*7/315 + c**6/30 + 2*c**5/45 + c**4/36 + 11*c**2. Factor w(r).
2*r*(r + 1)**4/3
Let p(y) be the third derivative of y**5/90 + y**4/18 - 2*y**2. Factor p(i).
2*i*(i + 2)/3
Determine n, given that -2/5*n**4 - 6/5*n**2 + 2/5*n + 6/5*n**3 + 0 = 0.
0, 1
Let v = -5 + 6. Let d be (0/((-8)/(-2)))/v. Solve d*b + 0 + 1/5*b**2 = 0 for b.
0
Suppose 233 = 3*n + 38. Let k = n - 321/5. Factor 2/5*d + k - 4/5*d**2 - 2/5*d**3.
-2*(d - 1)*(d + 1)*(d + 2)/5
Factor -1 + z - 1/4*z**2.
-(z - 2)**2/4
Factor -1/5*j**2 + 1/5*j**3 + 0 + 1/5*j**4 - 1/5*j**5 + 0*j.
-j**2*(j - 1)**2*(j + 1)/5
Find i such that -2/3*i**2 + 2/3*i**3 + 0*i + 0 = 0.
0, 1
Suppose -4*i + 36 = 16. Factor 2/9*z**3 + 0*z - 2/9*z**i + 0 + 2/9*z**4 - 2/9*z**2.
-2*z**2*(z - 1)**2*(z + 1)/9
Suppose 40 = 2*z + 3*z. Suppose 0*v + 3*v + 4*a - 6 = 0, 4*v - 2*a = z. Determine i, given that 4 - 3 + 10*i - 4*i**4 + 14*i**3 - 18*i**v - 3 = 0.
1/2, 1
Let x(n) = -2*n - 13. Suppose -l + 4*h - h - 11 = 0, 5*l + 5*h + 35 = 0. Let g be x(l). Factor 0*w**2 - 1/2*w**g - 1 + 3/2*w.
-(w - 1)**2*(w + 2)/2
Solve 2*r**4 + 0 + 8/3*r**3 + 8/9*r**2 + 0*r = 0.
-2/3, 0
Let n(s) be the third derivative of 1/13*s**3 - 1/130*s**5 + 0 + 0*s + 1/156*s**4 - 1/780*s**6 - 7*s**2. Factor n(a).
-2*(a - 1)*(a + 1)*(a + 3)/13
Suppose -2*m = 2*m - 20, 2*a = -2*m + 34. Let p be 39/a - 9/3. Factor -p*g**3 + 3/4*g**2 - 3/4*g + 1/4.
-(g - 1)**3/4
Determine n, given that -3 + n**4 + 2*n**4 + 6 - 6*n**2 = 0.
-1, 1
Let u(f) = f + 8. Let b = -19 - -16. Let v be u(b). Factor -a**3 + 1/2 - 1/2*a**v + 3/2*a + a**2 - 3/2*a**4.
-(a - 1)*(a + 1)**4/2
Let s(t) be the third derivative of -t**7/42 + t**6/6 - t**5/2 + 5*t**4/6 - 5*t**3/6 + 20*t**2. Factor s(g).
-5*(g - 1)**4
Let z(y) = -3*y**3 - 13*y**2 + 5*y - 4. Let u(d) = -d**3 + 0*d**3 - 7*d**2 - 2 - d**3 + 2*d. Let g(x) = 5*u(x) - 3*z(x). Suppose g(l) = 0. Calculate l.
1, 2
Let k be (4/(-10))/(5/(-25)). What is m in -m - k*m**3 - m**2 + 1 + 5*m**3 - 2*m**3 = 0?
-1, 1
Let k(b) = -b**3 + 4*b**2 + 6*b - 1. Let h be k(5). Let 8*v**3 - 8*v**3 - 12*v + 12*v**2 + 4 - h*v**3 = 0. Calculate v.
1
Let s(g) = -2*g**3 - 6*g - 5. Let r be s(-1). Factor v - 1/3*v**r - 2/3 + 0*v**2.
-(v - 1)**2*(v + 2)/3
Factor 1 - h + 5/4*h**4 - 15/4*h**2 - 1/2*h**3.
(h - 2)*(h + 1)**2*(5*h - 2)/4
Let m be ((-6)/21)/((-1)/7). Let -1 + 2 + 9*i - 3*i**2 - 7 + 0*i**m = 0. Calculate i.
1, 2
Let t be (-4)/(-10) - (-2)/(-5). Suppose t = -3*u + 3*y + 15, -u - 2*u + 5*y = -17. Factor -1/5 + 2/5*b**u - 1/5*b + b**3 + 3/5*b**2.
(b + 1)**3*(2*b - 1)/5
Let a(l) be the third derivative of -1/360*l**6 + 1/180*l**5 + l**2 + 0*l + 0*l**3 + 0*l**4 + 0. Solve a(y) = 0 for y.
