 3)
Factor -27/5*z**3 - 3/5*z**4 - 24/5*z**2 + 0*z + 0.
-3*z**2*(z + 1)*(z + 8)/5
Let r(u) be the third derivative of u**5/420 + 19*u**4/168 + 10*u**3/7 - 17*u**2 + 10*u. Determine j, given that r(j) = 0.
-15, -4
Let s(l) be the third derivative of 0 - 2/525*l**7 + 2/75*l**5 + 1/150*l**6 + 0*l**3 + 0*l + 0*l**4 - 10*l**2. Suppose s(v) = 0. What is v?
-1, 0, 2
Let b(r) be the third derivative of r**5/40 + 13*r**4/8 - 14*r**3 - 180*r**2. Find j such that b(j) = 0.
-28, 2
Solve 33/5*h - 39/5*h**4 + 6/5 - 12/5*h**5 + 33/5*h**2 - 21/5*h**3 = 0.
-2, -1, -1/4, 1
Let u = -962 + 683. Let y be u/(-105) + -2 + 3/21. Find d, given that y*d**2 + 0 + 4/5*d + 3/5*d**5 - 4/5*d**4 - 7/5*d**3 = 0.
-1, -2/3, 0, 1, 2
Suppose 3*u - 1343 = 5*f, -2*u + 117 - 667 = 2*f. Let w = -269 - f. Factor 2/15*n**w - 2/15*n - 4/15.
2*(n - 2)*(n + 1)/15
Let w(u) be the third derivative of -u**6/60 - 2*u**5/15 + 5*u**4/12 - 6*u**2 + 16. Suppose w(b) = 0. Calculate b.
-5, 0, 1
Let w = 30865 + -30864. Factor 1/4*p**2 - w - 3/4*p.
(p - 4)*(p + 1)/4
Let z(f) be the third derivative of -f**6/360 - 11*f**5/180 - 5*f**4/36 - 105*f**2. Factor z(q).
-q*(q + 1)*(q + 10)/3
Solve g**2 + 75*g - 73*g + 176 - 3*g**2 + 4 = 0.
-9, 10
Let p = 2772 + -2769. Find i such that -2*i + 2/3 - 2/3*i**p + 2*i**2 = 0.
1
Let a = -217 - -261. Let d be a/56 + (-2)/(-4). Factor 6/7 + 15/7*f + d*f**2.
3*(f + 1)*(3*f + 2)/7
Let s(z) be the second derivative of 5*z**7/14 + 6*z**6/5 + 3*z**5/5 - 5*z**4/2 - 9*z**3/2 - 3*z**2 + 54*z. Factor s(n).
3*(n - 1)*(n + 1)**3*(5*n + 2)
Suppose 0 = -4*y + o + 15 - 9, -2*y = -o - 2. Factor -29/6*g**y - 2/3 + 4*g + 3/2*g**3.
(g - 2)*(g - 1)*(9*g - 2)/6
Suppose -20 = -5*g + 2*g - 4*i, -g - 4*i = -12. Let k = -69 + 71. Factor 3*f**3 + f**5 - 6*f**2 + 0*f**5 - f**g - k*f**4 + 5*f**2.
f**2*(f - 1)**3
Let g be (-70)/(-770) - 75/(-264). Factor g*p**2 + 3/8 - 3/4*p.
3*(p - 1)**2/8
Let b(q) = -12*q**4 + 48*q**3 - 12*q**2 - 104*q - 16. Let c(u) = -4*u**4 + 16*u**3 - 4*u**2 - 34*u - 5. Let o(n) = -5*b(n) + 16*c(n). Factor o(i).
-4*i*(i - 3)*(i - 2)*(i + 1)
Factor 1/2*f + 5/3 + 1/6*f**3 - f**2.
(f - 5)*(f - 2)*(f + 1)/6
Let s(z) = -z**2 + 21*z - 108. Let l(v) = v**2 + 3*v. Let x(d) = -6*l(d) - 2*s(d). Let x(i) = 0. Calculate i.
-18, 3
Let j(o) be the third derivative of -1/18*o**3 - 1/90*o**5 - 1/24*o**4 + 0*o + 1/180*o**6 + 1/1008*o**8 + 1/210*o**7 + 20*o**2 + 0. Solve j(v) = 0.
-1, 1
Let j(a) be the first derivative of 11 - 14/33*a**3 + 0*a - 2/11*a**2. Factor j(m).
-2*m*(7*m + 2)/11
Let m(d) = -7*d**2 - 9*d + 5. Suppose 0*j - 5*r - 4 = j, -r + 16 = 3*j. Let i(q) = 8*q**2 + 10*q - 6. Let v(f) = j*m(f) + 5*i(f). Factor v(l).
-2*l*(l + 2)
Let t(r) = -3*r - 11. Let y be t(-5). Suppose 0 = 4*n + y*n - 16. Factor -2*z**3 + 15*z**4 - n*z**3 + 2*z**3 - 10*z**5 - 3*z**3.
