0
Let c = -11/36 + 5/9. Let s(a) be the first derivative of -1 - 1/3*a**3 + 0*a - 1/8*a**2 - c*a**4. Factor s(d).
-d*(2*d + 1)**2/4
Let w = -14 - -16. Factor w*l**3 + 18 - 18 - 2*l**4.
-2*l**3*(l - 1)
Determine q so that -2*q + 6/7 - 6/7*q**5 + 2*q**4 + 20/7*q**3 - 20/7*q**2 = 0.
-1, 1/3, 1, 3
Let f be 9/9 - (0 - 1). Factor 150*h**f - 181*h**3 + 2 - 70*h**3 - 30*h + h**3.
-2*(5*h - 1)**3
Let y(i) be the third derivative of -i**8/672 - i**7/210 + i**6/30 - i**5/60 - 7*i**4/48 + i**3/3 + 8*i**2. Let y(f) = 0. Calculate f.
-4, -1, 1
Let c(w) be the second derivative of w**5/20 - w**4/8 - 3*w**2/2 + 4*w. Let p(u) be the first derivative of c(u). Let p(f) = 0. Calculate f.
0, 1
Let g = 2/157 + 153/314. Factor -g - 1/2*d**2 - d.
-(d + 1)**2/2
Let x be 300/108 + 4/18. Factor 16 + 0 - x*a + 15*a - 4*a**2.
-4*(a - 4)*(a + 1)
Factor -2/11*a - 10/11*a**2 - 8/11*a**3 + 0.
-2*a*(a + 1)*(4*a + 1)/11
Let j(i) = -i**3 - 5*i**2 + 5*i + 7. Let r be j(-5). Let h be r/(-12) - (-5)/(-6). Factor -8/3*f + h*f**2 + 8/3.
2*(f - 2)**2/3
Suppose 2*v**5 + 182*v**3 + 0*v**5 - 180*v**3 - 4*v**4 = 0. What is v?
0, 1
Let m(w) be the third derivative of w**8/1176 - w**7/735 - w**6/210 + w**5/105 + w**4/84 - w**3/21 - 4*w**2. Factor m(c).
2*(c - 1)**3*(c + 1)**2/7
Let l(k) be the first derivative of 2*k**5/35 - 8*k**3/21 - 3. Find n, given that l(n) = 0.
-2, 0, 2
Let p(d) be the second derivative of -d**7/2100 + d**6/400 + d**5/100 + d**4/4 + 4*d. Let h(v) be the third derivative of p(v). Solve h(k) = 0.
-1/2, 2
Factor -12/5 - 2*h**2 + 34/5*h.
-2*(h - 3)*(5*h - 2)/5
Let p be (-15)/24*-2*4. Let -z**3 + p*z - 4*z - z**2 - 1 + 2*z**2 = 0. Calculate z.
-1, 1
Solve 2/7*z**3 + z**2 - 2/7*z + 0 - z**4 = 0 for z.
-1, 0, 2/7, 1
Let -8*b**5 - 5*b**4 + 10*b**5 - 25*b**2 + 15*b**5 - 60*b**3 + 3*b**5 + 10*b = 0. What is b?
-1, 0, 1/4, 2
Let j = 95/264 + -7/22. Let a(x) be the third derivative of 0*x - 1/180*x**5 - 2*x**2 + 0 + j*x**4 - 1/9*x**3. Solve a(h) = 0.
1, 2
Let v(b) be the second derivative of -b**5/40 - b**4/3 - 7*b**3/4 - 9*b**2/2 - 36*b - 2. Determine i, given that v(i) = 0.
-3, -2
Let a(p) be the first derivative of 5*p**6/252 - p**5/21 + p**4/21 + p**3/3 + 2. Let o(j) be the third derivative of a(j). Factor o(m).
2*(5*m - 2)**2/7
Let c = 74 - 72. Factor -4/7 - 18/7*l - 2*l**c.
-2*(l + 1)*(7*l + 2)/7
Let c(r) be the first derivative of -3*r**5/10 + 3*r**4/4 + 7*r**3/2 + 3*r**2 - 10. Factor c(d).
-3*d*(d - 4)*(d + 1)**2/2
Factor 4/5 - 4/5*d**2 - 2/5*d**3 + 2/5*d.
-2*(d - 1)*(d + 1)*(d + 2)/5
Let o(t) be the first derivative of -t**3/12 + t**2/2 + 5*t/4 + 4. Factor o(n).
-(n - 5)*(n + 1)/4
Let k(o) = 2*o**3 - 2*o**2 - 8*o + 2. Let v be (2 - 1/2)*2. Let m(u) = -5*u + 6*u + 4*u**v - 3*u**3. Let s(g) = -k(g) - 3*m(g). Factor s(c).
