1)/8
Let z(a) = -5*a**5 + 6*a**4 + 4*a**3 - 6*a**2 - 10*a. Let t(h) = -h**5 + h**4 + h**3 - h**2 - 2*h. Let g(m) = 11*t(m) - 2*z(m). Factor g(d).
-d*(d - 1)**2*(d + 1)*(d + 2)
Let q(v) = v**2 - v. Let i(p) = -5*p**2 - 6*p - 16. Let x(s) = -i(s) - 4*q(s). Let l be x(-8). Factor 1/3*h**3 + 0 - 1/3*h + l*h**2.
h*(h - 1)*(h + 1)/3
Let k(s) be the second derivative of 0*s**2 + 0 - 243/100*s**5 + 9/5*s**4 - 2/5*s**3 - 40*s. Determine i so that k(i) = 0.
0, 2/9
Let z be (27/(-135))/((-1)/15). Suppose -4*l + 56/5*l**4 + 4/5 + 22*l**z - 3*l**2 = 0. What is l?
-2, -1/2, 1/4, 2/7
Solve 0 - 2/9*z**5 + 0*z**4 + 0*z + 0*z**2 + 2/9*z**3 = 0 for z.
-1, 0, 1
Let q(x) be the third derivative of -x**6/200 + 7*x**5/25 + 91*x**4/40 + 31*x**3/5 - 485*x**2. Factor q(p).
-3*(p - 31)*(p + 1)*(p + 2)/5
Let l(r) = 18*r**2 - 4*r - 3. Let a be l(-2). Let u = -999/13 + a. Factor -2/13*z**3 + 4/13*z**2 - 4/13 + u*z.
-2*(z - 2)*(z - 1)*(z + 1)/13
Let a(o) be the third derivative of -o**8/336 - o**7/21 - 17*o**6/60 - 3*o**5/5 + 9*o**4/8 + 9*o**3 - 8*o**2 - o. Suppose a(g) = 0. What is g?
-3, -2, 1
Suppose 6 = 5*x - 8*x. Let d(f) = -2*f - 1. Let i be d(x). Factor 0 + 3/2*y**4 - 2*y**i - 1/2*y**2 + y.
y*(y - 1)**2*(3*y + 2)/2
Let l(m) be the third derivative of m**6/180 - m**5/10 - 7*m**4/12 - 11*m**3/9 - 38*m**2 - 3. Solve l(n) = 0.
-1, 11
Let g(f) be the third derivative of f**5/120 + 5*f**4/48 + f**3/3 + 25*f**2 - 1. Factor g(k).
(k + 1)*(k + 4)/2
Let z be 99/(-2)*14/(-21). Let i = z - 30. Find p, given that p**2 + 3/2*p**5 + 7/2*p**i + 0*p + 0 + 4*p**4 = 0.
-1, -2/3, 0
Let s be (-213)/(-5)*3/27 - 3. Let b(a) be the first derivative of 2*a**4 + s*a**3 + 2/5*a**2 + 18/25*a**5 - 1 + 0*a. Factor b(u).
2*u*(u + 1)**2*(9*u + 2)/5
Let f(u) be the second derivative of 7/12*u**6 - u + 0*u**2 + 11/20*u**5 + 0*u**3 + 1/6*u**4 - 23 + 25/168*u**7. Factor f(k).
k**2*(k + 2)*(5*k + 2)**2/4
Suppose 0 = 6*k - 355 + 283. Let i(p) be the first derivative of 6*p**2 - 3/5*p**5 - 3*p**4 - 3 - 3*p**3 + k*p. Suppose i(a) = 0. What is a?
-2, -1, 1
Let 1/4*m**3 + 5/4*m**2 + 7/4*m + 3/4 = 0. Calculate m.
-3, -1
Let p(z) be the first derivative of z**7/70 + z**6/10 + z**5/10 - z**4/2 - 3*z**3/2 - z**2 + 3. Let t(h) be the second derivative of p(h). Factor t(l).
3*(l - 1)*(l + 1)**2*(l + 3)
Suppose u = 5*b - 36 - 5, 0 = -4*b + 5*u + 37. Solve -74*n**2 - 47*n**3 - 8*n**4 + 64*n**3 + 25*n**3 + 48*n - b = 0.
1/4, 1, 2
Let q be (-4)/6 + (42/(-45) - 0) + 2. Factor 0 + 6/5*b**2 + 2/5*b**4 - 6/5*b**3 - q*b.
2*b*(b - 1)**3/5
Let l(r) be the third derivative of -r**8/168 + 2*r**7/35 - 7*r**6/30 + 8*r**5/15 - 3*r**4/4 + 2*r**3/3 + 14*r**2 + r. What is q in l(q) = 0?
1, 2
Suppose 0 = 8*d - 2*d. Let q(h) be the third derivative of -3*h**2 + 1/660*h**6 + 0*h**4 - 1/330*h**5 + 0*h + d*h**3 + 0. Factor q(w).
