et s(o) be the first derivative of -o**6/6 - 7*o**5/15 + 4*o**4/3 + 8*o**3/3 - 25*o**2/2 + 22. Let u(y) be the second derivative of s(y). Factor u(b).
-4*(b - 1)*(b + 2)*(5*b + 2)
Let g = -34 + 22. Let q = 14 + g. Let -3*f + 4*f**2 + q*f - 3*f - 8 = 0. Calculate f.
-1, 2
Let u(v) be the third derivative of 1/30*v**4 + 6*v**2 + 0*v + 0 + 1/300*v**5 + 2/15*v**3. Factor u(q).
(q + 2)**2/5
Let t be (1/15)/(10/20). Let h(m) be the first derivative of -t*m**3 + 1/30*m**4 - 4/15*m + 2/75*m**5 - 1/3*m**2 + 2. Factor h(w).
2*(w - 2)*(w + 1)**3/15
Let f = -31 + -86. Let w be (-260)/f - (-4)/(-18). Solve m**3 - m**w + m**4 - 5*m + 0*m**3 - 3*m**3 + 7*m = 0 for m.
-1, 0, 1, 2
Factor 85*b**2 - 154*b + 2628*b**3 + 2628*b**3 - 5261*b**3 - 56*b.
-5*b*(b - 14)*(b - 3)
Suppose 72*z**3 - 92*z**3 - z + z + 2*z**4 + 18*z**2 = 0. Calculate z.
0, 1, 9
Let c(h) = 243*h - 481. Let u be c(2). Find p such that 4/13*p**3 + 2/13*p**u + 0*p**2 - 6/13*p**4 + 0*p + 0 = 0.
0, 1, 2
Let n(h) be the first derivative of 11 + 1/2*h**2 + 2/5*h - 1/25*h**5 + 1/5*h**3 - 1/20*h**4. Factor n(v).
-(v - 2)*(v + 1)**3/5
Let v(x) = x**3 - x**2 + x - 1. Let m be v(4). Let c be m/18 - 1/(2/3). Determine u, given that -1/3 + 4/3*u**3 + c*u - 1/3*u**4 - 2*u**2 = 0.
1
Suppose 1 = -15*x + 16. Let g be (0*(-5)/(-20))/x. Factor 1/3*c**2 + 0*c + g.
c**2/3
Let y = 136 + -134. Let f(q) be the second derivative of 0 - 1/36*q**4 + 1/3*q**y - 1/18*q**3 + 4*q. What is r in f(r) = 0?
-2, 1
Let v = -16 - -18. Let b(c) = 11*c**4 + 19*c**3 + 11*c**2 - 9*c - 8. Let w(t) = t**4 - t**3 + t**2 - 1. Let k(n) = v*w(n) - b(n). What is i in k(i) = 0?
-1, 2/3
Let r(g) be the first derivative of g**6/480 - g**5/32 + g**4/8 + 5*g**3/3 + 3. Let h(s) be the third derivative of r(s). Factor h(b).
3*(b - 4)*(b - 1)/4
Let k be 3 - -7*9/(-49). Determine s, given that -2*s - 6/7*s**2 + 6/7*s**3 + k + 2/7*s**4 = 0.
-3, -2, 1
Let y(a) = -15*a**3 - 369*a**2 + 57*a + 369. Let j(x) = 3*x**3 + 74*x**2 - 11*x - 74. Let h(i) = 21*j(i) + 4*y(i). Solve h(g) = 0.
-26, -1, 1
Let v(o) = 4*o**4 - 36*o**3 + 76*o**2 - 60*o - 4. Let j(f) = -4*f**4 + 35*f**3 - 77*f**2 + 61*f + 3. Let d(a) = 4*j(a) + 3*v(a). Factor d(n).
-4*n*(n - 4)*(n - 2)**2
Let b(j) be the first derivative of -2*j**4/3 + 662*j**3/9 + 83*j**2/3 - 40. Factor b(p).
-2*p*(p - 83)*(4*p + 1)/3
Suppose 2*h + 4*r = 0, -2*r + 6*r = 3*h - 20. Factor -7*k**5 - 10*k**3 + 5*k - h*k**5 + 16*k**5.
5*k*(k - 1)**2*(k + 1)**2
Let r = 79/240 - -27/80. Factor -4/3*n - r*n**2 + 0.
-2*n*(n + 2)/3
Let d be (2 - (-9)/(-2))*-2. Suppose -2*z - 5*a + 21 = 0, -d*z + 0*a + 27 = 4*a. Suppose -5*m**4 + 2*m**4 + 6*m**3 + z*m + 3*m**3 - 9*m**2 = 0. Calculate m.
0, 1
Factor -122*w**2 + 160*w**2 - 7*w**3 - 2*w**3 + 2*w**4 + 60*w - 11*w**3.
