Let l(c) be the second derivative of c**6/165 + c**5/110 - c**4/66 - c**3/33 - 20*c. Factor l(t).
2*t*(t - 1)*(t + 1)**2/11
Let i = 2284/5 - 455. Let w = -22/15 + i. Solve -1/3 - w*p**2 + 2/3*p = 0 for p.
1
Let d(o) = o**2 + 6*o - 5. Let q be (-1)/((-4)/(1*-28)). Let n be d(q). Factor 4/5*a - 2/5 - 2/5*a**n.
-2*(a - 1)**2/5
Let l(d) be the second derivative of -d**8/5040 + d**3/6 + 2*d. Let i(s) be the second derivative of l(s). Determine h so that i(h) = 0.
0
Let m(n) be the second derivative of 0*n**3 + 0*n**2 + 2/15*n**6 + 0 + 3/20*n**5 + 1/18*n**4 + 5/126*n**7 + 4*n. Factor m(d).
d**2*(d + 1)**2*(5*d + 2)/3
Suppose -6 + s**2 - 12*s - s**2 - 4*s**2 - 2 = 0. What is s?
-2, -1
Let h be 1 - (-1)/((-12)/3). Let v be -7 - (-6)/1 - (1 + -6). Factor 1/2*x**2 - 1/4*x**5 + x**3 - 1/2 + 0*x**v - h*x.
-(x - 2)*(x - 1)*(x + 1)**3/4
Let p = -5 - -8. Find v, given that -3*v**3 - 3*v**2 + p*v + 0*v + 3*v**4 + 0*v**2 = 0.
-1, 0, 1
Factor 1/2*k**4 + 0 - 1/2*k**2 + 0*k**3 + 0*k.
k**2*(k - 1)*(k + 1)/2
Let t = -2/41 - -96/287. Suppose 0 - 4/7*h + t*h**3 - 2/7*h**2 = 0. Calculate h.
-1, 0, 2
Let c(k) be the third derivative of 8*k**2 - 1/60*k**4 + 1/150*k**6 + 0*k + 0*k**3 - 1/150*k**5 + 0. Factor c(s).
2*s*(s - 1)*(2*s + 1)/5
Suppose 0 = 2*d + 2 + 8. Let j = d + 9. Determine x so that 0 + 14*x**j - 4/3*x**2 + 0*x - 2/3*x**3 = 0.
-2/7, 0, 1/3
Let f(d) = d**4 + d**3 - d**2 + d. Let s(p) = 26*p**4 - 2*p**3 - 34*p**2 + 6*p + 8. Let o(v) = -2*f(v) + s(v). Suppose o(y) = 0. Calculate y.
-1, -1/2, 2/3, 1
Suppose -71 = -i - 71. Let d(b) be the second derivative of -1/110*b**5 + 0 - 1/231*b**7 - 2*b + 0*b**3 - 2/165*b**6 + 0*b**2 + i*b**4. Factor d(p).
-2*p**3*(p + 1)**2/11
Let m(f) be the second derivative of f**8/840 - f**7/336 + f**6/720 + f**3/6 - 3*f. Let y(c) be the second derivative of m(c). Factor y(p).
p**2*(p - 1)*(4*p - 1)/2
Let k(l) = -l**3 + 2*l**2 - 1. Let c be k(-1). Suppose 14*x = 32*x. Let -q**4 + 1/3*q**5 - 1/3*q**c + q**3 + x*q + 0 = 0. Calculate q.
0, 1
Let v(p) = -3*p - 5. Let w be v(-3). Suppose 5*z = 3*z + 4, -3*t = -4*z + 2. Factor -2*u**2 - 4*u**3 + 4*u**3 + t*u**w.
2*u**2*(u - 1)*(u + 1)
Let -4/3*a + 8/3*a**2 + 0 + 7/3*a**4 + 19/3*a**3 = 0. What is a?
-2, -1, 0, 2/7
Let k = -23 - -23. Let m(a) be the first derivative of 0*a**2 - 7/15*a**5 - 1/12*a**4 - 2/3*a**6 + 3 + k*a + 0*a**3. Solve m(i) = 0 for i.
-1/3, -1/4, 0
Let m be (-2)/(-7) - (-984)/84. Let h be (1/(-8))/((-3)/m). Factor -h*d**2 + 0*d + 1/2.
-(d - 1)*(d + 1)/2
Let b be (-25)/5*6/(-50). Let u(j) be the second derivative of -1/3*j**4 + 0*j**2 + b*j**6 + 7/10*j**5 + 0*j**3 + 0 - 2*j. Factor u(t).
2*t**2*(t + 1)*(9*t - 2)
Let x be (-5)/((-10)/6) - -1. Suppose -5*t + 29 = 2*n - 4, -2 = 2*t - 3*n. Find j such that -j**5 + 3*j**x + j**t + 3*j**3 - 3*j**2 - 3*j**5 = 0.