2*w**2*(w - 1)/11
Factor 187*b**4 + 18*b**2 - 21*b**3 - 187*b**4 + 3*b**5.
3*b**2*(b - 2)*(b - 1)*(b + 3)
Let w = 37 + -33. Factor -w*p + 6*p + 15*p**2 + 3*p.
5*p*(3*p + 1)
Let c = -3683 + 3686. Factor 0*w**4 + 4/5*w**c + 0 + 0*w**2 - 4/5*w**5 + 0*w.
-4*w**3*(w - 1)*(w + 1)/5
Suppose -1 + 9 = 4*y. Let p be (-24)/(-36)*(1 + y). Solve 13*a**2 - 9*a**4 + 6*a**3 + 4*a**3 - 14*a**5 + 4*a - 9*a**4 + 5*a**p = 0 for a.
-1, -2/7, 0, 1
Let q(h) be the third derivative of 2*h**7/105 - 17*h**6/30 + 8*h**5/5 + 416*h**4/3 - 7168*h**3/3 + 313*h**2. Factor q(v).
4*(v - 8)**3*(v + 7)
Let x(q) be the second derivative of 0*q**3 - 1/15*q**5 + 27*q + 0 + 0*q**2 - 1/3*q**4. Factor x(i).
-4*i**2*(i + 3)/3
Suppose 0 = -5*w + 2*w - 2*b + 14, -5*b - 10 = 0. Let p be (-1)/((-1)/w) + (1 - 4). Solve -2*l + 1 - 1/4*l**p + 5/4*l**2 = 0 for l.
1, 2
Let u = 240 - 238. Let l(c) be the third derivative of -1/1176*c**8 + 4/735*c**7 + 0*c**3 - 1/84*c**4 - 1/70*c**6 + 2/105*c**5 + 0*c + 5*c**u + 0. Factor l(a).
-2*a*(a - 1)**4/7
Let s(n) be the first derivative of -4*n**3/3 - 28*n**2 - 196*n - 338. Factor s(p).
-4*(p + 7)**2
Solve -1/4*b**2 + 15/2 - 1/4*b = 0 for b.
-6, 5
Let w be 1*240/306 + 24/(-36). Let 2/17*q**3 + 6/17*q - w - 6/17*q**2 = 0. What is q?
1
Let p = 38840/7 + -5548. Factor 6/7*y + p + 2/7*y**2.
2*(y + 1)*(y + 2)/7
Let p(g) be the first derivative of 49*g**4/3 - 28*g**3 + 18*g**2 + 10*g - 14. Let f(a) be the first derivative of p(a). Factor f(d).
4*(7*d - 3)**2
Determine g so that 15 - 12*g**2 + 25*g**3 + 18*g**2 - 15 - 5*g + 14*g**2 = 0.
-1, 0, 1/5
Let x be (365/(-65))/(-18 + 17) + -5. Let 2/13*f**3 + x*f**2 + 0 + 6/13*f = 0. Calculate f.
-3, -1, 0
Let k(b) = 2*b**3 + 49*b**2 + 21*b - 70. Let d be k(-24). Factor -160/7*p - 8/7*p**3 - 64/7 - 68/7*p**d.
-4*(p + 4)**2*(2*p + 1)/7
Let k(f) be the first derivative of -21/5*f**5 - 12*f**2 - 27/2*f**4 - 1/2*f**6 - 20*f**3 - 22 + 0*f. Factor k(h).
-3*h*(h + 1)*(h + 2)**3
Suppose -7 = -r + h, 3*r = -0*h - 2*h + 31. Suppose -5 = -f, -6 - r = 5*p - 5*f. Factor -4*y - 2*y - 4*y**4 + 6*y + 3*y**p + y.
-y*(y - 1)*(2*y + 1)**2
Suppose f - 15 = -2*f. Let w(a) be the first derivative of 2/55*a**f - 2/11*a**3 + 0*a**4 + 8 - 2/11*a**2 + 0*a. Factor w(q).
2*q*(q - 2)*(q + 1)**2/11
Let g be (204/(-918))/((-4)/125). Let a(t) be the third derivative of g*t**3 + 1/36*t**5 + 3*t**2 + 0*t + 25/36*t**4 + 0. Find x, given that a(x) = 0.
-5
Let v(u) be the second derivative of -41*u**4/12 + 13*u**3/2 + u**2 - 17*u. Factor v(f).
-(f - 1)*(41*f + 2)
Let w = -15 - -17. Suppose 0 = -0*s + w*s + s. Factor 0 + s*q - 2/3*q**2.
-2*q**2/3
Let j(g) be the second derivative of -g**5/4 + 10*g**4/3 + 5*g**3/6 - 20*g**2 - 509*g. Factor j(u).