-(c - 1)*(c + 1)*(5*c - 2)
Suppose -4*t + 69 = 3*b, -b = t - 3*t + 27. Let 6*a + 3*a**3 - 8*a**3 + 3*a**3 - t*a**2 - 7*a**3 = 0. What is a?
-2, 0, 1/3
Suppose -4/5*u - 1/5*u**2 + 0 = 0. Calculate u.
-4, 0
Let -16*b + 5*b**2 + 4*b**2 - 10*b**2 + 5*b**2 = 0. What is b?
0, 4
Let v be ((-2)/10)/(-1 - 0). Suppose -y + 4*t = -4, y + t + 0 = -1. Factor 1/5*o**3 + 0*o**2 - v*o + y.
o*(o - 1)*(o + 1)/5
Determine p, given that 0 - 6/13*p**4 - 2/13*p**2 + 0*p + 6/13*p**3 + 2/13*p**5 = 0.
0, 1
Let f be (-1)/(-1*(-1)/(-4)) + -2. Factor -4/3*z + 0 + 14/3*z**f.
2*z*(7*z - 2)/3
Factor 16/5*q**4 - 19/5*q - 56/5*q**3 + 2/5 + 57/5*q**2.
(q - 2)*(q - 1)*(4*q - 1)**2/5
Find h such that -5*h**2 - 5*h**3 - 3*h**2 - 4*h + 7*h**4 - 8*h**4 = 0.
-2, -1, 0
Factor -1/5*g**2 + 2/5 - 1/5*g.
-(g - 1)*(g + 2)/5
Let s = 10 - 5. Factor s*y + 3 + 0*y + 3*y**2 + y**2 + y**3 - 1.
(y + 1)**2*(y + 2)
Let t(x) be the second derivative of -x**9/22680 - x**8/10080 + x**7/3780 + x**6/1080 - 7*x**4/12 - 3*x. Let l(f) be the third derivative of t(f). Factor l(q).
-2*q*(q - 1)*(q + 1)**2/3
Factor x**3 + 1/2*x**2 - 1/2*x**4 - x + 0.
-x*(x - 2)*(x - 1)*(x + 1)/2
Let t be (2/4)/((-3)/178). Let u = t - -31. Factor 4/3*g - 2/3*g**2 - u*g**3 + 2/3.
-2*(g - 1)*(g + 1)*(2*g + 1)/3
Factor -7*d**4 - 72*d**3 + 8*d - 25*d**4 - 4*d**5 + 100*d.
-4*d*(d - 1)*(d + 3)**3
Let h(b) be the second derivative of 1/4*b**4 + 3/2*b**3 + 0 + b**2 - 1/5*b**5 + 4*b. Solve h(f) = 0 for f.
-1, -1/4, 2
Factor 2*u - 2/7*u**2 - 12/7.
-2*(u - 6)*(u - 1)/7
Let n(k) = -k**3 + 8*k**2 - 6*k - 7. Let q be n(7). Let b(t) be the third derivative of 1/300*t**5 + 2/15*t**3 - t**2 + 1/30*t**4 + q + 0*t. Solve b(w) = 0.
-2
Let n(g) be the second derivative of 1/25*g**6 + 0*g**4 + 0*g**3 + 3*g + 0 - 1/70*g**7 - 3/100*g**5 + 0*g**2. Solve n(t) = 0 for t.
0, 1
Let a(v) = v**2 - v. Let w(y) = y**2 - 1. Let c(s) = -3*a(s) - 3*w(s). Factor c(j).
-3*(j - 1)*(2*j + 1)
Let j(w) = -11*w**4 + 9*w**3 - 19*w**2 - 23*w + 16. Let p(m) = -6*m**4 + 4*m**3 - 10*m**2 - 12*m + 8. Let c(k) = -4*j(k) + 7*p(k). Factor c(t).
2*(t - 2)**2*(t - 1)*(t + 1)
Let p(q) be the second derivative of -5/27*q**6 - 23/18*q**4 + 7/9*q**5 - 4/9*q**2 + q + 0 + 28/27*q**3. Suppose p(k) = 0. What is k?
2/5, 1
Let d(l) be the second derivative of 1/6*l**3 + 1/36*l**4 + 8*l + 1/3*l**2 + 0. Factor d(s).
(s + 1)*(s + 2)/3
Let z(y) be the third derivative of y**7/630 - y**6/360 - 4*y**2. Solve z(n) = 0.
0, 1
Suppose 2 = t - 2*l + 1, 0 = -2*t + l + 5. Let r(o) be the first derivative of -3*o**2 + 0 + 1 - 9*o + o**t + 0*o**3 + 1. Factor r(s).
3*(s - 3)*(s + 1)
Suppose 34 - 8 = 5*b - 4*m, 0 = b - 2*m - 10. Factor 4*r**b + 7/4*r**3 + 1/2 + 11/4*r.
