- 31. Let 1/4*y**q + 0 - 1/4*y**5 - 1/4*y**4 + 1/4*y**2 + 0*y = 0. Calculate y.
-1, 0, 1
Factor 2 + 3*o - 4 + 11*o**2 - 8*o**2 - 4*o**2.
-(o - 2)*(o - 1)
Let u(k) = -7*k. Let b be u(-1). Factor b*l**4 + 3*l**3 + 2*l**3 + 3*l**4 - 5*l**4.
5*l**3*(l + 1)
Let b be -2 - 0 - (19 - 23). Let l(q) be the first derivative of 0*q - 6 - 2/11*q**b + 6/11*q**3. Determine j, given that l(j) = 0.
0, 2/9
Let r(x) be the second derivative of x**4/60 + 211*x**3/15 + 44521*x**2/10 + 8*x + 10. Factor r(g).
(g + 211)**2/5
Let i = -50328 - -50331. Factor 2/11*a**i + 10/11 + 14/11*a**2 + 2*a.
2*(a + 1)**2*(a + 5)/11
Factor 26/15*k**2 + 2*k**3 + 2/15*k**5 + 8/15*k + 14/15*k**4 + 0.
2*k*(k + 1)**3*(k + 4)/15
Let f be (-4)/(-18) - (-5 + 174/54). Let t be 8/(-6) - (-2 + (f - 2)). Factor -t*y**2 - 6 + 4*y.
-2*(y - 3)**2/3
Let l(c) = 3*c**4 + 30*c**3 - 57*c**2 - 5*c - 5. Let r(u) = u**4 + 15*u**3 - 28*u**2 - 2*u - 2. Let v(f) = 2*l(f) - 5*r(f). Factor v(x).
x**2*(x - 13)*(x - 2)
Suppose 3*c - 5 = 52. What is y in c + 31 + 2*y**2 + 3416*y - 3436*y = 0?
5
Let u(g) = g + 1. Let m(o) = 5*o**4 - 20*o**3 + 30*o**2 - 35*o - 10. Let x(f) = m(f) + 15*u(f). Factor x(d).
5*(d - 1)**4
Suppose 5 + 4 = y. Let m = y + 4. Factor 0*k**2 - k - m - 7*k - 2*k**2 + 5.
-2*(k + 2)**2
Let b(g) be the third derivative of -g**5/140 - 17*g**4/56 - 8*g**3/7 - 81*g**2 - g. Suppose b(f) = 0. Calculate f.
-16, -1
Let l = 6 - 0. Let o be 5*-3*(-2)/l. Let -4*q - 20*q + 69*q**2 - 165*q**4 - 12 + 27*q**3 + 30*q**3 + 75*q**o = 0. Calculate q.
-2/5, 1
Let d(h) = -h**3 + 8*h**2 - h - 8. Let x be d(4). Let o = -7 + x. What is s in -10*s - 10*s + o - 9*s - s + 5*s**2 = 0?
3
Let l(i) be the third derivative of i**8/336 + i**7/14 + 67*i**6/120 + 43*i**5/20 + 14*i**4/3 + 6*i**3 + 12*i**2 + 4. Factor l(z).
(z + 1)**2*(z + 2)**2*(z + 9)
Let g(t) be the third derivative of -45*t**2 + 2*t - 1/210*t**7 + 0 + 1/40*t**6 + 1/20*t**5 - 7/24*t**4 - t**3. What is l in g(l) = 0?
-1, 2, 3
Determine u so that -16/5*u**3 - 2/5*u**4 + 0 + 0*u**2 + 0*u = 0.
-8, 0
Let x = 3144/13 + -32556/143. Suppose x*k + 6/11*k**4 - 144/11*k**2 - 54/11 + 36/11*k**3 = 0. What is k?
-9, 1
Solve -43 - 528*u - 10*u**2 + 568 + 22*u**2 - 11*u**2 + 2*u**2 = 0 for u.
1, 175
Let x(u) be the second derivative of u**4/66 - 23*u**3/11 - 70*u**2/11 - 498*u. Factor x(f).
2*(f - 70)*(f + 1)/11
Let a(c) be the second derivative of 0*c**2 + 0 + 0*c**3 + 9/10*c**5 - 7/10*c**6 + 35*c + 1/14*c**7 + 0*c**4. Factor a(z).
3*z**3*(z - 6)*(z - 1)
Suppose 20 = -33*q + 43*q. Factor -1/9*s**3 - 4/9*s**q + 0 + 4/9*s**4 + 1/9*s.
s*(s - 1)*(s + 1)*(4*s - 1)/9
Suppose 14*t - 65 = -9. Let g(p) be the first derivative of -1/11*p**2 + 6 + 0*p**t + 0*p + 1/33*p**6 - 4/55*p**5 + 4/33*p**3. Let g(r) = 0. Calculate r.