-1, 0, 1
Let j(z) be the second derivative of z**6/40 - z**4/8 + 3*z**2/2 - 3*z. Let x(r) be the first derivative of j(r). Factor x(y).
3*y*(y - 1)*(y + 1)
Let z(y) = -y**4 + 2*y**3 + 3*y + 1. Let d = 1 + -6. Let j(v) = -v**4 + 2*v**3 + 2*v + 1. Let a(m) = d*j(m) + 4*z(m). Factor a(q).
(q - 1)**3*(q + 1)
Let i = 1078 - 3232/3. Factor -2/3*n**2 + i*n + 0.
-2*n*(n - 1)/3
Let a = 176 + -878/5. Factor -2/5*k**2 + 0 - a*k.
-2*k*(k + 1)/5
Let t(r) be the first derivative of -r**5/25 - r**4/4 - 3*r**3/5 - 7*r**2/10 - 2*r/5 + 30. Factor t(u).
-(u + 1)**3*(u + 2)/5
Let o(q) be the first derivative of 0*q + 1/36*q**4 - 1/2*q**2 + 2 + 0*q**3 - 1/180*q**6 + 0*q**5. Let j(w) be the second derivative of o(w). Solve j(u) = 0.
-1, 0, 1
Suppose 8*j = 11*j + 6. Let c be j/24*(-40)/15. Factor 0*l**2 + 0 - 2/9*l**3 + c*l.
-2*l*(l - 1)*(l + 1)/9
Let c be (6/(-28))/((-3)/16). Factor 18/7*t + c*t**2 + 4/7.
2*(t + 2)*(4*t + 1)/7
Let a(s) = -6*s**5 + 3*s**4 + 3*s**3 - 6*s**2 - 6*s + 3. Let h(f) = -f**5 - f**3 - f. Let w(n) = a(n) - 3*h(n). Factor w(d).
-3*(d - 1)**3*(d + 1)**2
Let m = 26 - 37. Let z = m + 13. Factor 1/2*s**z - 1/2*s**4 + 1/4*s + 0 - 1/4*s**3.
-s*(s - 1)*(s + 1)*(2*s + 1)/4
Suppose -4*x - 2*p - 18 = 4, 5*p = -5*x - 20. Let z(l) = -2*l - 9. Let d be z(x). Determine w so that -3*w - d*w + 3*w + 2*w**2 + w = 0.
0, 2
Let r(p) be the third derivative of p**7/420 + p**6/90 - 4*p**3/3 + 8*p**2. Let q(d) be the first derivative of r(d). Solve q(m) = 0 for m.
-2, 0
Let t be (-10)/(-126) - (-4)/(-18). Let j = t - -17/21. Let 1/3*b**2 - j*b + 0 = 0. Calculate b.
0, 2
Let g be 4 + 2 + -1 + 0. Let q = -4 + g. Solve -q + 6*a**3 + 1 - 4*a**2 = 0.
0, 2/3
Let x(q) = -13*q**3 + 8*q**2 - 3*q - 8. Let s(c) = -8*c**3 + 5*c**2 - 2*c - 5. Let y(j) = 8*s(j) - 5*x(j). Let y(r) = 0. Calculate r.
-1, 0, 1
Let z = -69 + 277/4. Let x(s) be the third derivative of 0*s - z*s**4 - 1/3*s**3 - 3*s**2 - 1/60*s**6 - 1/10*s**5 + 0. Factor x(y).
-2*(y + 1)**3
Let k(l) be the first derivative of l**5/15 + l**4/4 + 2. Factor k(m).
m**3*(m + 3)/3
Suppose 3*k + 6 = 6*k. Let l(n) be the first derivative of 0*n + 0*n**2 + 2/15*n**3 + 1/25*n**5 - k - 3/20*n**4. Factor l(a).
a**2*(a - 2)*(a - 1)/5
Let l(a) be the third derivative of -3/20*a**4 + 0*a + 0 + 9/10*a**3 + 1/100*a**5 + 4*a**2. Factor l(o).
3*(o - 3)**2/5
Determine h, given that 9*h + 1 + 3 + 2*h**2 - 16*h + h = 0.
1, 2
Let f(z) = z**3 - 2*z**2 - z + 6. Let x be f(2). Determine a, given that -2/5*a**x + 2/5*a**3 - 2/5*a - 4/5 + 6/5*a**2 = 0.
-1, 1, 2
Let a(s) be the third derivative of 1/20*s**5 - 4*s**2 + 1/40*s**6 - 1/4*s**4 + 0*s + 0*s**3 + 0. Factor a(b).
3*b*(b - 1)*(b + 2)
Let x = 6 + -4. Suppose -x*g - 4 - 2*g + g + 3*g**2 - 2 = 0. What is g?