-5*(u - 8)*(u - 1)*(u + 1)
Let z(j) be the second derivative of 0 + 1/24*j**5 + 1/72*j**4 + 0*j**3 + 0*j**2 + 9*j + 7/180*j**6 + 1/84*j**7. Factor z(m).
m**2*(m + 1)**2*(3*m + 1)/6
Let 16/11*r**3 + 12/11*r**2 - 80/11*r + 2/11*r**4 + 50/11 = 0. Calculate r.
-5, 1
Let s(z) be the second derivative of 4*z**7/21 - 34*z**6/15 + 27*z**5/5 + 26*z**4/3 - 88*z**3/3 - 48*z**2 - 3*z + 17. Determine b, given that s(b) = 0.
-1, -1/2, 2, 6
Let g(l) be the first derivative of l**4/4 - l**3/3 - l**2/2 + l + 12. Factor g(a).
(a - 1)**2*(a + 1)
Suppose 0*t + 2*t - 3*m = 64, 3*t - 96 = -3*m. Factor t*h - 7 + 7 - 37*h + 5*h**3.
5*h*(h - 1)*(h + 1)
Let f(r) = -r**3 - r. Let o(q) = q**3 - 53*q**2 + 11*q + 60*q**2 + q**3. Let u(a) = -5*f(a) - o(a). Find k, given that u(k) = 0.
-2/3, 0, 3
Suppose n + 64 = -4*s + 176, -4*n = -2*s + 20. Factor 15/2*q**2 + 6 - 2*q**3 + s*q.
-(q - 6)*(q + 2)*(4*q + 1)/2
Let y(v) be the first derivative of -2*v**5 - 4*v**4/3 + 7*v**3/3 + 3*v**2 + 38*v + 47. Let b(z) be the first derivative of y(z). Find o, given that b(o) = 0.
-1/2, 3/5
Let -116/5*h**3 - 12*h + 132/5*h**2 + 8/5 + 36/5*h**4 = 0. What is h?
2/9, 1
Let n(v) = v - 4. Let l be 40/(-60)*(-6)/4*6. Let y be n(l). Factor 0 + y*d - 2/3*d**2.
-2*d*(d - 3)/3
Solve 12*i**2 - 16*i**3 + 13/3*i**4 + 0*i + 0 - 1/3*i**5 = 0.
0, 1, 6
Factor 3/4*m**3 - 3/4*m**4 + 0 + 6*m**2 - 9*m.
-3*m*(m - 2)**2*(m + 3)/4
Let q(t) be the second derivative of -t**4/6 + 8*t**3 - 229*t. Factor q(v).
-2*v*(v - 24)
Factor 0 + 0*p**2 + 2/11*p**3 - 2/11*p.
2*p*(p - 1)*(p + 1)/11
Suppose -5*y + 29 = -6. Let f = -5 + y. Factor 16/9*v + 2/9*v**3 + 8/9 + 10/9*v**f.
2*(v + 1)*(v + 2)**2/9
Let r(z) be the third derivative of z**2 - 1/1680*z**8 + 0*z - 1/150*z**6 + 0 - 2/525*z**7 + 1/15*z**3 + 1/150*z**5 + 1/24*z**4. Factor r(g).
-(g - 1)*(g + 1)**3*(g + 2)/5
Suppose -5*r - 60 = 4*k, 3*r = -3*k - 30 - 12. Let q be 25 + -27 + k/(-4). Determine p, given that 1/6*p**2 + 0 - q*p = 0.
0, 3
Let j(p) be the second derivative of 2/9*p**2 + 0 - 1/54*p**4 - 1/9*p**3 - 1/135*p**6 + 1/30*p**5 + 9*p. Solve j(r) = 0.
-1, 1, 2
Factor 2/3*a**3 - 4*a + 0 - 10/3*a**2.
2*a*(a - 6)*(a + 1)/3
Let z(o) be the third derivative of 0 - 5/27*o**3 + 1/270*o**5 + 0*o + 5*o**2 - 1/27*o**4. Factor z(m).
2*(m - 5)*(m + 1)/9
Suppose 3*l - s - s = 12, 3*l = s + 15. Let k(y) = 4 + y**3 - l + 2. Let u(b) = -76*b**3 + 106*b**2 - 38*b + 4. Let h(v) = 4*k(v) + u(v). Factor h(o).
-2*(o - 1)*(4*o - 1)*(9*o - 2)
Factor 12/5*a - 3/5*a**3 - 3/5*a**2 + 12/5.
-3*(a - 2)*(a + 1)*(a + 2)/5
Factor 15 + 36*h**2 - 3*h**4 - 6*h**3 - 48*h + 5*h + h.
-3*(h - 1)**3*(h + 5)
Let t(h) be the third derivative of -h**6/660 - 107*h**5/330 - 265*h**4/12 - 2809*h**3/33 + 679*h**2. Determine g so that t(g) = 0.
-53, -1
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