-1, 0, 1
Let f = -783/56 + 113/8. Factor 1/7*z - 2/7*z**3 + 1/7*z**4 + f*z**5 + 1/7 - 2/7*z**2.
(z - 1)**2*(z + 1)**3/7
Let o be 9/(-12) - 75/(-4). Let b be (4/(-6))/2 - (-6)/o. Factor b*l + 1/5*l**3 + 0 + 1/5*l**2.
l**2*(l + 1)/5
Let a be (6/3 - 3)*(-1 - 0). Suppose 4 = h - a. Let -6/7*x**2 + 51/7*x**3 + 0 - 120/7*x**4 + 48/7*x**h + 0*x = 0. Calculate x.
0, 1/4, 2
Factor -5/3*y + 13/6*y**2 - 1/3*y**3 + 0 - 1/6*y**4.
-y*(y - 2)*(y - 1)*(y + 5)/6
Suppose 2/7*r**4 + 138/7*r**2 + 32/7*r**3 + 188/7*r + 80/7 = 0. Calculate r.
-10, -4, -1
Suppose -4*u - 25 = 5*y, 341*y - 25 = 3*u + 346*y. Find b such that -2/17*b**2 + 0*b + u = 0.
0
Let f(t) be the first derivative of 26*t**5/5 + 3*t**4/2 - 4*t**3/3 + 22*t + 2. Let q(l) = -l**4 - 1. Let k(x) = -2*f(x) - 44*q(x). Solve k(i) = 0 for i.
-2, 0, 1/2
Let z(n) be the third derivative of n**5/120 - 53*n**4/24 + 35*n**3/4 - 2*n**2 + 260. Solve z(y) = 0.
1, 105
Let h(y) be the second derivative of y**7/210 - y**6/45 + 2*y**3 - 5*y. Let x(z) be the second derivative of h(z). Let x(s) = 0. What is s?
0, 2
Suppose -48 = 3*p + r + 61, 0 = 5*p - 2*r + 189. Let i = -110/3 - p. Determine y, given that 1/3*y + i - 1/3*y**3 - 1/3*y**2 = 0.
-1, 1
Let g(y) be the second derivative of y**7/399 + y**6/285 - y**5/19 - 5*y**4/57 + 3*y**3/19 + 9*y**2/19 - 7*y - 10. Suppose g(x) = 0. Calculate x.
-3, -1, 1, 3
Solve 16*i**3 + 0*i**4 - 27622 + 27814 + 448*i + i**4 + 165*i**2 - 13*i**4 + 91*i**2 = 0.
-2, -2/3, 6
Let l(f) be the first derivative of f**4/36 - f**3/9 + 4*f/9 + 91. Suppose l(v) = 0. Calculate v.
-1, 2
Factor -7*z**4 - 5*z - 7*z**4 + 13*z**4 - z**5 + 3 + 6*z**3 - 2*z**2.
-(z - 1)**3*(z + 1)*(z + 3)
Find a, given that -20 - 5*a**2 - 30*a + 5/2*a**4 + 15/2*a**3 = 0.
-2, -1, 2
Let v be (-18)/(-6) + 2 - 5. Let m(d) be the third derivative of -1/80*d**5 + 1/6*d**3 + v + 0*d**4 + 0*d + d**2 + 1/480*d**6. Factor m(c).
(c - 2)**2*(c + 1)/4
Let f be (-6556)/7 + -9*6/(-54). Let n = f + 939. Factor 4/7*l**4 - 16/7*l - 16/7*l**3 + 4/7 + n*l**2.
4*(l - 1)**4/7
Let s(v) be the third derivative of 1/3*v**4 - 3*v**2 + 0*v + 5/3*v**3 - 1/30*v**5 + 0. Factor s(w).
-2*(w - 5)*(w + 1)
Let v(j) = -6*j**2 - 7*j + 5. Let m(h) = 25*h**2 + 28*h - 23. Let g(q) = 6*m(q) + 26*v(q). Factor g(a).
-2*(a + 1)*(3*a + 4)
Let i = 1290 + -3868/3. Let c(x) be the second derivative of -1/3*x**4 + 0 + x + 0*x**2 - i*x**3. Factor c(u).
-4*u*(u + 1)
Let y = 57674/5 - 11534. Suppose -12/5*f + y*f**2 + 8/5 = 0. Calculate f.
1, 2
Let w = 27 + -29. Let x be -2 - w - (-12)/20. Factor -9/5*l**2 - 3/5*l**3 - 9/5*l - x.
-3*(l + 1)**3/5
What is n in 37*n - 199*n + 900 + 3*n**2 + 1287 = 0?
27
Factor 25*u**3 - 8640*u + 69120 + 502*u**2 - 142*u**2 - 55*u**3 + 25*u**3.