(r + 1)**2*(7*r + 2)/4
Let t(k) = -k**4 + k**3 - k**2 + 1. Let d(x) = 4*x**5 + 12*x**4 + 36*x**3 + 4*x**2 + 8. Let a(i) = d(i) - 8*t(i). Solve a(o) = 0.
-3, -1, 0
Let v = 43/152 + -5/152. Factor v*a + 3/4*a**2 + 0.
a*(3*a + 1)/4
Let l(o) be the first derivative of 5/6*o**4 - 3 + 2/3*o**2 + 0*o - 14/9*o**3. Determine b so that l(b) = 0.
0, 2/5, 1
Find o, given that 1/4*o**5 + 3/2*o**3 - 2*o + 0 + o**2 - 5/4*o**4 = 0.
-1, 0, 2
Let z(b) = -b**2 + b + 2. Let h(p) = -2*p + 5. Let c be h(-4). Suppose 14 = 3*x - c. Let w(u) = 5*u**2 - 5*u - 9. Let d(o) = x*z(o) + 2*w(o). Factor d(m).
m*(m - 1)
Suppose 4*t = -4*u + 24, -5*u + 2 = -5*t + 12. Let p be -4 + u - (-4 - 1). Suppose 1/2*r**4 + 1/4*r**5 + 0*r**p - 1/4*r - 1/2*r**2 + 0 = 0. What is r?
-1, 0, 1
Let m(c) be the second derivative of 2/3*c**3 + 1/2*c**4 + 0 + 0*c**2 - c. Factor m(a).
2*a*(3*a + 2)
Let z(t) be the first derivative of -t**4/2 - 2*t**3 - 3*t**2 - 2*t - 5. Factor z(r).
-2*(r + 1)**3
Let l = 10 + -10. Let j(v) be the first derivative of 0*v**3 - 4/15*v**5 + 0*v**2 + 1/9*v**6 + l*v + 1/6*v**4 - 2. Find d, given that j(d) = 0.
0, 1
Let r = -52 - -52. Let w(a) be the second derivative of -1/6*a**2 + 1/36*a**4 + a + r*a**3 + 0. Factor w(k).
(k - 1)*(k + 1)/3
Let g(r) be the first derivative of r**5/50 - r**4/60 + 2*r**2 - 3. Let o(s) be the second derivative of g(s). Find j, given that o(j) = 0.
0, 1/3
Let f(b) be the first derivative of b**6/18 + b**5/15 - b**4/4 - b**3/9 + b**2/3 - 8. Solve f(j) = 0 for j.
-2, -1, 0, 1
Suppose 4*q + 2*d - 22 = 0, 19 = -3*q + 4*q + 5*d. Suppose 7 = 2*k - 5*g, 3*k + 3*g - 23 = -2*g. Factor -3*r**q - 2*r**3 - 5*r**4 + 2*r + 2*r**4 + k*r**2.
-2*r*(r - 1)*(r + 1)*(3*r + 1)
Let z = 50 + -48. Let o be (-11)/22*(-3)/z. Suppose -o*m**2 - 1/4*m**4 + 0 + 3/4*m**3 + 1/4*m = 0. Calculate m.
0, 1
Let z(u) be the second derivative of 0 - 1/48*u**4 + 0*u**2 + 0*u**3 - u. Factor z(t).
-t**2/4
Let w(y) = 3*y**4 - 7*y**3 - 13*y**2 + 11*y - 2. Let x(z) = -6*z**4 + 15*z**3 + 27*z**2 - 21*z + 3. Let u(i) = 9*w(i) + 4*x(i). Let u(j) = 0. Calculate j.
-2, 1
Let o(m) be the second derivative of 5*m - 1/30*m**4 + 0 + 0*m**2 - 2/15*m**3. What is q in o(q) = 0?
-2, 0
Factor 4/7 + 6/7*c - 2/7*c**3 + 0*c**2.
-2*(c - 2)*(c + 1)**2/7
Factor -75*o**2 + o**4 + 154*o**2 - 80*o**2 + o**5 + 2*o - 3*o**3.
o*(o - 1)**2*(o + 1)*(o + 2)
Let v(l) = 11*l - 77. Let x be v(7). Let p(g) be the first derivative of 0*g - 3/20*g**5 - 2 - 1/6*g**3 - 5/16*g**4 + x*g**2. Solve p(m) = 0 for m.
-1, -2/3, 0
Factor 0*j**4 + 0*j + 0 + 2/15*j**5 - 2/15*j**3 + 0*j**2.
2*j**3*(j - 1)*(j + 1)/15
Suppose -5*v + 19 + 1 = 0. Suppose y - o = 4*o - 23, 3*y + 9 = 3*o. Factor 5*f**v - 2*f**4 - y*f**4.
f**4
Suppose 2*a + 0*q - q - 43 = 0, -3*a - 3*q = -60. Suppose -2*t - u - 2*u + a = 0, -t = 5*u - 28. Factor 0 + 0*d**3 + 12*