2*w*(w - 6)*(w - 5)*(w + 1)
Let 7*h - 4*h - h**3 + 688*h**2 + 69 + 3*h - 757*h**2 - 5*h = 0. What is h?
-69, -1, 1
Suppose a - 2*k = 4, 0 = -14*k + 10*k - 4. Factor 8/7 - s - 1/7*s**a.
-(s - 1)*(s + 8)/7
Factor 15*p**4 - 6804 + 5*p**3 + 4*p**5 - 15*p**2 + p**5 + 6804 - 10*p.
5*p*(p - 1)*(p + 1)**2*(p + 2)
Let m(q) be the first derivative of 1/5*q**2 + 2/15*q**3 + 5*q + 5 + 1/30*q**4. Let j(p) be the first derivative of m(p). Factor j(f).
2*(f + 1)**2/5
Factor -32/7*u - 18/7*u**2 + 8/7.
-2*(u + 2)*(9*u - 2)/7
Let n(g) be the second derivative of -g**6/300 + g**5/90 - g**4/90 - 55*g**2/2 + 5*g + 3. Let j(u) be the first derivative of n(u). What is v in j(v) = 0?
0, 2/3, 1
Let o(m) = 3*m - 18. Let w be o(6). Let s be -3 + 3 + w*2/(-8). Let 0 + s*z**2 + 1/4*z**3 + 0*z = 0. What is z?
0
Let i = 107 + -88. Find l such that l**2 + i*l - 9*l + 4*l + 49 = 0.
-7
Suppose 33081*d + 42 = 33095*d. Factor 0 + 0*u - 2/11*u**d - 2/11*u**2.
-2*u**2*(u + 1)/11
Factor 3/4*n**2 + 1452 - 66*n.
3*(n - 44)**2/4
Let l(z) be the third derivative of -z**7/840 - z**6/180 + z**5/120 + z**4/12 - z**3/3 + 7*z**2. Let j(w) be the first derivative of l(w). Factor j(v).
-(v - 1)*(v + 1)*(v + 2)
Factor 7/8*z**2 + 15/8*z - 1/8*z**4 - 3/8*z**3 - 9/4.
-(z - 2)*(z - 1)*(z + 3)**2/8
Suppose -2*o - 4 = 66. Let z = -33 - o. Suppose z*g - 1/3 - 3*g**2 = 0. What is g?
1/3
Factor 0*f - 6*f**4 + 3/2*f**5 + 6*f**3 + 0*f**2 + 0.
3*f**3*(f - 2)**2/2
Factor -2/15*m**2 - 4/5*m + 14/15.
-2*(m - 1)*(m + 7)/15
Suppose 0 = -4*w - 307 + 1075. Factor -a**5 + w*a + 5*a**3 + 3*a**2 + a**4 - 192*a.
-a**2*(a - 3)*(a + 1)**2
Suppose 4*f - 6 - 12 = -2*d, -3*d = 5*f - 24. Let z be (-4*3/(-144))/(f/6). Factor -13/6*o**3 - 2*o**2 - z*o**5 - o**4 - 2/3*o + 0.
-o*(o + 1)**2*(o + 2)**2/6
Let c(m) = 2*m**2. Suppose 4*o = 3*q - 9, -5*q - 1 = -4*o - 8. Let z be c(q). Determine k, given that -4*k**z + 2*k**3 - 6*k + 2*k + 2*k**3 - 5*k**3 = 0.
-2, 0
What is z in -580*z - 2324 + 0*z**2 + 7785 - 2*z**2 - 27162 - 20349 = 0?
-145
Let d(q) be the second derivative of -q**7/3360 - q**6/320 - q**5/80 - q**4/12 - 2*q. Let a(r) be the third derivative of d(r). Determine m so that a(m) = 0.
-2, -1
Let l = -5916 + 41532/7. Let t be -1 + 3 + (-132)/(-42). Factor -100/7*r**2 + l*r - t.
-4*(5*r - 3)**2/7
Let i(m) be the third derivative of 0 + 1/18*m**4 + 0*m + 5/3*m**3 + 0*m**5 - 1/270*m**6 + 8*m**2. Let y(z) be the first derivative of i(z). Factor y(s).
-4*(s - 1)*(s + 1)/3
Let w(p) be the first derivative of p**4/4 + 5*p**3/2 + 6*p**2 + 6*p - 9. Let y(r) be the first derivative of w(r). Factor y(s).
3*(s + 1)*(s + 4)
Let m = -6278 + 69106/11. What is s in -2/11 - m*s - 288/11*s**2 = 0?
-1/12
Let n = -1601 - -1601. Factor n*b + 20/3*b**3 + 0 - 8/3*b**2 - 16/3*b**4 + 4/3*b**5.