-1, 2
Find j, given that 4/5*j**2 - 2/5*j**3 - 4/5 + 2/5*j = 0.
-1, 1, 2
Let w(i) be the second derivative of 0 - 5/12*i**4 + i + 4/3*i**3 - 2*i**2 + 1/20*i**5. Determine l, given that w(l) = 0.
1, 2
Let s be 1/(-1) - 19*-1. Find i such that -3*i**3 + 3*i**2 + 4*i**3 + 1 + s*i - 15*i = 0.
-1
Let h(b) be the third derivative of -b**8/6720 - b**7/3360 - b**3/6 + 3*b**2. Let v(w) be the first derivative of h(w). Factor v(s).
-s**3*(s + 1)/4
Let o(q) be the second derivative of 3*q + 1/30*q**5 + 0 + 0*q**4 + 0*q**2 - 1/9*q**3. Let o(u) = 0. What is u?
-1, 0, 1
Let d(i) be the second derivative of i**5/60 - 7*i**4/36 + 11*i**3/18 - 5*i**2/6 - 10*i. Solve d(f) = 0 for f.
1, 5
Let z = 17 + -12. Factor -13*f**4 + 3*f**4 - f + z*f**4 + 5*f**2 - 3*f**3 + 4*f**5.
f*(f - 1)**2*(f + 1)*(4*f - 1)
Suppose 5*i - 7 = 3. Let -2/5*m**4 + 2/5*m + 2/5*m**5 - 2/5 - 4/5*m**3 + 4/5*m**i = 0. What is m?
-1, 1
Let l be -7 - (-6 - (-2 + 3)). Determine i, given that 1/8*i**3 - 1/8*i**4 + l + 0*i - 1/8*i**5 + 1/8*i**2 = 0.
-1, 0, 1
Let i(u) = u**3 - 11*u**2 + 8*u + 2. Let w(x) = 8*x**2 - 4*x**3 - 2 - 12 + 3 - 41*x + 48*x**2. Let z(d) = 11*i(d) + 2*w(d). Determine p, given that z(p) = 0.
0, 1, 2
Let u(i) be the second derivative of i**4/8 + i**3/4 - 3*i. Determine b so that u(b) = 0.
-1, 0
Let g = -3 + 4. Let q = g + 1. Factor -y**2 + y**q + 2*y**3 - 2*y.
2*y*(y - 1)*(y + 1)
Let q(h) be the first derivative of h**6/6 - h**5/10 - h**4/8 + 9. Determine v so that q(v) = 0.
-1/2, 0, 1
Suppose -18/7*d**2 + 0 - 2/7*d**4 - 12/7*d**3 + 0*d = 0. Calculate d.
-3, 0
Let c(s) = -3*s**2 + 11*s - 2*s**2 - 3*s**2. Let t(q) = 2*q**2 - 3*q. Let u(i) = 6*c(i) + 22*t(i). Suppose u(f) = 0. What is f?
0
Let h = -56 + 58. What is j in 0 + 2/3*j**5 + 1/3*j + 1/3*j**h - j**3 - 1/3*j**4 = 0?
-1, -1/2, 0, 1
Let j(b) be the first derivative of -b**4/12 - b**3/9 + b**2/6 + b/3 + 11. Factor j(q).
-(q - 1)*(q + 1)**2/3
Factor 8 + 13*b - 57*b + 37*b**3 - 53*b**3 + 52*b**2.
-4*(b - 2)*(b - 1)*(4*b - 1)
Suppose 0 = -2*j + 6 - 0. Suppose -14 = -j*p + 10. Find r, given that 2*r**3 + 8 - 2*r**2 - p = 0.
0, 1
Let g(r) be the first derivative of -5*r**3/3 - 25*r**2/2 - 30*r + 13. Factor g(b).
-5*(b + 2)*(b + 3)
Let u(h) = -2*h**2 + 16*h - 37. Let d(c) = -6*c**2 + 48*c - 112. Let n(y) = -5*d(y) + 16*u(y). Solve n(s) = 0 for s.
4
Find n, given that 1/4*n**2 + 1/4 + 1/2*n = 0.
-1
Let o(q) = 5*q**3 + 10*q**2 - q + 7. Let v(n) = -4*n**3 - 9*n**2 + n - 6. Let g(f) = 6*o(f) + 7*v(f). Factor g(z).
z*(z - 1)*(2*z - 1)
Factor -36*r - 10*r**3 + 24*r**2 + 10*r**3 - 4*r**3.
-4*r*(r - 3)**2
Find k, given that -2/23*k**4 - 4/23*k + 4/23*k**3 + 0 + 2/23*k**2 = 0.
-1, 0, 1, 2
Let l(n) be the third derivative of -n**5/72 + 5*n**4/144 + 5*n**3/18 - 4*n**