-5*(u - 24)**3
Let i(u) be the third derivative of 1/672*u**8 + 1/15*u**5 - 1/80*u**6 + 0 - 1/210*u**7 - 1/12*u**4 + 0*u**3 + 0*u + 31*u**2. Factor i(v).
v*(v - 2)*(v - 1)**2*(v + 2)/2
What is p in 3/2*p**3 + p**5 + 0 - 2*p**2 + 9/2*p**4 + 0*p = 0?
-4, -1, 0, 1/2
Let l(o) be the third derivative of 0 + 2/3*o**3 + 0*o + 6*o**2 + 1/60*o**5 - 1/6*o**4. Factor l(d).
(d - 2)**2
Let r(w) be the second derivative of 0*w**5 + 0 + 12*w + 1/18*w**4 - 1/6*w**2 + 0*w**3 - 1/90*w**6. Factor r(n).
-(n - 1)**2*(n + 1)**2/3
Let i(m) be the first derivative of -2*m**3/27 + 10*m**2/9 - 2*m + 152. Factor i(s).
-2*(s - 9)*(s - 1)/9
Let z(o) be the first derivative of -o**8/168 - o**7/105 + o**6/60 + o**5/30 + 27*o**2/2 + 10. Let f(p) be the second derivative of z(p). Factor f(g).
-2*g**2*(g - 1)*(g + 1)**2
Let y(m) be the third derivative of m**6/840 - m**5/210 - m**4/168 + m**3/21 + 3*m**2. Determine g so that y(g) = 0.
-1, 1, 2
Let t = 200 + -198. Solve -1/2*y**2 - 7/2*y**3 - 1/2*y**5 + 4*y - t + 5/2*y**4 = 0.
-1, 1, 2
Let c(z) be the third derivative of -z**6/120 - z**5/20 + z**4 + 40*z**3/3 - 18*z**2 + 8*z. Factor c(t).
-(t - 5)*(t + 4)**2
Let l be -4 - (-8 - (-33)/22). Factor 0 - 15/4*o**3 + 0*o - 5/4*o**4 - l*o**2.
-5*o**2*(o + 1)*(o + 2)/4
Let x(i) be the third derivative of -i**5/480 - 85*i**4/48 - 7225*i**3/12 - 644*i**2. Factor x(g).
-(g + 170)**2/8
Let p(d) be the first derivative of -d**6/10 - 11*d**5/30 - d**4/3 - 11*d**3 + 29. Let f(q) be the third derivative of p(q). Solve f(z) = 0 for z.
-1, -2/9
Let d(z) = -z**2 - 11*z + 29. Let u be d(-13). Let r(x) be the second derivative of -1/30*x**4 - x + 1/15*x**u + 0 + 0*x**2. Factor r(i).
-2*i*(i - 1)/5
Suppose 21*z - 435 = 16*z. Let a = 87 - z. Suppose a*b - b**3 - 2/3*b**2 + 0 - 1/3*b**4 = 0. Calculate b.
-2, -1, 0
Let a(r) be the first derivative of 9*r**5/5 - 15*r**4/4 - 11*r**3 - 9*r**2/2 - 119. Factor a(z).
3*z*(z - 3)*(z + 1)*(3*z + 1)
Factor -6*m**2 - 4*m**5 + 0*m**5 - 945 + 3*m + 945 + m**5 + 6*m**4.
-3*m*(m - 1)**3*(m + 1)
Let r(t) be the second derivative of -t**7/28 + t**6/4 + 3*t**5/20 - 5*t**4/4 - t**3/4 + 15*t**2/4 + 2*t - 56. Solve r(s) = 0 for s.
-1, 1, 5
Let x(n) be the third derivative of n**5/240 - 5*n**4/96 - 4*n**2 - 1. Factor x(g).
g*(g - 5)/4
Let f(m) be the second derivative of -2/105*m**6 - 1/147*m**7 + 1/21*m**4 + 0*m**2 - 14*m + 1/70*m**5 + 0*m**3 + 0. Let f(y) = 0. What is y?
-2, -1, 0, 1
Let t(s) be the second derivative of 1/3*s**3 - 7/30*s**5 - 7/18*s**4 - 8/63*s**7 - 3*s + 0 + 2/5*s**6 + 1/3*s**2. Solve t(i) = 0 for i.
-1/2, -1/4, 1
Let c(w) = -w**3 - 3*w**2 - w - 5. Let k be c(-3). Let h be k/11 + (-7 - 573/(-66)). Factor 3/2 - h*y**2 - 3/2*y + 3/2*y**3.
3*(y - 1)**2*(y + 1)/2
Let p = -67 + 69. Let i(c) be the second derivative of -1/10*c**6 + 0 + 3/5*c*