4*b**2*(b - 2)*(b - 1)**2/3
Let j(x) be the first derivative of 14*x**3/3 + 53*x**2/2 - 12*x - 148. Factor j(a).
(a + 4)*(14*a - 3)
Let y be -5*3*(-5 - 355/(-75)). Factor -q - 3/2*q**3 + 9/2*q**2 + 0 - 2*q**y.
-q*(q - 1)*(q + 2)*(4*q - 1)/2
Let u(a) = -a**3 + 2*a**2 + 4*a + 6. Let t be u(-5). Find i, given that -4*i**3 - 176 + 317 - 44*i - t - 28*i**2 = 0.
-5, -1
Let g(p) be the second derivative of 0*p**3 - 2/35*p**5 + 21*p + 0 - 1/7*p**4 + 0*p**2 + 2/105*p**6. Factor g(q).
4*q**2*(q - 3)*(q + 1)/7
Let d(g) be the first derivative of g**3/12 + 23*g**2 - 30. Let d(a) = 0. What is a?
-184, 0
Let w(g) = -g + 11. Let h be w(11). Suppose 0*o + 0*o + 10*o = h. Factor -1/3*c**4 + 0*c + 0*c**3 + 0 + o*c**2.
-c**4/3
Factor 1 + 2408*w**2 + 2*w**3 - 1 - 32*w - 2420*w**2.
2*w*(w - 8)*(w + 2)
Let g be ((-69)/27 + 3)/((-46)/(-9) + -4). Find n such that -1/5*n**2 - g*n + 0 = 0.
-2, 0
Let h(j) be the second derivative of -j**6/80 + 3*j**5/8 - 19*j**4/32 - 18*j + 7. Factor h(x).
-3*x**2*(x - 19)*(x - 1)/8
Let u(w) be the first derivative of w**3 + 1/6*w**4 - 1 + 0*w - 1/30*w**5 + 0*w**2 + 1/360*w**6. Let y(l) be the third derivative of u(l). Factor y(x).
(x - 2)**2
Factor 2/3*w**3 - 74/3*w + 34/3*w**2 + 38/3.
2*(w - 1)**2*(w + 19)/3
Factor 8*l + 617*l**2 + 613*l**2 + 16 - 1229*l**2.
(l + 4)**2
Factor 8/15 - 2/15*k**4 - 16/15*k - 2/15*k**5 + 2/15*k**2 + 2/3*k**3.
-2*(k - 1)**3*(k + 2)**2/15
Let p(k) be the second derivative of -13*k + 0 + 1/8*k**4 + 3/2*k**2 - 3/4*k**3. Factor p(j).
3*(j - 2)*(j - 1)/2
Factor -95/3*g + 5/3*g**2 + 170/3.
5*(g - 17)*(g - 2)/3
Let g(c) be the third derivative of 1/3*c**4 + 37/150*c**5 + 0 - 6*c**2 + 1/10*c**6 + 0*c + 4/15*c**3 + 3/175*c**7. Factor g(r).
2*(r + 1)**2*(3*r + 2)**2/5
Let b(o) be the first derivative of 8/3*o - 1 - 10/3*o**2 - 28/9*o**3. Factor b(q).
-4*(q + 1)*(7*q - 2)/3
Let g(j) be the third derivative of -j**7/42 + 5*j**6/4 + 8*j**5 + 245*j**4/12 + 55*j**3/2 - 8*j**2 - 13*j. Factor g(y).
-5*(y - 33)*(y + 1)**3
Let h(y) be the first derivative of 2*y**3/3 + 4*y**2 + 8*y - 38. Factor h(n).
2*(n + 2)**2
Suppose 0 = 5*p - 25, -4*c + 4*p + 1 = p. Suppose -c + 10 = 3*u. Factor 2*r**3 - u*r**3 + 0*r**3 - r**3.
-r**3
Factor -26*z + 76/3 + 2/3*z**2.
2*(z - 38)*(z - 1)/3
Let t(u) be the first derivative of -12 + 0*u - 1/6*u**2 - 1/2*u**4 + 4/9*u**3 + 4/15*u**5 - 1/18*u**6. Factor t(d).
-d*(d - 1)**4/3
Let 2*a**5 + 4*a**2 - a**5 + a**5 - 2*a**3 + 0*a**5 - 4*a**3 = 0. What is a?
-2, 0, 1
Let i = 30085 - 121061/4. Let z = i - -5111/28. Suppose -12/7*b**2 + 24/7*b + 2/7*b**3 - z = 0. What is b?
2
Suppose 0 = -k - 101 + 351. What is x in -k + 250 - 5*x - 5*x**2 + 5*x**4 + 5*x**3 = 0?
-1, 0, 1
Let q(k) be the third derivative of 1/168*k**4 + 0*k**3 + 0*k + 1/840*k**