0, 1
Let r = 13 + -7. Suppose -6 = 3*b - r*b. Suppose -2*g**b + 3*g**3 - 2*g**2 + 3*g**2 - 2*g**3 = 0. What is g?
0, 1
Let c(d) be the first derivative of 2/5*d**5 + 1/3*d**6 + 0*d - 1 + 0*d**2 - 1/2*d**4 - 2/3*d**3. Factor c(z).
2*z**2*(z - 1)*(z + 1)**2
Suppose 12*s**2 + s**5 + 69*s**3 + 27*s**4 - 48 - 72*s + s**2 + 2*s**5 + 8*s**2 = 0. What is s?
-4, -1, 1
Factor v**2 - 3/2*v - 1.
(v - 2)*(2*v + 1)/2
Suppose -5*j + 21 = g, j = -4*j + g + 19. Let z be (-2)/1 - (-4 - j). Factor -3*a**5 - 6*a**2 - 2*a**3 - z - a**4 + 6*a + 9*a - 10*a**3 + 13*a**4.
-3*(a - 2)*(a - 1)**3*(a + 1)
Let q(v) be the second derivative of -v**6/35 + 13*v**5/70 - 19*v**4/42 + 11*v**3/21 - 2*v**2/7 - 10*v. What is z in q(z) = 0?
1/3, 1, 2
Let j be -2 - (-2 - 5/4). Let n = j - 1. Suppose -n*o**3 + 1/4*o - 1/4*o**2 + 1/4 = 0. What is o?
-1, 1
Let f(r) = -r**5 - 8*r**4 - 5*r**3 + 8*r**2 + r. Let u(a) = 4*a**4 + 2*a**3 - 4*a**2. Let t(o) = 2*f(o) + 5*u(o). Suppose t(m) = 0. Calculate m.
-1, 0, 1
Suppose 5*d = -4*c + 22, 5*c + 2*d - 5 = 7*d. Let b(i) be the third derivative of i**2 - 1/60*i**5 - 1/6*i**c + 0 + 0*i - 1/12*i**4. Factor b(j).
-(j + 1)**2
Let s(y) = -y - 2. Let d(i) = -2*i + 5. Let a be d(5). Let z be s(a). Factor 0 + 1/2*u**2 - u + 1/2*u**z.
u*(u - 1)*(u + 2)/2
Let l(s) = -s**3 - s + 6*s - 6*s**2 + 4 - 1 + 2*s. Let k be l(-7). Determine g so that 2/7*g**2 + 0 + 0*g - 4/7*g**k + 2/7*g**4 = 0.
0, 1
Let x be (24/(-14))/((-4)/14). Let r(g) be the second derivative of 0*g**2 + 0 - 2*g + 0*g**3 - 1/6*g**4 - 1/4*g**7 + 13/60*g**x + 3/10*g**5. Solve r(v) = 0.
-2/3, 0, 2/7, 1
Suppose 5*u + 6 = 16. Let i be u*-1 - 14/(-5). Factor -i*g - 1/5*g**2 - 4/5.
-(g + 2)**2/5
Determine g, given that -15*g + 2*g**2 + 2 + 24*g - 4 - 9*g**3 = 0.
-1, 2/9, 1
Let d(g) = -g. Let y be d(-2). Determine u so that 1/3*u**4 + 0*u + 2/3*u**3 + 0 + 1/3*u**y = 0.
-1, 0
Factor 6/13*n + 2/13*n**3 + 0 + 8/13*n**2.
2*n*(n + 1)*(n + 3)/13
Let g be 5/(50/(-28)) - 9/(-3). Suppose 5*n = 2*n. Solve 0*q**2 - g*q**3 + 0*q + n = 0.
0
Let w(j) be the third derivative of 1/9*j**3 + 3*j**2 + 1/90*j**5 + 0*j + 1/18*j**4 + 0. Factor w(m).
2*(m + 1)**2/3
Find j such that -2 + 24/7*j - 10/7*j**2 = 0.
1, 7/5
Let f(z) be the second derivative of z**4/72 + z**3/18 - z**2/4 - 12*z. Suppose f(m) = 0. Calculate m.
-3, 1
Let p(w) = 3*w**4 - 8*w**3 - 19*w**2 + 35*w - 11. Let k(a) = -16*a**4 + 44*a**3 + 104*a**2 - 192*a + 60. Let b(z) = 5*k(z) + 28*p(z). Factor b(s).
4*(s - 1)**3*(s + 2)
Let i(d) be the third derivative of -d**9/15120 + d**7/4200 + d**3/3 + 5*d**2. Let l(a) be the first derivative of i(a). Solve l(m) = 0 for m.
-1, 0, 1
Suppose -5*o = -8 - 2. Suppose 5*d + o = -4*v - 3, -v - 3*d = 10. Suppose -4*i**4 + 1 - 2*i**4 + 0 - 2*i**3 + 2*i**2 + 3*i + 3*i**4 - i**v = 0. What is i?