-5*z**3*(z - 1)*(2*z - 1)
Let g(s) be the second derivative of 5*s**7/42 + 4*s**6/3 - s**5/4 - 10*s**4/3 + 295*s. Let g(t) = 0. Calculate t.
-8, -1, 0, 1
Factor 27/2*t + 27/8*t**3 + 21/2*t**2 + 6 + 3/8*t**4.
3*(t + 1)*(t + 2)**2*(t + 4)/8
Let q(s) = 8*s**3 + 15*s**2 - 62*s + 55. Let g(z) = -13*z**3 - 22*z**2 + 93*z - 82. Let w(p) = 5*g(p) + 8*q(p). Determine r so that w(r) = 0.
2, 3, 5
Let g(x) = 4*x**2 - 35*x - 34. Let u(p) = 20*p**2 - 176*p - 172. Let a(h) = -24*g(h) + 5*u(h). Factor a(j).
4*(j - 11)*(j + 1)
Let y(d) = 13*d**2 - 2*d. Let u be y(-2). Suppose u - 12 = 11*k. Let 1/2*z + 0 - 1/2*z**k - 1/2*z**3 + 1/2*z**2 = 0. Calculate z.
-1, 0, 1
Let f(b) be the third derivative of 2*b**2 + 0*b + 1/32*b**5 + 0*b**3 - 1/32*b**4 + 0. Factor f(k).
3*k*(5*k - 2)/8
Determine v so that 22/3 - 68/3*v + 24*v**2 - 28/3*v**3 + 2/3*v**4 = 0.
1, 11
Let n(q) = 27*q**2 + 312*q + 305. Let t(r) = -16*r**2 - 156*r - 152. Let u(s) = 3*n(s) + 5*t(s). Factor u(j).
(j + 1)*(j + 155)
Let z(b) be the first derivative of b**6/36 - b**5/5 - b**4/3 + b**3/3 + 7*b**2/12 - 266. Factor z(j).
j*(j - 7)*(j - 1)*(j + 1)**2/6
Let z be (2 + 9/36)/2. Solve 15/8*t - z*t**2 - 3/4 = 0.
2/3, 1
Suppose -3*l + 4 = 2*d, 5*l - 6 - 5 = d. Let x(g) be the first derivative of -4/3*g**3 + 4*g + 2*g**l - 5 - g**4. Factor x(o).
-4*(o - 1)*(o + 1)**2
Let u = 393 - 388. Let d(n) be the first derivative of -2/13*n + 0*n**3 + 2/65*n**5 + 1/13*n**4 + u - 2/13*n**2. Factor d(b).
2*(b - 1)*(b + 1)**3/13
Let f(j) be the second derivative of 0 - 1/12*j**4 + 2*j**2 - 1/2*j**3 + 37*j. Factor f(n).
-(n - 1)*(n + 4)
Let u = -741451/2295 - -8719/27. Let d = -2/153 - u. Determine a so that -2/5*a**2 - d*a**3 - 2/15 - 2/5*a = 0.
-1
Suppose 10*w - 70 = 5*w. Factor -4 + 5*l**2 + 13 - w.
5*(l - 1)*(l + 1)
Let n(t) be the first derivative of t**5/5 - 2*t**3/3 + t + 57. Factor n(p).
(p - 1)**2*(p + 1)**2
Let f(n) be the third derivative of 2/105*n**7 + 0*n**4 - 1/20*n**6 + 0*n + 1/30*n**5 - 10*n**2 + 0*n**3 + 0. Factor f(a).
2*a**2*(a - 1)*(2*a - 1)
Let d(o) be the first derivative of -o**5/420 - o**4/168 + 27*o**2/2 + 36. Let g(u) be the second derivative of d(u). Factor g(t).
-t*(t + 1)/7
Let g(v) be the first derivative of 5*v**6/6 + 14*v**5 + 245*v**4/4 - 76. Let g(l) = 0. What is l?
-7, 0
Suppose 0 = -5*o - 2 + 12. Factor m**2 + 2*m**o - 2 + m**2 - 6*m**2 - 5*m.
-(m + 2)*(2*m + 1)
Let d be (-22)/(-154) + (-3)/(-28). Factor -d*g**4 + 1/2*g + 1/4*g**2 + 0 - 1/2*g**3.
-g*(g - 1)*(g + 1)*(g + 2)/4
Suppose 0 = -4*t - 59 + 67. Let x(z) be the third derivative of 3*z**t + 0*z + 0 - 1/21*z**3 - 5/42*z**5 + 5/42*z**4. Factor x(r).
-2*(5*r - 1)**2/7
Let x(u) = -u**3 + 7*u**2 + 2. Let b = 12 + -5. Let d be x(b). Factor 6*z**2 + z**2 + z**d - 4*z**3.
-4*z**2*(z - 2)
Suppose -4/5*w**4 + 3/5*w**