-1, 1
Let w(k) be the first derivative of -2*k**3/27 + k**2/9 - 1. Determine r, given that w(r) = 0.
0, 1
Solve 0 + 2/5*x**2 - 6/5*x - 2/5*x**4 + 6/5*x**3 = 0.
-1, 0, 1, 3
Let p(j) = j**3 + 38*j**2 + 70*j - 69. Let n be p(-36). Factor 2/9*w**2 + 0*w + 2/3*w**4 + 0 + 2/3*w**n + 2/9*w**5.
2*w**2*(w + 1)**3/9
Let w(x) = 2*x - 29. Let u be w(17). Let l(h) be the third derivative of 0*h**3 - 2*h**2 + 0 + 1/48*h**4 + 3/40*h**6 - 17/240*h**u + 0*h. Factor l(b).
b*(4*b - 1)*(9*b - 2)/4
Let x(w) be the third derivative of -w**5/15 + 5*w**4/6 - 8*w**3/3 + 9*w**2. Factor x(i).
-4*(i - 4)*(i - 1)
Suppose 23 = f + 4. Let s = f + -16. Solve 1/4 - 1/2*j**s - 1/4*j**5 + 3/4*j - 3/4*j**4 + 1/2*j**2 = 0 for j.
-1, 1
Factor -1/5*k**2 + 2/5 - 1/5*k.
-(k - 1)*(k + 2)/5
Let g(l) be the third derivative of -l**8/896 - 3*l**7/280 - l**6/40 + 3*l**5/80 + 9*l**4/64 + 7*l**2. Find y, given that g(y) = 0.
-3, -1, 0, 1
Let o(h) be the second derivative of -4*h**4 + 4*h**3 - 3*h**2/2 - 11*h. Factor o(g).
-3*(4*g - 1)**2
Factor -3/2 + 2*f - 1/2*f**2.
-(f - 3)*(f - 1)/2
Let v(b) = -b - 2. Let y be v(-4). Factor 3*d**2 - 6*d**2 + 0*d**2 + d + 2*d**y.
-d*(d - 1)
Let b = 31/14 - 51/14. Let j = -23/21 - b. Factor -1/3 - j*p**3 - p - p**2.
-(p + 1)**3/3
Let v(j) be the second derivative of 0 - 9/2*j**2 + 4*j - 1/2*j**3 + 5/12*j**4 - 1/20*j**5. Factor v(m).
-(m - 3)**2*(m + 1)
Let z be ((-6)/21)/(45/(-35)). Determine w so that 2/9*w**3 + z - 2/9*w**2 - 2/9*w = 0.
-1, 1
Factor 0 + 4/3*p**4 + 8/3*p**2 - 8/9*p - 2/9*p**5 - 26/9*p**3.
-2*p*(p - 2)**2*(p - 1)**2/9
Let b(g) be the first derivative of g**4/6 - 2*g**3/3 + 17. Factor b(t).
2*t**2*(t - 3)/3
Let q(w) be the third derivative of -w**8/336 - w**7/35 - 7*w**6/60 - 4*w**5/15 - 3*w**4/8 - w**3/3 - 9*w**2. Factor q(z).
-(z + 1)**4*(z + 2)
Let a(j) be the third derivative of j**6/900 + j**5/150 + j**4/90 - j**2. Factor a(b).
2*b*(b + 1)*(b + 2)/15
Let m(f) = 3*f - 3. Let g be m(2). Determine k, given that 3*k**3 - 2*k + 2*k**2 - 2*k**4 + k**g - 2*k**3 = 0.
-1, 0, 1
Let b(v) = -v**3 - 8*v + 1. Let m(n) = n**2 + 1 - 3*n**2 + 3*n**2. Suppose -5*w = 5*r - 36 + 6, 1 = r. Let c(t) = w*m(t) - b(t). Factor c(q).
(q + 1)*(q + 2)**2
Suppose 2*h = 3*h. Let o(a) be the second derivative of h - 1/12*a**4 - 1/6*a**3 - a + 0*a**2. Solve o(q) = 0 for q.
-1, 0
Let y(s) be the second derivative of 0*s**3 - 1/18*s**4 + 0 - 4*s + 0*s**2. What is o in y(o) = 0?
0
Factor 48/5 + 3/5*s**2 - 24/5*s.
3*(s - 4)**2/5
Let g(o) be the first derivative of o**2 + 1/180*o**5 + 0*o**4 + 0*o**3 + 0*o + 2. Let b(x) be the second derivative of g(x). Factor b(y).
y**2/3
Let b = 229 - 75. Let w = b + -613/4. Find i, given that 1/4*i**3 - w*i + 0*i**2 + 1/2 = 0.
-2, 1
Suppose -s - 3*w - 15 = 0, -s - w - 5 = -6*s. Factor s - 1/3*h + 1/3*h**2.
h*(h - 1)/3
Let q(w) be the first derivative of 0*w**2 + 1/1